Solução Halliday resnick Fundamentos de Física 6 ed

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Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_001.pdf
1. The metric prefixes (micro, pico, nano, . . .) are given for ready reference on the inside front cover of the
textbook (see also Table 1-2).
(a) Since 1 km = 1× 103m and 1m = 1× 106 µm,
1 km = 103m = (103m)(106 µm/m) = 109 µm .
The given measurement is 1.0 km (two significant figures), which implies our result should be
written as 1.0× 109 µm.
(b) We calculate the number of microns in 1 centimeter. Since 1 cm = 10−2m,
1 cm = 10−2m = (10−2m)(106 µm/m) = 104 µm .
We conclude that the fraction of one centimeter equal to 1.0µm is 1.0× 10−4.
(c) Since 1 yd = (3 ft)(0.3048m/ft) = 0.9144m,
1.0 yd = (0.91m)(106 µm/m) = 9.1× 105 µm .
		Main Menu
		Chapter 1 Measurement
		1.1 - 1.10
		1.1
		1.2
		1.3
		1.4
		1.5
		1.6
		1.7
		1.8
		1.9
		1.10
		1.11 - 1.20
		1.11
		1.12
		1.13
		1.14
		1.15
		1.16
		1.17
		1.18
		1.19
		1.20
		1.21 - 1.30
		1.21
		1.22
		1.23
		1.24
		1.25
		1.26
		1.27
		1.28
		1.29
		1.30
		1.31 - 1.40
		1.31
		1.32
		1.33
		1.34
		1.35
		1.36
		1.37
		1.38
		1.39
		1.40
		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_002.pdf
2. The customer expects 20× 7056 in3 and receives 20× 5826 in3, the difference being 24600 cubic inches,
or (
24600 in3
)(2.54 cm
1 inch
)3( 1 L
1000 cm3
)
= 403 L
where Appendix D has been used (see also Sample Problem 1-2).
		Main Menu
		Chapter 1 Measurement
		1.1 - 1.10
		1.1
		1.2
		1.3
		1.4
		1.5
		1.6
		1.7
		1.8
		1.9
		1.10
		1.11 - 1.20
		1.11
		1.12
		1.13
		1.14
		1.15
		1.16
		1.17
		1.18
		1.19
		1.20
		1.21 - 1.30
		1.21
		1.22
		1.23
		1.24
		1.25
		1.26
		1.27
		1.28
		1.29
		1.30
		1.31 - 1.40
		1.31
		1.32
		1.33
		1.34
		1.35
		1.36
		1.37
		1.38
		1.39
		1.40
		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_003.pdf
3. Using the given conversion factors, we find
(a) the distance d in rods to be
d = 4.0 furlongs =
(4.0 furlongs)(201.168m/furlong)
5.0292m/rod
= 160 rods ,
(b) and that distance in chains to be
d =
(4.0 furlongs)(201.168m/furlong)
20.117m/chain
= 40 chains .
		Main Menu
		Chapter 1 Measurement
		1.1 - 1.10
		1.1
		1.2
		1.3
		1.4
		1.5
		1.6
		1.7
		1.8
		1.9
		1.10
		1.11 - 1.20
		1.11
		1.12
		1.13
		1.14
		1.15
		1.16
		1.17
		1.18
		1.19
		1.20
		1.21 - 1.30
		1.21
		1.22
		1.23
		1.24
		1.25
		1.26
		1.27
		1.28
		1.29
		1.30
		1.31 - 1.40
		1.31
		1.32
		1.33
		1.34
		1.35
		1.36
		1.37
		1.38
		1.39
		1.40
		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_004.pdf
4. (a) Recalling that 2.54 cm equals 1 inch (exactly), we obtain
(0.80 cm)
(
1 inch
2.54 cm
)(
6 picas
1 inch
)(
12 points
1 pica
)
≈ 23 points ,
(b) and
(0.80 cm)
(
1 inch
2.54 cm
)(
6 picas
1 inch
)
≈ 1.9 picas .
		Main Menu
		Chapter 1 Measurement
		1.1 - 1.10
		1.1
		1.2
		1.3
		1.4
		1.5
		1.6
		1.7
		1.8
		1.9
		1.10
		1.11 - 1.20
		1.11
		1.12
		1.13
		1.14
		1.15
		1.16
		1.17
		1.18
		1.19
		1.20
		1.21 - 1.30
		1.21
		1.22
		1.23
		1.24
		1.25
		1.26
		1.27
		1.28
		1.29
		1.30
		1.31 - 1.40
		1.31
		1.32
		1.33
		1.34
		1.35
		1.36
		1.37
		1.38
		1.39
		1.40
		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_005.pdf
5. Various geometric formulas are given in Appendix E.
(a) Substituting
R =
(
6.37× 106m) (10−3 km/m) = 6.37× 103 km
into circumference= 2πR, we obtain 4.00× 104 km.
(b) The surface area of Earth is
4πR2 = 4π
(
6.37× 103 km)2 = 5.10× 108 km2 .
(c) The volume of Earth is
4π
3
R3 =
4π
3
(
6.37× 103 km)3 = 1.08× 1012 km3 .
		Main Menu
		Chapter 1 Measurement
		1.1 - 1.10
		1.1
		1.2
		1.3
		1.4
		1.5
		1.6
		1.7
		1.8
		1.9
		1.10
		1.11 - 1.20
		1.11
		1.12
		1.13
		1.14
		1.15
		1.16
		1.17
		1.18
		1.19
		1.20
		1.21 - 1.30
		1.21
		1.22
		1.23
		1.24
		1.25
		1.26
		1.27
		1.28
		1.29
		1.30
		1.31 - 1.40
		1.31
		1.32
		1.33
		1.34
		1.35
		1.36
		1.37
		1.38
		1.39
		1.40
		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_006.pdf
6. (a) Using the fact that the area A of a rectangle is width×length, we find
Atotal = (3.00 acre) + (25.0 perch)(4.00 perch)
= (3.00 acre)
(
(40 perch)(4 perch)
1 acre
)
+ 100 perch2
= 580 perch2 .
We multiply this by the perch2 → rood conversion factor (1 rood/40 perch2) to obtain the answer:
Atotal = 14.5 roods.
(b) We convert our intermediate result in part (a):
Atotal = (580 perch2)
(
16.5 ft
1 perch
)2
= 1.58× 105 ft2 .
Now, we use the feet→ meters conversion given in Appendix D to obtain
Atotal =
(
1.58× 105 ft2)
(
1 m
3.281 ft
)2
= 1.47× 104 m2 .
		Main Menu
		Chapter 1 Measurement
		1.1 - 1.10
		1.1
		1.2
		1.3
		1.4
		1.5
		1.6
		1.7
		1.8
		1.9
		1.10
		1.11 - 1.20
		1.11
		1.12
		1.13
		1.14
		1.15
		1.16
		1.17
		1.18
		1.19
		1.20
		1.21 - 1.30
		1.21
		1.22
		1.23
		1.24
		1.25
		1.26
		1.27
		1.28
		1.29
		1.30
		1.31 - 1.40
		1.31
		1.32
		1.33
		1.34
		1.35
		1.36
		1.37
		1.38
		1.39
		1.40
		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter
27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_007.pdf
7. The volume of ice is given by the product of the semicircular surface area and the thickness. The
semicircle area is A = πr2/2, where r is the radius. Therefore, the volume is
V =
π
2
r2 z
where z is the ice thickness. Since there are 103 m in 1 km and 102 cm in 1 m, we have
r = (2000 km)
(
103m
1km
)(
102 cm
1m
)
= 2000× 105 cm .
In these units, the thickness becomes
z = (3000m)
(
102 cm
1m
)
= 3000× 102 cm .
Therefore,
V =
π
2
(
2000× 105 cm)2 (3000× 102 cm) = 1.9× 1022 cm3 .
		Main Menu
		Chapter 1 Measurement
		1.1 - 1.10
		1.1
		1.2
		1.3
		1.4
		1.5
		1.6
		1.7
		1.8
		1.9
		1.10
		1.11 - 1.20
		1.11
		1.12
		1.13
		1.14
		1.15
		1.16
		1.17
		1.18
		1.19
		1.20
		1.21 - 1.30
		1.21
		1.22
		1.23
		1.24
		1.25
		1.26
		1.27
		1.28
		1.29
		1.30
		1.31 - 1.40
		1.31
		1.32
		1.33
		1.34
		1.35
		1.36
		1.37
		1.38
		1.39
		1.40
		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_008.pdf
8. The total volume V of the real house is that of a triangular prism (of height h = 3.0 m and base area
A = 20× 12 = 240 m2) in addition to a rectangular box (height h′ = 6.0 m and same base). Therefore,
V =
1
2
hA+ h′A =
(
h
2
+ h′
)
A = 1800 m3 .
(a) Each dimension is reduced by a factor of 1/12, and we find
Vdoll =
(
1800 m3
)( 1
12
)3
≈ 1.0 m3 .
(b) In this case, each dimension (relative to the real house) is reduced by a factor of 1/144. Therefore,
Vminiature =
(
1800 m3
)( 1
144
)3
≈ 6.0× 10−4 m3 .
		Main Menu
		Chapter 1 Measurement
		1.1 - 1.10
		1.1
		1.2
		1.3
		1.4
		1.5
		1.6
		1.7
		1.8
		1.9
		1.10
		1.11 - 1.20
		1.11
		1.12
		1.13
		1.14
		1.15
		1.16
		1.17
		1.18
		1.19
		1.20
		1.21 - 1.30
		1.21
		1.22
		1.23
		1.24
		1.25
		1.26
		1.27
		1.28
		1.29
		1.30
		1.31 - 1.40
		1.31
		1.32
		1.33
		1.34
		1.35
		1.36
		1.37
		1.38
		1.39
		1.40
		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_009.pdf
9. We use the conversion factors found in Appendix D.
1 acre · ft = (43, 560 ft2) · ft = 43, 560 ft3 .
Since 2 in. = (1/6) ft, the volume of water that fell during the storm is
V = (26 km2)(1/6 ft) = (26 km2)(3281 ft/km)2(1/6 ft) = 4.66× 107 ft3 .
Thus,
V =
4.66× 107 ft3
4.3560× 104 ft3/acre · ft = 1.1× 10
3 acre · ft .
		Main Menu
		Chapter 1 Measurement
		1.1 - 1.10
		1.1
		1.2
		1.3
		1.4
		1.5
		1.6
		1.7
		1.8
		1.9
		1.10
		1.11 - 1.20
		1.11
		1.12
		1.13
		1.14
		1.15
		1.16
		1.17
		1.18
		1.19
		1.20
		1.21 - 1.30
		1.21
		1.22
		1.23
		1.24
		1.25
		1.26
		1.27
		1.28
		1.29
		1.30
		1.31 - 1.40
		1.31
		1.32
		1.33
		1.34
		1.35
		1.36
		1.37
		1.38
		1.39
		1.40
		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_010.pdf
10. The metric prefixes (micro (µ), pico, nano, . . .) are given for ready reference on the inside front cover of
the textbook (also, Table 1-2).
1µcentury =
(
10−6 century
)( 100 y
1 century
)(
365 day
1 y
)(
24 h
1 day
)(
60min
1 h
)
= 52.6min .
The percent difference is therefore
52.6min− 50min
50min
= 5.2% .
		Main Menu
		Chapter 1 Measurement
		1.1 - 1.10
		1.1
		1.2
		1.3
		1.4
		1.5
		1.6
		1.7
		1.8
		1.9
		1.10
		1.11 - 1.20
		1.11
		1.12
		1.13
		1.14
		1.15
		1.16
		1.17
		1.18
		1.19
		1.20
		1.21 - 1.30
		1.21
		1.22
		1.23
		1.24
		1.25
		1.26
		1.27
		1.28
		1.29
		1.30
		1.31 - 1.40
		1.31
		1.32
		1.33
		1.34
		1.35
		1.36
		1.37
		1.38
		1.39
		1.40
		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_011.pdf
11. We use the conversion factors given in Appendix D and the definitions of the SI prefixes given in Table 1-
2 (also listed on the inside front cover of the textbook). Here, “ns” represents the nanosecond unit, “ps”
represents the picosecond unit, and so on.
(a) 1m = 3.281 ft and 1 s = 109 ns. Thus,
3.0× 108m/s =
(
3.0× 108m
s
)(
3.281 ft
m
)( s
109 ns
)
= 0.98 ft/ns .
(b) Using 1m = 103mm and 1 s = 1012 ps, we find
3.0× 108m/s =
(
3.0× 108m
s
)(
103mm
m
)(
s
1012 ps
)
= 0.30 mm/ps .
		Main Menu
		Chapter 1 Measurement
		1.1 - 1.10
		1.1
		1.2
		1.3
		1.4
		1.5
		1.6
		1.7
		1.8
		1.9
		1.10
		1.11 - 1.20
		1.11
		1.12
		1.13
		1.14
		1.15
		1.16
		1.17
		1.18
		1.19
		1.20
		1.21 - 1.30
		1.21
		1.22
		1.23
		1.24
		1.25
		1.26
		1.27
		1.28
		1.29
		1.30
		1.31 - 1.40
		1.31
		1.32
		1.33
		1.34
		1.35
		1.36
		1.37
		1.38
		1.39
		1.40
		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_012.pdf
12. The number of seconds in a year is 3.156×107. This is listed in Appendix D and results from the product
(365.25 day/y)(24 h/day)(60min/h)(60 s/min) .
(a) The number of shakes in a second is 108; therefore, there are indeed more shakes per second than
there are seconds per year.
(b) Denoting the age of the universe as 1 u-day (or 86400 u-sec), then the time during which humans
have existed is given by
106
1010
= 10−4 u-day ,
which we may also express as
(
10−4 u-day
)(86400 u-sec
1 u-day
)
= 8.6 u-sec .
		Main Menu
		Chapter 1 Measurement
		1.1 - 1.10
		1.1
		1.2
		1.3
		1.4
		1.5
		1.6
		1.7
		1.8
		1.9
		1.10
		1.11 - 1.20
		1.11
		1.12
		1.13
		1.14
		1.15
		1.16
		1.17
		1.18
		1.19
1.20
		1.21 - 1.30
		1.21
		1.22
		1.23
		1.24
		1.25
		1.26
		1.27
		1.28
		1.29
		1.30
		1.31 - 1.40
		1.31
		1.32
		1.33
		1.34
		1.35
		1.36
		1.37
		1.38
		1.39
		1.40
		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_013.pdf
13. None of the clocks advance by exactly 24 h in a 24-h period but this is not the most important criterion
for judging their quality for measuring time intervals. What is important is that the clock advance by
the same amount in each 24-h period. The clock reading can then easily be adjusted to give the correct
interval. If the clock reading jumps around from one 24-h period to another, it cannot be corrected since
it would impossible to tell what the correction should be. The following gives the corrections (in seconds)
that must be applied to the reading on each clock for each 24-h period. The entries were determined by
subtracting the clock reading at the end of the interval from the clock reading at the beginning.
CLOCK Sun. Mon. Tues. Wed. Thurs. Fri.
-Mon. -Tues. -Wed. -Thurs. -Fri. -Sat
A −16 −16 −15 −17 −15 −15
B −3 +5 −10 +5 +6 −7
C −58 −58 −58 −58 −58 −58
D +67 +67 +67 +67 +67 +67
E +70 +55 +2 +20 +10 +10
Clocks C and D are both good timekeepers in the sense that each is consistent in its daily drift (relative
to WWF time); thus, C and D are easily made “perfect” with simple and predictable corrections. The
correction for clock C is less than the correction for clock D, so we judge clock C to be the best and
clock D to be the next best. The correction that must be applied to clock A is in the range from 15 s
to 17s. For clock B it is the range from −5 s to +10 s, for clock E it is in the range from −70 s to −2 s.
After C and D, A has the smallest range of correction, B has the next smallest range, and E has the
greatest range. From best the worst, the ranking of the clocks is C, D, A, B, E.
		Main Menu
		Chapter 1 Measurement
		1.1 - 1.10
		1.1
		1.2
		1.3
		1.4
		1.5
		1.6
		1.7
		1.8
		1.9
		1.10
		1.11 - 1.20
		1.11
		1.12
		1.13
		1.14
		1.15
		1.16
		1.17
		1.18
		1.19
		1.20
		1.21 - 1.30
		1.21
		1.22
		1.23
		1.24
		1.25
		1.26
		1.27
		1.28
		1.29
		1.30
		1.31 - 1.40
		1.31
		1.32
		1.33
		1.34
		1.35
		1.36
		1.37
		1.38
		1.39
		1.40
		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_014.pdf
14. The time on any of these clocks is a straight-line function of that on another, with slopes �= 1 and
y-intercepts �= 0. From the data in the figure we deduce
tC =
2
7
tB +
594
7
tB =
33
40
tA − 6625 .
These are used in obtaining the following results.
(a) We find
t′B − tB =
33
40
(t′A − tA) = 495 s
when t′A − tA = 600 s.
(b) We obtain
t′C − tC =
2
7
(t′B − tB) =
2
7
(495) = 141 s .
(c) Clock B reads tB = (33/40)(400)− (662/5) ≈ 198 s when clock A reads tA = 400 s.
(d) From tC = 15 = (2/7)tB + (594/7), we get tB ≈ −245 s.
		Main Menu
		Chapter 1 Measurement
		1.1 - 1.10
		1.1
		1.2
		1.3
		1.4
		1.5
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		1.7
		1.8
		1.9
		1.10
		1.11 - 1.20
		1.11
		1.12
		1.13
		1.14
		1.15
		1.16
		1.17
		1.18
		1.19
		1.20
		1.21 - 1.30
		1.21
		1.22
		1.23
		1.24
		1.25
		1.26
		1.27
		1.28
		1.29
		1.30
		1.31 - 1.40
		1.31
		1.32
		1.33
		1.34
		1.35
		1.36
		1.37
		1.38
		1.39
		1.40
		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter
20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_015.pdf
15. We convert meters to astronomical units, and seconds to minutes, using
1000m = 1km
1AU = 1.50× 108 km
60 s = 1min .
Thus, 3.0× 108m/s becomes
(
3.0× 108m
s
)(
1 km
1000m
)(
AU
1.50× 108 km
)(
60 s
min
)
= 0.12AU/min .
		Main Menu
		Chapter 1 Measurement
		1.1 - 1.10
		1.1
		1.2
		1.3
		1.4
		1.5
		1.6
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		1.8
		1.9
		1.10
		1.11 - 1.20
		1.11
		1.12
		1.13
		1.14
		1.15
		1.16
		1.17
		1.18
		1.19
		1.20
		1.21 - 1.30
		1.21
		1.22
		1.23
		1.24
		1.25
		1.26
		1.27
		1.28
		1.29
		1.30
		1.31 - 1.40
		1.31
		1.32
		1.33
		1.34
		1.35
		1.36
		1.37
		1.38
		1.39
		1.40
		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_016.pdf
16. Since a change of longitude equal to 360◦ corresponds to a 24 hour change, then one expects to change
longitude by 360◦/24 = 15◦ before resetting one’s watch by 1.0 h.
		Main Menu
		Chapter 1 Measurement
		1.1 - 1.10
		1.1
		1.2
		1.3
		1.4
		1.5
		1.6
		1.7
		1.8
		1.9
		1.10
		1.11 - 1.20
		1.11
		1.12
		1.13
		1.14
		1.15
		1.16
		1.17
		1.18
		1.19
		1.20
		1.21 - 1.30
		1.21
		1.22
		1.23
		1.24
		1.25
		1.26
		1.27
		1.28
		1.29
		1.30
		1.31 - 1.40
		1.31
		1.32
		1.33
		1.34
		1.35
		1.36
		1.37
		1.38
		1.39
		1.40
		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_017.pdf
17. The last day of the 20 centuries is longer than the first day by
(20 century)(0.001 s/century) = 0.02 s .
The average day during the 20 centuries is (0 + 0.02)/2 = 0.01 s longer than the first day. Since the
increase occurs uniformly, the cumulative effect T is
T = (average increase in length of a day)(number of days)
=
(
0.01 s
day
)(
365.25 day
y
)
(2000 y)
= 7305 s
or roughly two hours.
		Main Menu
		Chapter 1 Measurement
		1.1 - 1.10
		1.1
		1.2
		1.3
		1.4
		1.5
		1.6
		1.7
		1.8
		1.9
		1.10
		1.11 - 1.20
		1.11
		1.12
		1.13
		1.14
		1.15
		1.16
		1.17
		1.18
		1.19
		1.20
		1.21 - 1.30
		1.21
		1.22
		1.23
		1.24
		1.25
		1.26
		1.27
		1.28
		1.29
		1.30
		1.31 - 1.40
		1.31
		1.32
		1.33
		1.34
		1.35
		1.36
		1.37
		1.38
		1.39
		1.40
		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_018.pdf
18. We denote the pulsar rotation rate f (for frequency).
f =
1 rotation
1.55780644887275× 10−3 s
(a) Multiplying f by the time-interval t = 7.00 days (which is equivalent to 604800 s, if we ignore
significant figure considerations for a moment), we obtain the number of rotations:
N =
(
1 rotation
1.55780644887275× 10−3 s
)
(604800 s) = 388238218.4
which should now be rounded to 3.88 × 108 rotations since the time-interval was specified in the
problem to three significant figures.
(b) We note that the problem specifies the exact number of pulsar revolutions (one million). In this
case, our unknown is t, and an equation similar to the one we set up in part (a) takes the form
N = ft
1× 106 =
(
1 rotation
1.55780644887275× 10−3 s
)
t
which yields the result t = 1557.80644887275 s (though students who do this calculation on their
calculator might not obtain those last several digits).
(c) Careful reading of the problem shows that the time-uncertainty per revolution is ±3 × 10−17 s.
We therefore expect that as a result of one million revolutions, the uncertainty should be (±3 ×
10−17)(1× 106) = ±3× 10−11 s.
		Main Menu
		Chapter 1 Measurement
		1.1 - 1.10
		1.1
		1.2
		1.3
		1.4
		1.5
		1.6
		1.7
		1.8
		1.9
		1.10
		1.11 - 1.20
		1.11
		1.12
		1.13
		1.14
		1.15
		1.16
		1.17
		1.18
		1.19
		1.20
		1.21 - 1.30
		1.21
		1.22
		1.23
		1.24
		1.25
		1.26
		1.27
		1.28
		1.29
		1.30
		1.31 - 1.40
		1.31
		1.32
		1.33
		1.34
		1.35
		1.36
		1.37
		1.38
		1.39
		1.40
		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_019.pdf
19. IfME is the mass of Earth,m is the average mass of an atom in Earth, andN is the number of atoms, then
ME = Nm or N =ME/m. We convert mass m to kilograms using Appendix D (1 u = 1.661×10−27 kg).
Thus,
N =
ME
m
=
5.98× 1024 kg
(40 u)(1.661× 10−27 kg/u) = 9.0× 10
49 .
		Main Menu
		Chapter 1 Measurement
		1.1 - 1.10
		1.1
		1.2
		1.3
		1.4
		1.5
		1.6
		1.7
		1.8
		1.9
		1.10
		1.11 - 1.20
		1.11
		1.12
		1.13
		1.14
		1.15
		1.16
		1.17
		1.18
		1.19
		1.20
		1.21 - 1.30
		1.21
		1.22
		1.23
		1.24
		1.25
		1.26
		1.27
		1.28
		1.29
		1.30
		1.31 - 1.40
		1.31
		1.32
		1.33
		1.34
		1.35
		1.36
		1.37
		1.38
		1.39
		1.40
		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_020.pdf
20. To organize the calculation, we introduce the notion of density (which the students have probably seen
in other courses):
ρ =
m
V
.
(a) We take the volume of the leaf to be its area A multiplied by its thickness z. With density
ρ = 19.32 g/cm3 and mass m = 27.63 g, the volume of the leaf is found to be
V =
m
ρ
= 1.430 cm3 .
We convert the volume to SI units:
(
1.430 cm3
)( 1 m
100 cm
)3
= 1.430× 10−6 m3 .
And since V = Az where z = 1× 10−6 m (metric prefixes can be found in Table 1-2), we obtain
A =
1.430× 10−6m3
1× 10−6m = 1.430 m
2 .
(b) The volume of a cylinder
of length � is V = A� where the cross-section area is that of a circle:
A = πr2. Therefore, with r = 2.500× 10−6 m and V = 1.430× 10−6m3, we obtain
� =
V
πr2
= 7.284× 104 m .
		Main Menu
		Chapter 1 Measurement
		1.1 - 1.10
		1.1
		1.2
		1.3
		1.4
		1.5
		1.6
		1.7
		1.8
		1.9
		1.10
		1.11 - 1.20
		1.11
		1.12
		1.13
		1.14
		1.15
		1.16
		1.17
		1.18
		1.19
		1.20
		1.21 - 1.30
		1.21
		1.22
		1.23
		1.24
		1.25
		1.26
		1.27
		1.28
		1.29
		1.30
		1.31 - 1.40
		1.31
		1.32
		1.33
		1.34
		1.35
		1.36
		1.37
		1.38
		1.39
		1.40
		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_021.pdf
21. We introduce the notion of density (which the students have probably seen in other courses):
ρ =
m
V
and convert to SI units: 1 g = 1× 10−3 kg.
(a) For volume conversion, we find 1 cm3 = (1× 10−2m)3 = 1× 10−6m3. Thus, the density in kg/m3
is
1 g/cm3 =
(
1 g
cm3
)(
10−3 kg
g
)(
cm3
10−6m3
)
= 1× 103 kg/m3 .
Thus, the mass of a cubic meter of water is 1000 kg.
(b) We divide the mass of the water by the time taken to drain it. The mass is found from M = ρV
(the product of the volume of water and its density):
M = (5700m3)(1× 103 kg/m3) = 5.70× 106 kg .
The time is t = (10 h)(3600 s/h) = 3.6× 104 s, so the mass flow rate R is
R =
M
t
=
5.70× 106 kg
3.6× 104 s = 158 kg/s .
		Main Menu
		Chapter 1 Measurement
		1.1 - 1.10
		1.1
		1.2
		1.3
		1.4
		1.5
		1.6
		1.7
		1.8
		1.9
		1.10
		1.11 - 1.20
		1.11
		1.12
		1.13
		1.14
		1.15
		1.16
		1.17
		1.18
		1.19
		1.20
		1.21 - 1.30
		1.21
		1.22
		1.23
		1.24
		1.25
		1.26
		1.27
		1.28
		1.29
		1.30
		1.31 - 1.40
		1.31
		1.32
		1.33
		1.34
		1.35
		1.36
		1.37
		1.38
		1.39
		1.40
		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_022.pdf
22. The volume of the water that fell is
V = (26 km2)(2.0 in.)
= (26 km2)
(
1000m
1 km
)2
(2.0 in.)
(
0.0254m
1 in.
)
= (26× 106m2)(0.0508m)
= 1.3× 106 m3 .
We write the mass-per-unit-volume (density) of the water as:
ρ =
m
V
= 1× 103 kg/m3 .
The mass of the water that fell is therefore given by m = ρV :
m =
(
1× 103 kg/m3
) (
1.3× 106m3)
= 1.3× 109 kg .
		Main Menu
		Chapter 1 Measurement
		1.1 - 1.10
		1.1
		1.2
		1.3
		1.4
		1.5
		1.6
		1.7
		1.8
		1.9
		1.10
		1.11 - 1.20
		1.11
		1.12
		1.13
		1.14
		1.15
		1.16
		1.17
		1.18
		1.19
		1.20
		1.21 - 1.30
		1.21
		1.22
		1.23
		1.24
		1.25
		1.26
		1.27
		1.28
		1.29
		1.30
		1.31 - 1.40
		1.31
		1.32
		1.33
		1.34
		1.35
		1.36
		1.37
		1.38
		1.39
		1.40
		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_023.pdf
23. We introduce the notion of density (which the students have probably seen in other courses):
ρ =
m
V
and convert to SI units: 1000 g = 1 kg, and 100 cm = 1 m.
(a) The density ρ of a sample of iron is therefore
ρ =
(
7.87 g/cm3
)( 1 kg
1000 g
)(
100 cm
1m
)3
which yields ρ = 7870 kg/m3. If we ignore the empty spaces between the close-packed spheres, then
the density of an individual iron atom will be the same as the density of any iron sample. That is,
if M is the mass and V is the volume of an atom, then
V =
M
ρ
=
9.27× 10−26 kg
7.87× 103 kg/m3 = 1.18× 10
−29 m3 .
(b) We set V = 4πR3/3, where R is the radius of an atom (Appendix E contains several geometry
formulas). Solving for R, we find
R =
(
3V
4π
)1/3
=
(
3(1.18× 10−29m3)
4π
)1/3
= 1.41× 10−10m .
The center-to-center distance between atoms is twice the radius, or 2.82× 10−10 m.
		Main Menu
		Chapter 1 Measurement
		1.1 - 1.10
		1.1
		1.2
		1.3
		1.4
		1.5
		1.6
		1.7
		1.8
		1.9
		1.10
		1.11 - 1.20
		1.11
		1.12
		1.13
		1.14
		1.15
		1.16
		1.17
		1.18
		1.19
		1.20
		1.21 - 1.30
		1.21
		1.22
		1.23
		1.24
		1.25
		1.26
		1.27
		1.28
		1.29
		1.30
		1.31 - 1.40
		1.31
		1.32
		1.33
		1.34
		1.35
		1.36
		1.37
		1.38
		1.39
		1.40
		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_024.pdf
24. The metric prefixes (micro (µ), pico, nano, . . .) are given for ready reference on the inside front cover of the
textbook (see also Table 1-2). The surface area A of each grain of sand of radius r = 50µm = 50×10−6 m
is given by A = 4π(50×10−6)2 = 3.14×10−8 m2 (Appendix E contains a variety of geometry formulas).
We introduce the notion of density (which the students have probably seen in other courses):
ρ =
m
V
so that the mass can be found from m = ρV , where ρ = 2600 kg/m3. Thus, using V = 4πr3/3, the mass
of each grain is
m =
(
4π
(
50× 10−6m)3
3
)(
2600
kg
m3
)
= 1.36× 10−9 kg .
We observe that (because a cube has six equal faces) the indicated surface area is 6 m2. The number of
spheres (the grains of sand) N which have a total surface area of 6 m2 is given by
N =
6m2
3.14× 10−8m2 = 1.91× 10
8 .
Therefore, the total mass M is given by
M = Nm =
(
1.91× 108) (1.36× 10−9 kg) = 0.260 kg .
		Main Menu
		Chapter 1 Measurement
		1.1 - 1.10
		1.1
		1.2
		1.3
		1.4
		1.5
		1.6
		1.7
		1.8
		1.9
		1.10
		1.11 - 1.20
		1.11
		1.12
		1.13
		1.14
		1.15
		1.16
		1.17
		1.18
		1.19
		1.20
		1.21 - 1.30
		1.21
		1.22
		1.23
		1.24
		1.25
		1.26
		1.27
		1.28
		1.29
		1.30
		1.31 - 1.40
		1.31
		1.32
		1.33
		1.34
		1.35
		1.36
		1.37
		1.38
		1.39
		1.40
		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_025.pdf
25. From the Figure we see that, regarding differences in positions ∆x, 212 S is equivalent to 258 W and
180 S is equivalent to 156 Z. Whether or not the origin of the Zelda path coincides with the origins of
the other paths is immaterial to consideration of ∆x.
(a)
∆x = (50.0 S)
(
258 W
212 S
)
= 60.8 W
(b)
∆x = (50.0 S)
(
156 Z
180 S
)
= 43.3 Z
		Main Menu
		Chapter 1 Measurement
		1.1 - 1.10
		1.1
		1.2
		1.3
		1.4
		1.5
		1.6
		1.7
		1.8
		1.9
		1.10
		1.11 - 1.20
		1.11
		1.12
		1.13
		1.14
		1.15
		1.16
		1.17
		1.18
		1.19
		1.20
		1.21 - 1.30
		1.21
		1.22
		1.23
		1.24
		1.25
		1.26
		1.27
		1.28
		1.29
		1.30
1.31 - 1.40
		1.31
		1.32
		1.33
		1.34
		1.35
		1.36
		1.37
		1.38
		1.39
		1.40
		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_026.pdf
26. The first two conversions are easy enough that a formal conversion is not especially called for, but in
the interest of practice makes perfect we go ahead and proceed formally:
(a)
(11 tuffet)
(
2 peck
1 tuffet
)
= 22 peck
(b)
(11 tuffet)
(
0.50 bushel
1 tuffet
)
= 5.5 bushel
(c)
(5.5 bushel)
(
36.3687 L
1 bushel
)
≈ 200 L
		Main Menu
		Chapter 1 Measurement
		1.1 - 1.10
		1.1
		1.2
		1.3
		1.4
		1.5
		1.6
		1.7
		1.8
		1.9
		1.10
		1.11 - 1.20
		1.11
		1.12
		1.13
		1.14
		1.15
		1.16
		1.17
		1.18
		1.19
		1.20
		1.21 - 1.30
		1.21
		1.22
		1.23
		1.24
		1.25
		1.26
		1.27
		1.28
		1.29
		1.30
		1.31 - 1.40
		1.31
		1.32
		1.33
		1.34
		1.35
		1.36
		1.37
		1.38
		1.39
		1.40
		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_027.pdf
27. We make the assumption that the clouds are directly overhead, so that Figure 1-3 (and the calculations
that accompany it) apply. Following the steps in Sample Problem 1-4, we have
θ
360◦
=
t
24 h
which, for t = 38 min = 38/60 h yields θ = 9.5◦. We obtain the altitude h from the relation
d2 = r2 tan2 θ = 2rh
which is discussed in that Sample Problem, where r = 6.37×106 m is the radius of the earth. Therefore,
h = 8.9× 104 m.
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		1.8
		1.9
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		1.11 - 1.20
		1.11
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		1.13
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		1.15
		1.16
		1.17
		1.18
		1.19
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		1.21 - 1.30
		1.21
		1.22
		1.23
		1.24
		1.25
		1.26
		1.27
		1.28
		1.29
		1.30
		1.31 - 1.40
		1.31
		1.32
		1.33
		1.34
		1.35
		1.36
		1.37
		1.38
		1.39
		1.40
		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_028.pdf
28. In the simplest approach, we set up a ratio for the total increase in horizontal depth x (where ∆x = 0.05 m
is the increase in horizontal depth per step)
x = Nsteps∆x =
(
4.57
0.19
)
(0.05) = 1.2 m .
However, we can approach this more carefully by noting that if there are N = 4.57/.19 ≈ 24 rises then
under normal circumstances we would expect N −1 = 23 runs (horizontal pieces) in that staircase. This
would yield (23)(0.05) = 1.15 m, which – to two significant figures – agrees with our first result.
		Main Menu
		Chapter 1 Measurement
		1.1 - 1.10
		1.1
		1.2
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		1.7
		1.8
		1.9
		1.10
		1.11 - 1.20
		1.11
		1.12
		1.13
		1.14
		1.15
		1.16
		1.17
		1.18
		1.19
		1.20
		1.21 - 1.30
		1.21
		1.22
		1.23
		1.24
		1.25
		1.26
		1.27
		1.28
		1.29
		1.30
		1.31 - 1.40
		1.31
		1.32
		1.33
		1.34
		1.35
		1.36
		1.37
		1.38
		1.39
		1.40
		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_029.pdf
29. Abbreviating wapentake as “wp” and assuming a hide to be 110 acres, we set up the ratio 25wp/11 barn
along with appropriate conversion factors:
(25wp)
(
100 hide
1wp
) ( 110 acre
1 hide
) ( 4047m2
1 acre
)
(11 barn)
(
1×10−28m2
1 barn
) ≈ 1× 1036 .
		Main Menu
		Chapter 1 Measurement
		1.1 - 1.10
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		1.2
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		1.8
		1.9
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		1.11 - 1.20
		1.11
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		1.13
		1.14
		1.15
		1.16
		1.17
		1.18
		1.19
		1.20
		1.21 - 1.30
		1.21
		1.22
		1.23
		1.24
		1.25
		1.26
		1.27
		1.28
		1.29
		1.30
		1.31 - 1.40
		1.31
		1.32
		1.33
		1.34
		1.35
		1.36
		1.37
		1.38
		1.39
		1.40
		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_030.pdf
30. It is straightforward to compute how many seconds in a year (about 3 × 107). Now, if we estimate
roughly one breath per second (or every two seconds, or three seconds – it won’t affect the result) then
to within an order of magnitude, a person takes 107 breaths in a year.
		Main Menu
		Chapter 1 Measurement
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		1.8
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		1.11
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		1.21
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		1.31
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		1.38
		1.39
		1.40
		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_031.pdf
31. A day is equivalent to 86400 seconds and a meter is equivalent to a million micrometers, so
(3.7m)(106 µm/m)
(14 day)(86400 s/day)
= 3.1 µm/s .
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		1.31
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		1.33
		1.34
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		1.38
		1.39
		1.40
		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_032.pdf
32. The mass in kilograms is
(28.9 piculs)
(
100 gin
1 picul
)(
16 tahil
1 gin
)(
10 chee
1 tahil
)(
10 hoon
1 chee
)(
0.3779 g
1 hoon
)
which yields 1.747× 106 g or roughly 1750 kg.
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		1.31
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		1.37
		1.38
		1.39
		1.40
		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_033.pdf
33. (a) In atomic mass units, the mass of one molecule is 16 + 1 + 1 = 18 u. Using Eq. 1-9, we find
(18 u)
(
1.6605402× 10−27 kg
1 u
)
= 3.0× 10−26 kg .
(b) We divide the total mass by the mass of each molecule and obtain the (approximate) number of
water molecules:
1.4× 1021
3.0× 10−26 ≈ 5× 10
46 .
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		1.31 - 1.40
		1.31
		1.32
		1.33
		1.34
		1.35
		1.36
		1.37
		1.38
		1.39
		1.40
		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_034.pdf
34. (a) We find the volume in cubic centimeters
(193 gal)
(
231 in3
1 gal
)(
2.54 cm
1 in
)3
= 7.31× 105 cm3
and subtract this from 1× 106 cm3 to obtain 2.69× 105 cm3. The conversion gal→ in3 is given in
Appendix D (immediately below the table of Volume conversions).
(b) The volume found in part (a) is converted (by dividing by
(100 cm/m)3) to 0.731 m3, which corre-
sponds to a mass of (
1000 kg/m3
) (
0.731m2
)
= 731 kg
using the density given in the problem statement. At a rate of 0.0018 kg/min, this can be filled in
731 kg
0.0018 kg/min
= 4.06× 105 min
which we convert to 0.77 y, by dividing by the number of minutes in a year (365 days)(24 h/day)(60min/h).
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		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_035.pdf
35. (a) When θ is measured in radians, it is equal to the arclength divided by the radius. For very large
radius circles and small values of θ, such as we deal with in this problem,
the arcs may be
approximated as
straight lines –
which for our
purposes corre-
spond to the di-
ameters d and
D of the Moon
and Sun, respec-
tively. Thus,
............. .............
............. .............
............. .............
............. .............
............. .............
............. .............
............. .............
............. .............
.............
............. ............. ............. ............. ............. ............. ............. ............. ............. ............. ............. ............. ............. ............. ............. ............. .............
........................................
........................................
........................................
........................................
........................................
........................................
........................................
........................................
........................................
........................................
..................................
............................
........................................................................................................................................................................................................... .......
..............
.......
Dd
R Sun
RMoon
θ
��
��
.....................................
................
............
...........
..........
.........
.........
........
........
........
........
........
........
........
.........
.........
.........
..........
...........
.............
..................
..........................................................................................................................................................................................................................................................................................................
θ =
d
RMoon
=
D
R Sun
=⇒ R Sun
RMoon
=
D
d
which yields D/d = 400.
(b) Various geometric formulas are given in Appendix E. Using rs and rm for the radius of the Sun and
Moon, respectively (noting that their ratio is the same as D/d), then the Sun’s volume divided by
that of the Moon is
4
3πr
3
s
4
3πr
3
m
=
(
rs
rm
)3
= 4003 = 6.4× 107 .
(c) The angle should turn out to be roughly 0.009 rad (or about half a degree). Putting this into the
equation above, we get
d = θRMoon = (0.009)
(
3.8× 105) ≈ 3.4× 103 km .
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		1.41
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		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_036.pdf
36. (a) For the minimum
(43 cm) case, 9 cubit converts as follows:
(9 cubit)
(
0.43m
1 cubit
)
= 3.9 m .
And for the maximum (43 cm) case we obtain
(9 cubit)
(
0.53 m
1 cubit
)
= 4.8 m .
(b) Similarly, with 0.43m → 430mm and 0.53m → 530mm, we find 3.9×103 mm and 4.8×103 mm,
respectively.
(c) We can convert length and diameter first and then compute the volume, or first compute the volume
and then convert. We proceed using the latter approach (where d is diameter and � is length).
Vcylinder,min =
π
4
� d2 = 28 cubit3
=
(
28 cubit3
)( 0.43m
1 cubit
)3
= 2.2 m3 .
Similarly, with 0.43m replaced by 0.53m, we obtain Vcylinder,max = 4.2m3.
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		1.41
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		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_037.pdf
37. (a) Squaring the relation 1 ken = 1.97m, and setting up the ratio, we obtain
1 ken2
1m2
=
1.972m2
1m2
= 3.88 .
(b) Similarly, we find
1 ken3
1m3
=
1.973m3
1m3
= 7.65 .
(c) The volume of a cylinder is the circular area of its base multiplied by its height. Thus,
πr2h = π(3.00)2(5.50) = 155.5 ken3 .
(d) If we multiply this by the result of part (b), we determine the volume in cubic meters: (155.5)(7.65) =
1.19× 103 m3.
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		1.41
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		Chapter 2 Motion Along a Straight Line
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		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_038.pdf
38. Although we can look up the distance from Cleveland to Los Angeles, we can just as well (for an order of
magnitude calculation) assume it’s some relatively small fraction of the circumference of Earth – which
suggests that (again, for an order of magnitude calculation) we can estimate the distance to be roughly
r, where r ≈ 6 × 106 m is the radius of Earth. If we take each toilet paper sheet to be roughly 10 cm
(0.1 m) then the number of sheets needed is roughly 6× 106/0.1 = 6× 107 ≈ 108.
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		1.11 - 1.20
		1.11
		1.12
		1.13
		1.14
		1.15
		1.16
		1.17
		1.18
		1.19
		1.20
		1.21 - 1.30
		1.21
		1.22
		1.23
		1.24
		1.25
		1.26
		1.27
		1.28
		1.29
		1.30
		1.31 - 1.40
		1.31
		1.32
		1.33
		1.34
		1.35
		1.36
		1.37
		1.38
		1.39
		1.40
		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_039.pdf
39. Using the (exact) conversion 2.54 cm = 1 in. we find that 1 ft = (12)(2.54)/100 = 0.3048 m (which also
can be found in Appendix D). The volume of a cord of wood is 8 × 4 × 4 = 128 ft3, which we convert
(multiplying by 0.30483 ) to 3.6 m3. Therefore, one cubic meter of wood corresponds to 1/3.6 ≈ 0.3 cord.
		Main Menu
		Chapter 1 Measurement
		1.1 - 1.10
		1.1
		1.2
		1.3
		1.4
		1.5
		1.6
		1.7
		1.8
		1.9
		1.10
		1.11 - 1.20
		1.11
		1.12
		1.13
		1.14
		1.15
		1.16
		1.17
		1.18
		1.19
		1.20
		1.21 - 1.30
		1.21
		1.22
		1.23
		1.24
		1.25
		1.26
		1.27
		1.28
		1.29
		1.30
		1.31 - 1.40
		1.31
		1.32
		1.33
		1.34
		1.35
		1.36
		1.37
		1.38
		1.39
		1.40
		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_040.pdf
40. (a) When θ is measured in radians, it is equal to the arclength s divided by the radius R. For a
very large radius circle and small value of θ, such as we deal with in Fig. 1-9, the arc may be
approximated as the straight line-segment of length 1 AU. First, we convert θ = 1 arcsecond to
radians:
(1 arcsecond)
(
1 arcminute
60 arcsecond
)(
1◦
60 arcminute
)(
2π radian
360◦
)
which yields θ = 4.85× 10−6 rad. Therefore, one parsec is
Ro =
s
θ
=
1AU
4.85× 10−6 = 2.06 × 10
5AU .
Now we use this to convert R = 1 AU to parsecs:
R = (1AU)
(
1 pc
2.06 × 105AU
)
= 4.9× 10−6 pc .
(b) Also, since it is straightforward to figure the number of seconds in a year (about 3.16× 107 s), and
(for constant speeds) distance= speed×time, we have
1 ly = (186, 000mi/s)
(
3.16× 107 s) 5.9× 1012 mi
which we convert to AU by dividing by 92.6 × 106 (given in the problem statement), obtaining
6.3× 104 AU. Inverting, the result is 1AU = 1/6.3× 104 = 1.6× 10−5 ly.
(c) As found in the previous part, 1 ly = 5.9× 1012mi.
(d) We now know what one parsec is in AU (denoted above as Ro ), and we also know how many miles
are in an AU. Thus, one parsec is equivalent to
(
92.9× 106mi/AU) (2.06 × 105AU) = 1.9× 1013 mi .
		Main Menu
		Chapter 1 Measurement
		1.1 - 1.10
		1.1
		1.2
		1.3
		1.4
		1.5
		1.6
		1.7
		1.8
		1.9
		1.10
		1.11 - 1.20
		1.11
		1.12
		1.13
		1.14
		1.15
		1.16
		1.17
		1.18
		1.19
		1.20
		1.21 - 1.30
		1.21
		1.22
		1.23
		1.24
		1.25
		1.26
		1.27
		1.28
		1.29
		1.30
		1.31 - 1.40
		1.31
		1.32
		1.33
		1.34
		1.35
		1.36
		1.37
		1.38
		1.39
		1.40
		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_041.pdf
41. We reduce the stock amount to British teaspoons:
1 breakfastcup = 2× 8× 2× 2 = 64 teaspoons
1 teacup = 8× 2× 2 = 32 teaspoons
6 tablespoons = 6× 2× 2 = 24 teaspoons
1 dessertspoon = 2 teaspoons
which totals to 122 teaspoons – which corresponds (since liquid measure is being used) to 122 U.S.
teaspoons. Since each U.S cup is 48 teaspoons, then upon dividing 122/48 ≈ 2.54, we find this amount
corresponds to two-and-a-half U.S. cups plus a remainder of precisely 2 teaspoons. For the nettle tops,
one-half quart is still one-half quart. For the rice, one British tablespoon is 4 British teaspoons which
(since dry-goods measure is being used) corresponds to 2 U.S. teaspoons. Finally, a British saltspoon is
1
2 British teaspoon which corresponds (since dry-goods measure is again being used) to
1 U.S. teaspoon.
		Main Menu
		Chapter 1 Measurement
		1.1 - 1.10
		1.1
		1.2
		1.3
		1.4
		1.5
		1.6
		1.7
		1.8
		1.9
		1.10
		1.11 - 1.20
		1.11
		1.12
		1.13
		1.14
		1.15
		1.16
		1.17
		1.18
		1.19
		1.20
		1.21 - 1.30
		1.21
		1.22
		1.23
		1.24
		1.25
		1.26
		1.27
		1.28
		1.29
		1.30
		1.31 - 1.40
		1.31
		1.32
		1.33
		1.34
		1.35
		1.36
		1.37
		1.38
		1.39
		1.40
		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_042.pdf
42. (a) Megaphone.
(b) microphone.
(c) dekacard (“deck of cards”).
(d) Gigalow (“gigalo”).
(e) terabull (“terrible”).
(f) decimate.
(g) centipede.
(h) nanonannette. (“No No Nanette”).
(i) picoboo (“peek-a-boo”).
(j) attoboy (“at-a-boy”).
(k) Two hectowithit (“to heck with it”).
(l) Two kilomockingbird (“to kill a mockingbird”).
		Main Menu
		Chapter 1 Measurement
		1.1 - 1.10
		1.1
		1.2
		1.3
		1.4
		1.5
		1.6
		1.7
		1.8
		1.9
		1.10
		1.11 - 1.20
		1.11
		1.12
		1.13
		1.14
		1.15
		1.16
		1.17
		1.18
		1.19
		1.20
		1.21 - 1.30
		1.21
		1.22
		1.23
		1.24
		1.25
		1.26
		1.27
		1.28
		1.29
		1.30
		1.31 - 1.40
		1.31
		1.32
		1.33
		1.34
		1.35
		1.36
		1.37
		1.38
		1.39
		1.40
		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_043.pdf
43. The volume removed in one year is
V =
(
75× 104m2) (26m) ≈ 2× 107 m3
which we convert to cubic kilometers:
V =
(
2× 107m3)
(
1 km
1000m
)3
= 0.020 km3 .
		Main Menu
		Chapter 1 Measurement
		1.1 - 1.10
		1.1
		1.2
		1.3
		1.4
		1.5
		1.6
		1.7
		1.8
		1.9
		1.10
		1.11 - 1.20
		1.11
		1.12
		1.13
		1.14
		1.15
		1.16
		1.17
		1.18
		1.19
		1.20
		1.21 - 1.30
		1.21
		1.22
		1.23
		1.24
		1.25
		1.26
		1.27
		1.28
		1.29
		1.30
		1.31 - 1.40
		1.31
		1.32
		1.33
		1.34
		1.35
		1.36
		1.37
		1.38
		1.39
		1.40
		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/p01_044.pdf
44. (a) Using Appendix D, we have 1 ft = 0.3048m, 1 gal = 231 in.3, and 1 in.3 = 1.639× 10−2 L. From the
latter two items, we find that 1 gal = 3.79 L. Thus, the quantity 460ft2/gal becomes
(
460 ft2
gal
)(
1m
3.28 ft
)2( 1 gal
3.79L
)
= 11.3 m2/L .
(b) Also, since 1 m3 is equivalent to 1000 L, our result from part (a) becomes
(
11.3m2
L
)(
1000L
1m3
)
= 1.13× 104 m−1 .
(c) The inverse of the original quantity is (460 ft2/gal)−1 = 2.17 × 10−3 gal/ft2, which is the volume
of the paint (in gallons) needed to cover a square foot of area. From this, we could also figure the
paint thickness (it turns out to be about a tenth of a millimeter, as one sees by taking the reciprocal
of the answer in part (b)).
		Main Menu
		Chapter 1 Measurement
		1.1 - 1.10
		1.1
		1.2
		1.3
		1.4
		1.5
		1.6
		1.7
		1.8
		1.9
		1.10
		1.11 - 1.20
		1.11
		1.12
		1.13
		1.14
		1.15
		1.16
		1.17
		1.18
		1.19
		1.20
		1.21 - 1.30
		1.21
		1.22
		1.23
		1.24
		1.25
		1.26
		1.27
		1.28
		1.29
		1.30
		1.31 - 1.40
		1.31
		1.32
		1.33
		1.34
		1.35
		1.36
		1.37
		1.38
		1.39
		1.40
		1.41 - 1.44
		1.41
		1.42
		1.43
		1.44
		Chapter 2 Motion Along a Straight Line
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 Systems of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fields
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap01/WS_FTP.LOG
2002.04.01 00:54 B C:\My Documents\HRW\problems\chap01\p01_001.pdf <-- ipswitch /HRW/problems/chap01 p01_001.pdf
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2002.04.01 00:54 B C:\My Documents\HRW\problems\chap01\p01_008.pdf <-- ipswitch /HRW/problems/chap01 p01_008.pdf
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2002.04.01 00:54 B C:\My Documents\HRW\problems\chap01\p01_013.pdf <-- ipswitch /HRW/problems/chap01 p01_013.pdf
2002.04.01 00:54 B C:\My Documents\HRW\problems\chap01\p01_014.pdf <-- ipswitch /HRW/problems/chap01 p01_014.pdf
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2002.04.01 00:54 B C:\My Documents\HRW\problems\chap01\p01_023.pdf <-- ipswitch /HRW/problems/chap01 p01_023.pdf
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2002.04.01 00:54 B C:\My Documents\HRW\problems\chap01\p01_036.pdf <-- ipswitch /HRW/problems/chap01 p01_036.pdf
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2002.04.01 00:54 B C:\My Documents\HRW\problems\chap01\p01_041.pdf <-- ipswitch /HRW/problems/chap01 p01_041.pdf
2002.04.01 00:54 B C:\My Documents\HRW\problems\chap01\p01_042.pdf <-- ipswitch /HRW/problems/chap01 p01_042.pdf
2002.04.01 00:54 B C:\My Documents\HRW\problems\chap01\p01_043.pdf <-- ipswitch /HRW/problems/chap01 p01_043.pdf
2002.04.01 00:54 B C:\My Documents\HRW\problems\chap01\p01_044.pdf <-- ipswitch /HRW/problems/chap01 p01_044.pdf
2002.04.01 01:52 B C:\My Documents\HRW\problems\chap01\p01_001.pdf --> ftp.50g.com /problems/chap01 p01_001.pdf
2002.04.01 01:52 B C:\My Documents\HRW\problems\chap01\p01_002.pdf
--> ftp.50g.com /problems/chap01 p01_002.pdf
2002.04.01 01:52 B C:\My Documents\HRW\problems\chap01\p01_003.pdf --> ftp.50g.com /problems/chap01 p01_003.pdf
2002.04.01 01:52 B C:\My Documents\HRW\problems\chap01\p01_004.pdf --> ftp.50g.com /problems/chap01 p01_004.pdf
2002.04.01 01:53 B C:\My Documents\HRW\problems\chap01\p01_005.pdf --> ftp.50g.com /problems/chap01 p01_005.pdf
2002.04.01 01:53 B C:\My Documents\HRW\problems\chap01\p01_006.pdf --> ftp.50g.com /problems/chap01 p01_006.pdf
2002.04.01 01:53 B C:\My Documents\HRW\problems\chap01\p01_007.pdf --> ftp.50g.com /problems/chap01 p01_007.pdf
2002.04.01 01:53 B C:\My Documents\HRW\problems\chap01\p01_008.pdf --> ftp.50g.com /problems/chap01 p01_008.pdf
2002.04.01 01:53 B C:\My Documents\HRW\problems\chap01\p01_009.pdf --> ftp.50g.com /problems/chap01 p01_009.pdf
2002.04.01 01:53 B C:\My Documents\HRW\problems\chap01\p01_010.pdf --> ftp.50g.com /problems/chap01 p01_010.pdf
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_001.pdf
1. Assuming the horizontal velocity of the ball is constant, the horizontal displacement is
∆x = v∆t
where ∆x is the horizontal distance traveled, ∆t is the time, and v is the (horizontal) velocity. Converting
v to meters per second, we have 160 km/h = 44.4m/s. Thus
∆t =
∆x
v
=
18.4m
44.4m/s
= 0.414 s .
The velocity-unit conversion implemented above can be figured “from basics” (1000 m = 1 km, 3600 s
= 1 h) or found in Appendix D.
		Main Menu
		Chapter 1 Measurement
		Chapter 2 Motion Along a Straight Line
		2.1 - 2.10
		2.1
		2.2
		2.3
		2.4
		2.5
		2.6
		2.7
		2.8
		2.9
		2.10
		2.11 - 2.20
		2.11
		2.12
		2.13
		2.14
		2.15
		2.16
		2.17
		2.18
		2.19
		2.20
		2.21 - 2.30
		2.21
		2.22
		2.23
		2.24
		2.25
		2.26
		2.27
		2.28
		2.29
		2.30
		2.31 - 2.40
		2.31
		2.32
		2.33
		2.34
		2.35
		2.36
		2.37
		2.38
		2.39
		2.40
		2.41 - 2.50
		2.41
		2.42
		2.43
		2.44
		2.45
		2.46
		2.47
		2.48
		2.49
		2.50
		2.51 - 2.60
		2.51
		2.52
		2.53
		2.54
		2.55
		2.56
		2.57
		2.58
		2.59
		2.60
		2.61 - 2.70
		2.61
		2.62
		2.63
		2.64
		2.65
		2.66
		2.67
		2.68
		2.69
		2.70
		2.71 - 2.80
		2.71
		2.72
		2.73
		2.74
		2.75
		2.76
		2.77
		2.78
		2.79
		2.80
		2.81 - 2.90
		2.81
		2.82
		2.83
		2.84
		2.85
		2.86
		2.87
		2.88
		2.89
		2.90
		2.91 - 2.100
		2.91
		2.92
		2.93
		2.94
		2.95
		2.96
		2.97
		2.98
		2.99
		2.100
		2.101 - 2.110
		2.101
		2.102
		2.103
		2.104
		2.105
		2.106
		2.107
		2.108
		2.109
		2.110
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_002.pdf
2. Converting to SI units, we use Eq. 2-3 with d for distance.
savg =
d
t
(110.6 km/h)
(
1000m/km
3600 s/h
)
=
200.0m
t
which yields t = 6.510 s. We converted the speed km/h→m/s by converting each unit (km→m, h→ s)
individually. But we mention that the “one-step” conversion can be found in Appendix D (1 km/h =
0.2778m/s).
		Main Menu
		Chapter 1 Measurement
		Chapter 2 Motion Along a Straight Line
		2.1 - 2.10
		2.1
		2.2
		2.3
		2.4
		2.5
		2.6
		2.7
		2.8
		2.9
		2.10
		2.11 - 2.20
		2.11
		2.12
		2.13
		2.14
		2.15
		2.16
		2.17
		2.18
		2.19
		2.20
		2.21 - 2.30
		2.21
		2.22
		2.23
		2.24
		2.25
		2.26
		2.27
		2.28
		2.29
		2.30
		2.31 - 2.40
		2.31
		2.32
		2.33
		2.34
		2.35
		2.36
		2.37
		2.38
		2.39
		2.40
		2.41 - 2.50
		2.41
		2.42
		2.43
		2.44
		2.45
		2.46
		2.47
		2.48
		2.49
		2.50
		2.51 - 2.60
		2.51
		2.52
		2.53
		2.54
		2.55
		2.56
		2.57
		2.58
		2.59
		2.60
		2.61 - 2.70
		2.61
		2.62
		2.63
		2.64
		2.65
		2.66
		2.67
		2.68
		2.69
		2.70
		2.71 - 2.80
		2.71
		2.72
		2.73
		2.74
		2.75
		2.76
		2.77
		2.78
		2.79
		2.80
		2.81 - 2.90
		2.81
		2.82
		2.83
		2.84
		2.85
		2.86
		2.87
		2.88
		2.89
		2.90
		2.91 - 2.100
		2.91
		2.92
		2.93
		2.94
		2.95
		2.96
		2.97
		2.98
		2.99
		2.100
		2.101 - 2.110
		2.101
		2.102
		2.103
		2.104
		2.105
		2.106
		2.107
		2.108
		2.109
		2.110
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_003.pdf
3. We use Eq. 2-2 and Eq. 2-3. During a time tc when the velocity remains a positive constant, speed is
equivalent to velocity, and distance is equivalent to displacement, with ∆x = v tc .
(a) During the first part of the motion, the displacement is ∆x1 = 40 km and the time interval is
t1 =
(40 km)
(30 km/h)
= 1.33 h .
During the second part the displacement is ∆x2 = 40 km and the time interval is
t2 =
(40 km)
(60 km/h)
= 0.67 h .
Both displacements are in the same direction, so the total displacement is ∆x = ∆x1 + ∆x2 =
40 km + 40 km = 80 km. The total time for the trip is t = t1 + t2 = 2.00 h. Consequently, the
average velocity is
vavg =
(80 km)
(2.0 h)
= 40 km/h .
(b) In this example, the numerical result for the average speed is the same as the average velocity
40 km/h.
(c) In the interest of saving space, we briefly describe the graph (with kilometers and hours understood):
two contiguous line segments, the first having a slope of 30 and connecting the origin to (t1, x1) =
(1.33, 40) and the second having a slope of 60 and connecting (t1, x1) to (t, x) = (2.00, 80). The
average velocity, from the graphical point of view, is the slope of a line drawn from the origin to
(t, x).
		Main Menu
		Chapter 1 Measurement
		Chapter 2 Motion Along a Straight Line
		2.1 - 2.10
		2.1
		2.2
		2.3
		2.4
		2.5
		2.6
		2.7
		2.8
		2.9
		2.10
		2.11 - 2.20
		2.11
		2.12
		2.13
		2.14
		2.15
		2.16
		2.17
		2.18
		2.19
		2.20
		2.21 - 2.30
		2.21
		2.22
		2.23
		2.24
		2.25
		2.26
		2.27
		2.28
		2.29
		2.30
		2.31 - 2.40
		2.31
		2.32
		2.33
		2.34
		2.35
		2.36
		2.37
		2.38
		2.39
		2.40
		2.41 - 2.50
		2.41
		2.42
		2.43
		2.44
		2.45
		2.46
		2.47
		2.48
		2.49
		2.50
		2.51 - 2.60
		2.51
		2.52
		2.53
		2.54
		2.55
		2.56
		2.57
		2.58
		2.59
		2.60
		2.61 - 2.70
		2.61
		2.62
		2.63
		2.64
		2.65
		2.66
		2.67
		2.68
		2.69
		2.70
		2.71 - 2.80
		2.71
		2.72
		2.73
		2.74
		2.75
		2.76
		2.77
		2.78
		2.79
		2.80
		2.81 - 2.90
		2.81
		2.82
		2.83
		2.84
		2.85
		2.86
		2.87
		2.88
		2.89
		2.90
		2.91 - 2.100
		2.91
		2.92
		2.93
		2.94
		2.95
		2.96
		2.97
		2.98
		2.99
		2.100
		2.101 - 2.110
		2.101
		2.102
		2.103
		2.104
		2.105
		2.106
		2.107
		2.108
		2.109
		2.110
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_004.pdf
4. If the plane (with velocity v) maintains its present course, and if the terrain continues its upward slope
of 4.3◦, then the plane will strike the ground after traveling
∆x =
h
tan θ
=
35m
tan 4.3◦
= 465.5 m ≈ 0.465 km .
This corresponds to a time of flight found from Eq. 2-2 (with v = vavg since it is constant)
t =
∆x
v
=
0.465 km
1300 km/h
= 0.000358 h ≈ 1.3 s .
This, then, estimates the time available to the pilot to make his correction.
		Main Menu
		Chapter 1 Measurement
		Chapter 2 Motion Along a Straight Line
		2.1 - 2.10
		2.1
		2.2
		2.3
		2.4
		2.5
		2.6
		2.7
		2.8
		2.9
		2.10
		2.11 - 2.20
		2.11
		2.12
		2.13
		2.14
		2.15
		2.16
		2.17
		2.18
		2.19
		2.20
		2.21 - 2.30
		2.21
		2.22
		2.23
		2.24
		2.25
		2.26
		2.27
		2.28
		2.29
		2.30
		2.31 - 2.40
		2.31
		2.32
		2.33
		2.34
		2.35
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		2.38
		2.39
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		2.41 - 2.50
		2.41
		2.42
		2.43
		2.44
		2.45
		2.46
		2.47
		2.48
		2.49
		2.50
		2.51 - 2.60
		2.51
		2.52
		2.53
		2.54
		2.55
		2.56
		2.57
		2.58
		2.59
		2.60
		2.61 - 2.70
		2.61
		2.62
		2.63
		2.64
		2.65
		2.66
		2.67
		2.68
		2.69
		2.70
		2.71 - 2.80
		2.71
		2.72
		2.73
		2.74
		2.75
		2.76
		2.77
		2.78
		2.79
		2.80
		2.81 - 2.90
		2.81
		2.82
		2.83
		2.84
		2.85
		2.86
		2.87
		2.88
		2.89
		2.90
		2.91 - 2.100
		2.91
		2.92
		2.93
		2.94
		2.95
		2.96
		2.97
		2.98
		2.99
		2.100
		2.101 - 2.110
		2.101
		2.102
		2.103
		2.104
		2.105
		2.106
		2.107
		2.108
		2.109
		2.110
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More
About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_005.pdf
5. (a) Denoting the travel time and distance from San Antonio to Houston as T and D, respectively, the
average speed is
savg 1 =
D
T
=
(55 km/h)T2 + (90 km/h)
T
2
T
= 72.5 km/h
which should be rounded to 73 km/h.
(b) Using the fact that time=distance/speed while the speed is constant, we find
savg 2 =
D
T
=
D
D/2
55 km/h +
D/2
90 km/h
= 68.3 km/h
which should be rounded to 68 km/h.
(c) The total distance traveled (2D) must not be confused with the net displacement (zero). We obtain
for the two-way trip
savg =
2D
D
72.5 km/h +
D
68.3 km/h
= 70 km/h .
(d) Since the net displacement vanishes, the average velocity for the trip in its entirety is zero.
(e) In asking for a sketch, the problem is allowing the student to arbitrarily set the distanceD (the intent
is not to make the student go to an Atlas to look it up); the student can just as easily arbitrarily
set T instead of D, as will be clear in the following discussion. In the interest of saving space, we
briefly describe the graph (with kilometers-per-hour understood for the slopes): two contiguous line
segments, the first having a slope of 55 and connecting the origin to (t1, x1) = (T/2, 55T/2) and
the second having a slope of 90 and connecting (t1, x1) to (T,D) where D = (55 + 90)T/2. The
average velocity, from the graphical point of view, is the slope of a line drawn from the origin to
(T,D).
		Main Menu
		Chapter 1 Measurement
		Chapter 2 Motion Along a Straight Line
		2.1 - 2.10
		2.1
		2.2
		2.3
		2.4
		2.5
		2.6
		2.7
		2.8
		2.9
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		2.11 - 2.20
		2.11
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		2.13
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		2.17
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		2.21 - 2.30
		2.21
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		2.23
		2.24
		2.25
		2.26
		2.27
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		2.31 - 2.40
		2.31
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		2.33
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		2.39
		2.40
		2.41 - 2.50
		2.41
		2.42
		2.43
		2.44
		2.45
		2.46
		2.47
		2.48
		2.49
		2.50
		2.51 - 2.60
		2.51
		2.52
		2.53
		2.54
		2.55
		2.56
		2.57
		2.58
		2.59
		2.60
		2.61 - 2.70
		2.61
		2.62
		2.63
		2.64
		2.65
		2.66
		2.67
		2.68
		2.69
		2.70
		2.71 - 2.80
		2.71
		2.72
		2.73
		2.74
		2.75
		2.76
		2.77
		2.78
		2.79
		2.80
		2.81 - 2.90
		2.81
		2.82
		2.83
		2.84
		2.85
		2.86
		2.87
		2.88
		2.89
		2.90
		2.91 - 2.100
		2.91
		2.92
		2.93
		2.94
		2.95
		2.96
		2.97
		2.98
		2.99
		2.100
		2.101 - 2.110
		2.101
		2.102
		2.103
		2.104
		2.105
		2.106
		2.107
		2.108
		2.109
		2.110
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_006.pdf
6. (a) Using the fact that time=distance/velocity while the velocity is constant, we find
vavg =
73.2m + 73.2m
73.2m
1.22m/s +
73.2m
3.05m
= 1.74m/s .
(b) Using the fact that distance = vt while the velocity v is constant, we find
vavg =
(1.22m/s)(60 s) + (3.05m/s)(60 s)
120 s
= 2.14m/s .
(c) The graphs are shown below (with meters and seconds understood). The first consists of two (solid)
line segments, the first having a slope of 1.22 and the second having a slope of 3.05. The slope of
the dashed line represents the average velocity (in both graphs). The second graph also consists of
two (solid) line segments, having the same slopes as before – the main difference (compared to the
first graph) being that the stage involving higher-speed motion lasts much longer.
..........
...
...........
..
..........
...
...........
..
..........
...
..........
...
...........
..
..........
...
...........
..
...........
..
..........
...
............
.............
............
.............
............
.............
.............
............
.............
............
.............
.............
............
...........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.
x
t60 84
73
146
..........
...
..........
...
..........
...
..........
...
..........
...
..........
...
..........
...
..........
...
..........
...
..........
...
..........
...
..........
...
..........
...
..........
...
..........
...
..........
...
..........
...
..........
...
............
............
.............
.............
............
.............
............
.............
.............
............
.............
.............
............
...........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
....
x
t60 120
73
256
		Main Menu
		Chapter 1 Measurement
		Chapter 2 Motion Along a Straight Line
		2.1 - 2.10
		2.1
		2.2
		2.3
		2.4
		2.5
		2.6
		2.7
		2.8
		2.9
		2.10
		2.11 - 2.20
		2.11
		2.12
		2.13
		2.14
		2.15
		2.16
		2.17
		2.18
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		2.21 - 2.30
		2.21
		2.22
		2.23
		2.24
		2.25
		2.26
		2.27
		2.28
		2.29
		2.30
		2.31 - 2.40
		2.31
		2.32
		2.33
		2.34
		2.35
		2.36
		2.37
		2.38
		2.39
		2.40
		2.41 - 2.50
		2.41
		2.42
		2.43
		2.44
		2.45
		2.46
		2.47
		2.48
		2.49
		2.50
		2.51 - 2.60
		2.51
2.52
		2.53
		2.54
		2.55
		2.56
		2.57
		2.58
		2.59
		2.60
		2.61 - 2.70
		2.61
		2.62
		2.63
		2.64
		2.65
		2.66
		2.67
		2.68
		2.69
		2.70
		2.71 - 2.80
		2.71
		2.72
		2.73
		2.74
		2.75
		2.76
		2.77
		2.78
		2.79
		2.80
		2.81 - 2.90
		2.81
		2.82
		2.83
		2.84
		2.85
		2.86
		2.87
		2.88
		2.89
		2.90
		2.91 - 2.100
		2.91
		2.92
		2.93
		2.94
		2.95
		2.96
		2.97
		2.98
		2.99
		2.100
		2.101 - 2.110
		2.101
		2.102
		2.103
		2.104
		2.105
		2.106
		2.107
		2.108
		2.109
		2.110
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_007.pdf
7. Using x = 3t− 4t2 + t3 with SI units understood is efficient (and is the approach we will use), but if we
wished to make the units explicit we would write x = (3m/s)t− (4m/s2)t2 + (1m/s3)t3. We will quote
our answers to one or two significant figures, and not try to follow the significant figure rules rigorously.
(a) Plugging in t = 1 s yields x = 0. With t = 2 s we get x = −2 m. Similarly, t = 3 s yields x = 0 and
t = 4 s yields x = 12 m. For later reference, we also note that the position at t = 0 is x = 0.
(b) The position at t = 0 is subtracted from the position at t = 4 s to find the displacement ∆x = 12 m.
(c) The position at t = 2 s is subtracted from the position at t = 4 s to give the displacement ∆x = 14 m.
Eq. 2-2, then, leads to
vavg =
∆x
∆t
=
14
2
= 7 m/s .
(d) The horizontal axis is 0 ≤ t ≤ 4 with SI units understood.
Not shown is
a straight line
drawn from
the point at
(t, x) = (2,−2)
to the highest
point shown (at
t = 4 s) which
would represent
the answer for
part (c).
t
0
10
x
		Main Menu
		Chapter 1 Measurement
		Chapter 2 Motion Along a Straight Line
		2.1 - 2.10
		2.1
		2.2
		2.3
		2.4
		2.5
		2.6
		2.7
		2.8
		2.9
		2.10
		2.11 - 2.20
		2.11
		2.12
		2.13
		2.14
		2.15
		2.16
		2.17
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		2.19
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		2.21 - 2.30
		2.21
		2.22
		2.23
		2.24
		2.25
		2.26
		2.27
		2.28
		2.29
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		2.31 - 2.40
		2.31
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		2.33
		2.34
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		2.36
		2.37
		2.38
		2.39
		2.40
		2.41 - 2.50
		2.41
		2.42
		2.43
		2.44
		2.45
		2.46
		2.47
		2.48
		2.49
		2.50
		2.51 - 2.60
		2.51
		2.52
		2.53
		2.54
		2.55
		2.56
		2.57
		2.58
		2.59
		2.60
		2.61 - 2.70
		2.61
		2.62
		2.63
		2.64
		2.65
		2.66
		2.67
		2.68
		2.69
		2.70
		2.71 - 2.80
		2.71
		2.72
		2.73
		2.74
		2.75
		2.76
		2.77
		2.78
		2.79
		2.80
		2.81 - 2.90
		2.81
		2.82
		2.83
		2.84
		2.85
		2.86
		2.87
		2.88
		2.89
		2.90
		2.91 - 2.100
		2.91
		2.92
		2.93
		2.94
		2.95
		2.96
		2.97
		2.98
		2.99
		2.100
		2.101 - 2.110
		2.101
		2.102
		2.103
		2.104
		2.105
		2.106
		2.107
		2.108
		2.109
		2.110
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_008.pdf
8. Recognizing that the gap between the trains is closing at a constant rate of 60 km/h, the total time
which elapses before they crash is t = (60 km)/(60 km/h) = 1.0 h. During this time, the bird travels a
distance of x = vt = (60 km/h)(1.0 h) = 60 km.
		Main Menu
		Chapter 1 Measurement
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		2.1 - 2.10
		2.1
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		2.6
		2.7
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		2.21 - 2.30
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		2.41
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		2.48
		2.49
		2.50
		2.51 - 2.60
		2.51
		2.52
		2.53
		2.54
		2.55
		2.56
		2.57
		2.58
		2.59
		2.60
		2.61 - 2.70
		2.61
		2.62
		2.63
		2.64
		2.65
		2.66
		2.67
		2.68
		2.69
		2.70
		2.71 - 2.80
		2.71
		2.72
		2.73
		2.74
		2.75
		2.76
		2.77
		2.78
		2.79
2.80
		2.81 - 2.90
		2.81
		2.82
		2.83
		2.84
		2.85
		2.86
		2.87
		2.88
		2.89
		2.90
		2.91 - 2.100
		2.91
		2.92
		2.93
		2.94
		2.95
		2.96
		2.97
		2.98
		2.99
		2.100
		2.101 - 2.110
		2.101
		2.102
		2.103
		2.104
		2.105
		2.106
		2.107
		2.108
		2.109
		2.110
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_009.pdf
9. Converting to seconds, the running times are t1 = 147.95 s and t2 = 148.15 s, respectively. If the runners
were equally fast, then
savg 1 = savg 2 =⇒
L1
t1
=
L2
t2
.
From this we obtain
L2 − L1 =
(
148.15
147.95
− 1
)
L1 ≈ 1.35 m
where we set L1 ≈ 1000 m in the last step. Thus, if L1 and L2 are no different than about 1.35 m, then
runner 1 is indeed faster than runner 2. However, if L1 is shorter than L2 than 1.4 m then runner 2 is
actually the faster.
		Main Menu
		Chapter 1 Measurement
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		2.1 - 2.10
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		2.6
		2.7
		2.8
		2.9
		2.10
		2.11 - 2.20
		2.11
		2.12
		2.13
		2.14
		2.15
		2.16
		2.17
		2.18
		2.19
		2.20
		2.21 - 2.30
		2.21
		2.22
		2.23
		2.24
		2.25
		2.26
		2.27
		2.28
		2.29
		2.30
		2.31 - 2.40
		2.31
		2.32
		2.33
		2.34
		2.35
		2.36
		2.37
		2.38
		2.39
		2.40
		2.41 - 2.50
		2.41
		2.42
		2.43
		2.44
		2.45
		2.46
		2.47
		2.48
		2.49
		2.50
		2.51 - 2.60
		2.51
		2.52
		2.53
		2.54
		2.55
		2.56
		2.57
		2.58
		2.59
		2.60
		2.61 - 2.70
		2.61
		2.62
		2.63
		2.64
		2.65
		2.66
		2.67
		2.68
		2.69
		2.70
		2.71 - 2.80
		2.71
		2.72
		2.73
		2.74
		2.75
		2.76
		2.77
		2.78
		2.79
		2.80
		2.81 - 2.90
		2.81
		2.82
		2.83
		2.84
		2.85
		2.86
		2.87
		2.88
		2.89
		2.90
		2.91 - 2.100
		2.91
		2.92
		2.93
		2.94
		2.95
		2.96
		2.97
		2.98
		2.99
		2.100
		2.101 - 2.110
		2.101
		2.102
		2.103
		2.104
		2.105
		2.106
		2.107
		2.108
		2.109
		2.110
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_010.pdf
10. The velocity (both magnitude and sign) is determined by the slope of the x versus t curve, in accordance
with Eq. 2-4.
(a) The armadillo is to the left of the coordinate origin on the axis between t = 2.0 s and t = 4.0 s.
(b) The velocity is negative between t = 0 and t = 3.0 s.
(c) The velocity is positive between t = 3.0 s and t = 7.0 s.
(d) The velocity is zero at the graph minimum (at t = 3.0 s).
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		2.11
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		2.13
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		2.18
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		2.21
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		2.31
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		2.41 - 2.50
		2.41
		2.42
		2.43
		2.44
		2.45
		2.46
		2.47
		2.48
		2.49
		2.50
		2.51 - 2.60
		2.51
		2.52
		2.53
		2.54
		2.55
		2.56
		2.57
		2.58
		2.59
		2.60
		2.61 - 2.70
		2.61
		2.62
		2.63
		2.64
		2.65
		2.66
		2.67
		2.68
		2.69
		2.70
		2.71 - 2.80
		2.71
		2.72
		2.73
		2.74
		2.75
		2.76
		2.77
		2.78
		2.79
		2.80
		2.81 - 2.90
		2.81
		2.82
		2.83
		2.84
		2.85
		2.86
		2.87
		2.88
		2.89
		2.90
		2.91 - 2.100
		2.91
		2.92
		2.93
		2.94
		2.95
		2.96
		2.97
		2.98
		2.99
		2.100
		2.101 - 2.110
		2.101
		2.102
		2.103
		2.104
		2.105
		2.106
		2.107
		2.108
		2.109
		2.110
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_011.pdf
11. We use Eq. 2-4.
(a) The velocity of the particle is
v =
dx
dt
=
d
dt
(
4− 12t+ 3t2) = −12 + 6t .
Thus, at t = 1 s, the velocity is v = (−12 + (6)(1)) = −6 m/s.
(b) Since v < 0, it is moving in the negative x direction at t = 1 s.
(c) At t = 1 s, the speed is |v| = 6 m/s.
(d) For 0 < t < 2 s, |v| decreases until it vanishes. For 2 < t < 3 s, |v| increases from zero to the value
it had in part (c). Then, |v| is larger than that value for t > 3 s.
(e) Yes, since v smoothly changes from negative values (consider the t = 1 result) to positive (note
that as t→ +∞, we have v → +∞). One can check that v = 0 when t = 2 s.
(f) No. In fact, from v = −12 + 6t, we know that v > 0 for t > 2 s.
		Main Menu
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		2.31
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		2.37
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		2.39
		2.40
		2.41 - 2.50
		2.41
		2.42
		2.43
		2.44
		2.45
		2.46
		2.47
		2.48
		2.49
		2.50
		2.51 - 2.60
		2.51
		2.52
		2.53
		2.54
		2.55
		2.56
		2.57
		2.58
		2.59
		2.60
		2.61 - 2.70
		2.61
		2.62
		2.63
		2.64
		2.65
		2.66
		2.67
		2.68
		2.69
		2.70
		2.71 - 2.80
		2.71
		2.72
		2.73
		2.74
		2.75
		2.76
		2.77
		2.78
		2.79
		2.80
		2.81 - 2.90
		2.81
		2.82
		2.83
		2.84
		2.85
		2.86
		2.87
		2.88
		2.89
		2.90
		2.91 - 2.100
		2.91
		2.92
		2.93
		2.94
		2.95
		2.96
		2.97
		2.98
		2.99
		2.100
		2.101 - 2.110
		2.101
		2.102
		2.103
		2.104
		2.105
		2.106
		2.107
		2.108
		2.109
		2.110
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_012.pdf
12. We use Eq. 2-2 for average velocity and Eq. 2-4 for instantaneous velocity, and work with distances in
centimeters and times in seconds.
(a) We plug into the given equation for x for t = 2.00 s and t = 3.00 s and obtain x2 = 21.75 cm and
x3 = 50.25 cm, respectively. The average velocity during the time interval 2.00 ≤ t ≤ 3.00 s is
vavg =
∆x
∆t
=
50.25 cm− 21.75 cm
3.00 s− 2.00 s
which yields vavg = 28.5 cm/s.
(b) The instantaneous velocity is v = dxdt = 4.5t
2, which yields v = (4.5)(2.00)2 = 18.0 cm/s at time
t = 2.00 s.
(c) At t = 3.00 s, the instantaneous velocity is v = (4.5)(3.00)2 = 40.5 cm/s.
(d) At t = 2.50 s, the instantaneous velocity is v = (4.5)(2.50)2 = 28.1 cm/s.
(e) Let tm stand for the moment when the particle is midway between x2 and x3 (that is, when the
particle is at xm = (x2 + x3)/2 = 36 cm). Therefore,
xm = 9.75 + 1.5t3m =⇒ tm = 2.596
in seconds. Thus, the instantaneous speed at this time is v = 4.5(2.596)2 = 30.3 cm/s.
(f) The answer to part (a) is given by the slope of the straight line
between t = 2 and
t = 3 in this x-
vs-t plot. The an-
swers to parts (b),
(c), (d) and (e)
correspond to the
slopes of tangent
lines (not shown
but easily imag-
ined) to the curve
at the appropriate
points.
(cm)x
(a)
20
40
60
2 3t
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		2.51 - 2.60
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		2.83
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		2.91 - 2.100
		2.91
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		2.93
		2.94
		2.95
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		2.99
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2.101 - 2.110
		2.101
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		2.106
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		2.108
		2.109
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		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_013.pdf
13. Since v = dxdt (Eq. 2-4), then ∆x =
∫
v dt, which corresponds to the area under the v vs t graph. Dividing
the total area A into rectangular (base×height) and triangular (12base×height) areas, we have
A = A0<t<2 +A2<t<10 +A10<t<12 +A12<t<16
=
1
2
(2)(8) + (8)(8) +
(
(2)(4) +
1
2
(2)(4)
)
+ (4)(4)
with SI units understood. In this way, we obtain ∆x = 100 m.
		Main Menu
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		2.83
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		2.91 - 2.100
		2.91
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		2.93
		2.94
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		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_014.pdf
14. From Eq. 2-4 and Eq. 2-9, we note that the sign of the velocity is the sign of the slope in an x-vs-t plot,
and the sign of the acceleration corresponds to whether such a curve is concave up or concave down. In
the interest of saving space, we indicate sample points for parts (a)-(d) in a single figure; this means
that all points are not at t = 1 s (which we feel is an acceptable modification of the problem – since the
datum t = 1 s is not used).
(c) (a)
(b)
(d)
Any change from zero
to non-zero values
of �v represents in-
creasing |�v| (speed).
Also, �v ‖ �a implies
that the particle is
going faster. Thus,
points (a), (b) and
(d) involve increasing
speed.
		Main Menu
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		2.31
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		2.41 - 2.50
		2.41
		2.42
		2.43
		2.44
		2.45
		2.46
		2.47
		2.48
		2.49
		2.50
		2.51 - 2.60
		2.51
		2.52
		2.53
		2.54
		2.55
		2.56
		2.57
		2.58
		2.59
		2.60
		2.61 - 2.70
		2.61
		2.62
		2.63
		2.64
		2.65
		2.66
		2.67
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		2.69
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		2.71 - 2.80
		2.71
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		2.73
		2.74
		2.75
		2.76
		2.77
		2.78
		2.79
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		2.81 - 2.90
		2.81
		2.82
		2.83
		2.84
		2.85
		2.86
		2.87
		2.88
		2.89
		2.90
		2.91 - 2.100
		2.91
		2.92
		2.93
		2.94
		2.95
		2.96
		2.97
		2.98
		2.99
		2.100
		2.101 - 2.110
		2.101
		2.102
		2.103
		2.104
		2.105
		2.106
		2.107
		2.108
		2.109
		2.110
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_015.pdf
15. We appeal to Eq. 2-4 and Eq. 2-9.
(a) This is v2 – that is, the velocity squared.
(b) This is the acceleration a.
(c) The SI units for these quantities are (m/s)2 = m2/s2 and m/s2, respectively.
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		2.51 - 2.60
		2.51
		2.52
		2.53
		2.54
		2.55
		2.56
		2.57
		2.58
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		2.81
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		2.83
		2.84
		2.85
		2.86
		2.87
		2.88
		2.89
		2.90
		2.91 - 2.100
		2.91
		2.92
		2.93
		2.94
		2.95
		2.96
		2.97
		2.98
		2.99
		2.100
		2.101 - 2.110
		2.101
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		2.103
		2.104
		2.105
		2.106
		2.107
		2.108
		2.109
		2.110
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_016.pdf
16. Eq. 2-9 indicates that acceleration is the slope of the v-vs-t graph.
Based on this, we
show here a sketch
of the acceleration (in
m/s2) as a function
of time. The values
along the acceleration
axis should not be
taken too seriously. –20
–10
0
10
a
5t
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		2.51 - 2.60
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		2.58
		2.59
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		2.61 - 2.70
		2.61
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		2.63
		2.64
		2.65
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		2.71 - 2.80
		2.71
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		2.73
		2.74
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		2.81 - 2.90
		2.81
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		2.83
		2.84
		2.85
		2.86
		2.87
		2.88
		2.89
		2.90
		2.91 - 2.100
		2.91
		2.92
		2.93
		2.94
		2.95
		2.96
		2.97
		2.98
		2.99
		2.100
		2.101 - 2.110
		2.101
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		2.103
		2.104
		2.105
		2.106
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		2.108
		2.109
		2.110
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy
from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_017.pdf
17. We represent its initial direction of motion as the +x direction, so that v0 = +18 m/s and v = −30 m/s
(when t = 2.4 s). Using Eq. 2-7 (or Eq. 2-11, suitably interpreted) we find
aavg =
(−30)− (+18)
2.4
= −20 m/s2
which indicates that the average acceleration has magnitude 20 m/s2 and is in the opposite direction to
the particle’s initial velocity.
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		2.51 - 2.60
		2.51
		2.52
		2.53
		2.54
		2.55
		2.56
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		2.58
		2.59
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		2.61
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		2.91 - 2.100
		2.91
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		2.93
		2.94
		2.95
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		2.99
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		2.101 - 2.110
		2.101
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		2.109
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		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_018.pdf
18. We use Eq. 2-2 (average velocity) and Eq. 2-7 (average acceleration). Regarding our coordinate choices,
the initial position of the man is taken as the origin and his direction of motion during 5min ≤ t ≤ 10min
is taken to be the positive x direction. We also use the fact that ∆x = v∆t′ when the velocity is constant
during a time interval ∆t′.
(a) Here, the entire interval considered is ∆t = 8− 2 = 6 min which is equivalent to 360 s, whereas the
sub-interval in which he is moving is only ∆t′ = 8 − 5 = 3 min= 180 s. His position at t = 2 min
is x = 0 and his position at t = 8 min is x = v∆t′ = (2.2)(180) = 396 m. Therefore,
vavg =
396m− 0
360 s
= 1.10 m/s .
(b) The man is at rest at t = 2 min and has velocity v = +2.2 m/s at t = 8 min. Thus, keeping the
answer to 3 significant figures,
aavg =
2.2m/s− 0
360 s
= 0.00611 m/s2 .
(c) Now, the entire interval considered is ∆t = 9 − 3 = 6 min (360 s again), whereas the sub-interval
in which he is moving is ∆t′ = 9− 5 = 4 min= 240 s). His position at t = 3 min is x = 0 and his
position at t = 9 min is x = v∆t′ = (2.2)(240) = 528 m. Therefore,
vavg =
528m− 0
360 s
= 1.47 m/s .
(d) The man is at rest at t = 3 min and has velocity v = +2.2 m/s at t = 9 min. Consequently,
aavg = 2.2/360 = 0.00611 m/s2 just as in part (b).
(e) The horizontal line near the bottom of this x-vs-t graph represents
the man stand-
ing at x = 0 for
0 ≤ t < 300 s
and the linearly
rising line for
300 ≤ t ≤ 600 s
represents his
constant-velocity
motion. The dotted
lines represent the
answers to part (a)
and (c) in the sense
that their slopes
yield those results.
(c)
(a)
0
500
x
0 500t
The graph of v-vs-t is not shown here, but would consist of two horizontal “steps” (one at v = 0
for 0 ≤ t < 300 s and the next at v = 2.2 m/s for 300 ≤ t ≤ 600 s). The indications of the
average accelerations found in parts (b) and (d) would be dotted lines connected the “steps” at the
appropriate t values (the slopes of the dotted lines representing the values of aavg).
		Main Menu
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		2.51 - 2.60
		2.51
		2.52
		2.53
		2.54
		2.55
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		2.57
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		2.59
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		2.61
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		2.71 - 2.80
		2.71
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		2.83
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		2.91 - 2.100
		2.91
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		2.93
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		2.101 - 2.110
		2.101
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		2.103
		2.104
		2.105
		2.106
		2.107
		2.108
		2.109
		2.110
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22
Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_019.pdf
19. In this solution, we make use of the notation x(t) for the value of x at a particular t. Thus, x(t) =
50t+ 10t2 with SI units (meters and seconds) understood.
(a) The average velocity during the first 3 s is given by
vavg =
x(3)− x(0)
∆t
=
(50)(3) + (10)(3)2 − 0
3
= 80 m/s .
(b) The instantaneous velocity at time t is given by v = dx/dt = 50 + 20t, in SI units. At t = 3.0 s,
v = 50 + (20)(3.0) = 110 m/s.
(c) The instantaneous acceleration at time t is given by a = dv/dt = 20 m/s2. It is constant, so the
acceleration at any time is 20m/s2.
(d) and (e) The graphs below show the coordinate x and velocity v as functions of time, with SI units
understood. The dotted line marked (a) in the first graph runs from t = 0, x = 0 to t = 3.0 s,
x = 240m. Its slope is the average velocity during the first 3 s of motion. The dotted line marked
(b) is tangent to the x curve at t = 3.0 s. Its slope is the instantaneous velocity at t = 3.0 s.
.................
................
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...
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..
...........
..
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..
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..
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..
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..
...........
..
...........
..
...........
..
...........
..
1.0 2.0 3.0 4.0
0
100
200
300
400
(a)
(b)
t
x
.....................
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1.0 2.0 3.0 4.0
50
0
100
150
200
t
v
		Main Menu
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		2.41
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		2.47
		2.48
		2.49
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		2.51 - 2.60
		2.51
		2.52
		2.53
		2.54
		2.55
		2.56
		2.57
		2.58
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		2.61
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		2.91 - 2.100
		2.91
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		2.93
		2.94
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		2.101 - 2.110
		2.101
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		Chapter 3 Vectors
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		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
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		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_020.pdf
20. Using the general property ddx exp(bx) = b exp(bx), we write
v =
dx
dt
=
(
d (19t)
dt
)
· e−t + (19t) ·
(
d e−t
dt
)
.
If a concern develops about the appearance of an argument of the exponential (−t) apparently having
units, then an explicit factor of 1/T where T = 1 second can be inserted and carried through the
computation (which does not change our answer). The result of this differentiation is
v = 16(1− t)e−t
with t and v in SI units (s and m/s, respectively). We see that this function is zero when t = 1 s.
Now that we know when it stops, we find out where it stops by plugging our result t = 1 into the given
function x = 16te−t with x in meters. Therefore, we find x = 5.9 m.
		Main Menu
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2.41 - 2.50
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		2.44
		2.45
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		2.47
		2.48
		2.49
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		2.51 - 2.60
		2.51
		2.52
		2.53
		2.54
		2.55
		2.56
		2.57
		2.58
		2.59
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		2.61 - 2.70
		2.61
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		2.71 - 2.80
		2.71
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		2.88
		2.89
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		2.91 - 2.100
		2.91
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		2.93
		2.94
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		Chapter 3 Vectors
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		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_021.pdf
21. In this solution, we make use of the notation x(t) for the value of x at a particular t. The notations v(t)
and a(t) have similar meanings.
(a) Since the unit of ct2 is that of length, the unit of c must be that of length/time2, or m/s2 in the SI
system. Since bt3 has a unit of length, b must have a unit of length/time3, or m/s3.
(b) When the particle reaches its maximum (or its minimum) coordinate its velocity is zero. Since the
velocity is given by v = dx/dt = 2ct− 3bt2, v = 0 occurs for t = 0 and for
t =
2c
3b
=
2(3.0m/s2)
3(2.0m/s3)
= 1.0 s .
For t = 0, x = x0 = 0 and for t = 1.0 s, x = 1.0m > x0. Since we seek the maximum, we reject the
first root (t = 0) and accept the second (t = 1 s).
(c) In the first 4 s the particle moves from the origin to x = 1.0m, turns around, and goes back to
x(4 s) = (3.0m/s2)(4.0 s)2 − (2.0m/s3)(4.0 s)3 = −80m .
The total path length it travels is 1.0m + 1.0m+ 80m = 82m.
(d) Its displacement is given by ∆x = x2 − x1, where x1 = 0 and x2 = −80m. Thus, ∆x = −80m.
(e) The velocity is given by v = 2ct− 3bt2 = (6.0m/s2)t− (6.0m/s3)t2. Thus
v(1 s) = (6.0m/s2)(1.0 s)− (6.0m/s3)(1.0 s)2 = 0
v(2 s) = (6.0m/s2)(2.0 s)− (6.0m/s3)(2.0 s)2 = −12m/s
v(3 s) = (6.0m/s2)(3.0 s)− (6.0m/s3)(3.0 s)2 = −36.0m/s
v(4 s) = (6.0m/s2)(4.0 s)− (6.0m/s3)(4.0 s)2 = −72m/s .
(f) The acceleration is given by a = dv/dt = 2c− 6b = 6.0m/s2 − (12.0m/s3)t. Thus
a(1 s) = 6.0m/s2 − (12.0m/s3)(1.0 s) = −6.0m/s2
a(2 s) = 6.0m/s2 − (12.0m/s3)(2.0 s) = −18m/s2
a(3 s) = 6.0m/s2 − (12.0m/s3)(3.0 s) = −30m/s2
a(4 s) = 6.0m/s2 − (12.0m/s3)(4.0 s) = −42m/s2 .
		Main Menu
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		Chapter 3 Vectors
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		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_022.pdf
22. For the automobile ∆v = 55− 25 = 30 km/h, which we convert to SI units:
a =
∆v
∆t
=
(30 km/h)
(
1000m/km
3600 s/h
)
(0.50min)(60 s/min)
= 0.28 m/s2 .
The change of velocity for the bicycle, for the same time, is identical to that of the car, so its acceleration
is also 0.28 m/s2.
		Main Menu
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		2.1 - 2.10
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		2.51 - 2.60
		2.51
		2.52
		2.53
		2.54
		2.55
		2.56
		2.57
		2.58
		2.59
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		2.61 - 2.70
		2.61
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		2.63
		2.64
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		2.71 - 2.80
		2.71
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		2.73
		2.74
		2.75
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		2.79
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		2.81 - 2.90
		2.81
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		2.83
		2.84
		2.85
		2.86
		2.87
		2.88
		2.89
		2.90
		2.91 - 2.100
		2.91
		2.92
		2.93
		2.94
		2.95
		2.96
		2.97
		2.98
		2.99
		2.100
		2.101 - 2.110
		2.101
		2.102
		2.103
		2.104
		2.105
		2.106
		2.107
		2.108
		2.109
		2.110
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_023.pdf
23. The constant-acceleration condition permits the use of Table 2-1.
(a) Setting v = 0 and x0 = 0 in v2 = v20 + 2a(x− x0), we find
x = −1
2
v20
a
= −1
2
(
5.00× 106
−1.25× 1014
)
= 0.100 m .
Since the muon is slowing, the initial velocity and the acceleration must have opposite signs.
(b) Below are the time-plots of the position x and velocity v of the muon from the moment it enters
the field to the time it stops. The computation in part (a) made no reference to t, so that other
equations from Table 2-1 (such as v = v0 + at and x = v0t+ 12at
2) are used in making these plots.
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
..........
..........
..........
..........
..........
..........
..........
...........
...........
...........
...........
...........
............
............
............
.............
..............
...............
.................
....................
............................
.................................
10 20 30 40
t (ns)
0
2.5
5.0
7.5
10
x (cm)
................................................................................................................................................................................................................................................................................................................................................................................................
10 20 30 40
t (ns)
0
2.0
4.0
6.0
8.0
v (Mm/s)
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		Chapter 39 Photons and Matter Waves
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		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_024.pdf
24. The time required is found from Eq. 2-11 (or, suitably interpreted, Eq. 2-7). First, we convert the
velocity change to SI units:
∆v = (100
km/h)
(
1000m/km
3600 s/h
)
= 27.8 m/s .
Thus, ∆t = ∆v/a = 27.8/50 = 0.556 s.
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		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_025.pdf
25. We use v = v0 + at, with t = 0 as the instant when the velocity equals +9.6 m/s.
(a) Since we wish to calculate the velocity for a time before t = 0, we set t = −2.5 s. Thus, Eq. 2-11
gives
v = (9.6m/s) +
(
3.2m/s2
)
(−2.5 s) = 1.6 m/s .
(b) Now, t = +2.5 s and we find
v = (9.6m/s) +
(
3.2m/s2
)
(2.5 s) = 18 m/s .
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		Chapter 25 Electric Potential
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		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
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		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_026.pdf
26. The bullet starts at rest (v0 = 0) and after traveling the length of the barrel (∆x = 1.2 m) emerges with
the given velocity (v = 640 m/s), where the direction of motion is the positive direction. Turning to the
constant acceleration equations in Table 2-1, we use
∆x =
1
2
(v0 + v) t .
Thus, we find t = 0.00375 s (about 3.8 ms).
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		Chapter 16 Oscillations
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		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_027.pdf
27. The constant acceleration stated in the problem permits the use of the equations in Table 2-1.
(a) We solve v = v0 + at for the time:
t =
v − v0
a
=
1
10
(
3.0× 108m/s)
9.8m/s2
= 3.1× 106 s
which is equivalent to 1.2 months.
(b) We evaluate x = x0 + v0t+ 12at
2, with x0 = 0. The result is
x =
1
2
(
9.8m/s2
) (
3.1× 106 s)2 = 4.7× 1013m .
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		Chapter 10 Collisions
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		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_028.pdf
28. From Table 2-1, v2 − v20 = 2a∆x is used to solve for a. Its minimum value is
amin =
v2 − v20
2∆xmax
=
(360 km/h)2
2(1.80 km)
= 36000 km/h2
which converts to 2.78 m/s2.
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		2.41
		2.42
		2.43
		2.44
		2.45
		2.46
		2.47
		2.48
		2.49
		2.50
		2.51 - 2.60
		2.51
		2.52
		2.53
		2.54
		2.55
		2.56
		2.57
		2.58
		2.59
		2.60
		2.61 - 2.70
		2.61
		2.62
		2.63
		2.64
		2.65
		2.66
		2.67
		2.68
		2.69
		2.70
		2.71 - 2.80
		2.71
		2.72
		2.73
		2.74
		2.75
		2.76
		2.77
		2.78
		2.79
		2.80
		2.81 - 2.90
		2.81
		2.82
		2.83
		2.84
		2.85
		2.86
		2.87
		2.88
		2.89
		2.90
		2.91 - 2.100
		2.91
		2.92
		2.93
		2.94
		2.95
		2.96
		2.97
		2.98
		2.99
		2.100
		2.101 - 2.110
		2.101
		2.102
		2.103
		2.104
		2.105
		2.106
		2.107
		2.108
		2.109
		2.110
		Chapter 3 Vectors
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		Chapter 9 System of Particles
		Chapter 10 Collisions
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		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter
16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_029.pdf
29. Assuming constant acceleration permits the use of the equations in Table 2-1. We solve v2 = v20+2a(x−
x0) with x0 = 0 and x = 0.010 m. Thus,
a =
v2 − v20
2x
=
(
5.7× 105)2 − (1.5× 105)2
2(0.01)
= 1.62× 1015 m/s2 .
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		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
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		Chapter 16 Oscillations
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		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
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		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_030.pdf
30. The acceleration is found from Eq. 2-11 (or, suitably interpreted, Eq. 2-7).
a =
∆v
∆t
=
(1020 km/h)
(
1000m/km
3600 s/h
)
1.4 s
= 202.4 m/s2 .
In terms of the gravitational acceleration g, this is expressed as a multiple of 9.8 m/s2 as follows:
a =
202.4
9.8
g = 21g .
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		2.51 - 2.60
		2.51
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		2.53
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		2.55
		2.56
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		2.61
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		2.71 - 2.80
		2.71
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		2.73
		2.74
		2.75
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		2.81
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		2.91
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		2.93
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		2.101
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		Chapter 17 Waves—I
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		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy
from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_031.pdf
31. We choose the positive direction to be that of the initial velocity of the car (implying that a < 0 since
it is slowing down). We assume the acceleration is constant and use Table 2-1.
(a) Substituting v0 = 137 km/h = 38.1m/s, v = 90 km/h = 25m/s, and a = −5.2m/s2 into v = v0+at,
we obtain
t =
25m/s− 38m/s
−5.2m/s2 = 2.5 s .
(b) We take the car to be at x = 0 when the brakes are applied
(at time t = 0). Thus, the
coordinate of the car as a
function of time is given by
x = (38)t+
1
2
(−5.2)t2
in SI units. This function
is plotted from t = 0 to t =
2.5 s on the graph to the
right. We have not shown
the v-vs-t graph here; it is
a descending straight line
from v0 to v.
............
............
............
............
............
............
............
............
............
............
............
............
............
............
.............
.............
.............
.............
.............
.............
.............
.............
.............
.............
.............
..............
..............
..............
..............
..............
..............
..............
......
0
20
40
60
80
0.5 1.0 1.5 2.0 2.5
x (m)
t (s)
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		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
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		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_032.pdf
32. From the figure, we see that x0 = −2.0 m. From Table 2-1, we can apply x − x0 = v0t + 12at2 with
t = 1.0 s, and then again with t = 2.0 s. This yields two equations for the two unknowns, v0 and a. SI
units are understood.
0.0− (−2.0) = v0 (1.0) + 12a(1.0)
2
6.0− (−2.0) = v0 (2.0) + 12a(2.0)
2 .
Solving these simultaneous equations yields the results v0 = 0.0 and a = 4.0 m/s2. The fact that the
answer is positive tells us that the acceleration vector points in the +x direction.
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		Chapter 20 The Kinetic Theory of Gases
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		Chapter 22 Electric Charge
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		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
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		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
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		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_033.pdf
33. The problem statement (see part (a)) indicates that a =constant, which allows us to use Table 2-1.
(a) We take x0 = 0, and solve x = v0t + 12at
2 (Eq. 2-15) for the acceleration: a = 2(x − v0t)/t2.
Substituting x = 24.0m, v0 = 56.0 km/h = 15.55m/s and t = 2.00 s, we find
a =
2 (24.0m− (15.55m/s)(2.00 s))
(2.00 s)2
= −3.56m/s2 .
The negative sign indicates that the acceleration is opposite to the direction of motion of the car.
The car is slowing down.
(b) We evaluate v = v0 + at as follows:
v = 15.55m/s−
(
3.56m/s2
)
(2.00 s) = 8.43 m/s
which is equivalent to 30.3 km/h.
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		2.32
		2.33
		2.34
		2.35
		2.36
		2.37
		2.38
		2.39
		2.40
		2.41 - 2.50
		2.41
		2.42
		2.43
		2.44
		2.45
		2.46
		2.47
		2.48
		2.49
		2.50
		2.51 - 2.60
		2.51
		2.52
		2.53
		2.54
		2.55
		2.56
		2.57
		2.58
		2.59
		2.60
		2.61 - 2.70
		2.61
		2.62
		2.63
		2.64
		2.65
		2.66
		2.67
		2.68
		2.69
		2.70
		2.71 - 2.80
		2.71
		2.72
		2.73
		2.74
		2.75
		2.76
		2.77
		2.78
		2.79
		2.80
		2.81 - 2.90
		2.81
		2.82
		2.83
		2.84
		2.85
		2.86
		2.87
		2.88
		2.89
		2.90
		2.91 - 2.100
		2.91
		2.92
		2.93
		2.94
		2.95
		2.96
		2.97
		2.98
		2.99
		2.100
		2.101 - 2.110
		2.101
		2.102
		2.103
		2.104
		2.105
		2.106
		2.107
		2.108
		2.109
		2.110
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_034.pdf
34. We take the moment of applying brakes to be t = 0. The deceleration is constant so that Table 2-1 can
be used. Our primed variables (such as v′o = 72 km/h = 20 m/s) refer to one train (moving in the +x
direction and located at the origin when t = 0) and unprimed variables refer to the other (moving in
the −x direction and located at x0 = +950 m when t = 0). We note that the acceleration vector of the
unprimed train points in the positive direction, even though the train is slowing down; its initial velocity
is vo = −144 km/h = −40 m/s. Since the primed train has the lower initial speed, it should stop sooner
than the other train would (were it not for the collision). Using Eq 2-16, it should stop (meaning v′ = 0)
at
x′ =
(v′)2 − (v′o)2
2a′
=
0− 202
−2 = 200 m .
The speed of the other train, when it reaches that location, is
v =
√
v2o + 2a∆x =
√
(−40)2 + 2(1.0)(200− 950) =
√
100 = 10 m/s
using Eq 2-16 again. Specifically, its velocity at that moment would be −10 m/s since it is still traveling
in the −x direction when it crashes. If the computation of v had failed (meaning that a negative number
would have been inside the square root) then we would have looked at the possibility that there was no
collision and examined how far apart they finally were. A concern that can be brought up is whether the
primed train collides before it comes to rest; this can be studied by computing the time it stops (Eq. 2-11
yields t = 20 s) and seeing where the unprimed train is at that moment (Eq. 2-18 yields x = 350 m, still
a good distance away from contact).
		Main Menu
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		2.6
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		2.11
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		2.21 - 2.30
		2.21
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		2.31
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		2.41 - 2.50
		2.41
		2.42
		2.43
		2.44
		2.45
		2.46
		2.47
		2.48
		2.49
		2.50
		2.51 - 2.60
		2.51
		2.52
		2.53
		2.54
		2.55
		2.56
		2.57
		2.58
		2.59
		2.60
		2.61 - 2.70
		2.61
		2.62
		2.63
		2.64
		2.65
		2.66
		2.67
		2.68
		2.69
		2.70
		2.71 - 2.80
		2.71
		2.72
		2.73
		2.74
		2.75
		2.76
		2.77
		2.78
		2.79
		2.80
		2.81 - 2.90
		2.81
		2.82
		2.83
		2.84
		2.85
		2.86
		2.87
		2.88
		2.89
		2.90
		2.91 - 2.100
		2.91
		2.92
		2.93
		2.94
		2.95
		2.96
		2.97
		2.98
		2.99
		2.100
		2.101 - 2.110
		2.101
		2.102
		2.103
		2.104
		2.105
		2.106
		2.107
		2.108
		2.109
		2.110
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull
Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_035.pdf
35. The acceleration is constant and we may use the equations in Table 2-1.
(a) Taking the first point as coordinate origin and time to be zero when the car is there, we apply
Eq. 2-17 (with SI units understood):
x =
1
2
(v + v0) t =
1
2
(15 + v0) (6) .
With x = 60.0 m (which takes the direction of motion as the +x direction) we solve for the initial
velocity: v0 = 5.00 m/s.
(b) Substituting v = 15 m/s, v0 = 5 m/s and t = 6 s into a = (v − v0)/t (Eq. 2-11), we find
a = 1.67 m/s2.
(c) Substituting v = 0 in v2 = v20 + 2ax and solving for x, we obtain
x = − v
2
0
2a
= − 5
2
2(1.67)
= −7.50 m .
(d) The graphs require computing the time when v = 0, in which case, we use v = v0 + at′ = 0. Thus,
t′ =
−v0
a
=
−5
1.67
= −3.0 s
indicates the moment the car was at rest. SI units are assumed.
.........................................................
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.......
.......
.......
......
......
......
......
......
......
......
......
......
.....
.....
.....
.....
.....
.....
.....
...
−5 5 10
t
−20
20
40
60 x
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
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.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
.........
..
−5 0 5 10
t
5
10
15
v
		Main Menu
		Chapter 1 Measurement
		Chapter 2 Motion Along a Straight Line
		2.1 - 2.10
		2.1
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		2.6
		2.7
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		2.11
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		2.21 - 2.30
		2.21
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		2.31 - 2.40
		2.31
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		2.33
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		2.37
		2.38
		2.39
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		2.41 - 2.50
		2.41
		2.42
		2.43
		2.44
		2.45
		2.46
		2.47
		2.48
		2.49
		2.50
		2.51 - 2.60
		2.51
		2.52
		2.53
		2.54
		2.55
		2.56
		2.57
		2.58
		2.59
		2.60
		2.61 - 2.70
		2.61
		2.62
		2.63
		2.64
		2.65
		2.66
		2.67
		2.68
		2.69
		2.70
		2.71 - 2.80
		2.71
		2.72
		2.73
		2.74
		2.75
		2.76
		2.77
		2.78
		2.79
		2.80
		2.81 - 2.90
		2.81
		2.82
		2.83
		2.84
		2.85
		2.86
		2.87
		2.88
		2.89
		2.90
		2.91 - 2.100
		2.91
		2.92
		2.93
		2.94
		2.95
		2.96
		2.97
		2.98
		2.99
		2.100
		2.101 - 2.110
		2.101
		2.102
		2.103
		2.104
		2.105
		2.106
		2.107
		2.108
		2.109
		2.110
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_036.pdf
36. We denote the required time as t, assuming the light turns green when the clock reads zero. By this
time, the distances traveled by the two vehicles must be the same.
(a) Denoting the acceleration of the automobile as a and the (constant) speed of the truck as v then
∆x =
(
1
2
at2
)
car
= (vt)truck
which leads to
t =
2v
a
=
2(9.5)
2.2
= 8.6 s .
Therefore,
∆x = vt = (9.5)(8.6) = 82 m .
(b) The speed of the car at that moment is
vcar = at = (2.2)(8.6) = 19 m/s .
		Main Menu
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		2.41
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		2.49
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		2.51 - 2.60
		2.51
		2.52
		2.53
		2.54
		2.55
		2.56
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		2.59
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		2.61 - 2.70
		2.61
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		2.63
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		2.69
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		2.71 - 2.80
		2.71
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		2.73
		2.74
		2.75
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		2.81 - 2.90
		2.81
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		2.83
		2.84
		2.85
		2.86
		2.87
		2.88
		2.89
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		2.91 - 2.100
		2.91
		2.92
		2.93
		2.94
		2.95
		2.96
		2.97
		2.98
		2.99
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		2.101 - 2.110
		2.101
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		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter
6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_037.pdf
37. We denote tr as the reaction time and tb as the braking time. The motion during tr is of the constant-
velocity (call it v0) type. Then the position of the car is given by
x = v0tr + v0tb +
1
2
at2b
where v0 is the initial velocity and a is the acceleration (which we expect to be negative-valued since we
are taking the velocity in the positive direction and we know the car is decelerating). After the brakes
are applied the velocity of the car is given by v = v0+atb. Using this equation, with v = 0, we eliminate
tb from the first equation and obtain
x = v0tr − v
2
0
a
+
1
2
v20
a
= v0tr − 12
v20
a
.
We write this equation for each of the initial velocities:
x1 = v01tr − 12
v201
a
and
x2 = v02tr − 12
v202
a
.
Solving these equations simultaneously for tr and a we get
tr =
v202x1 − v201x2
v01v02(v02 − v01)
and
a = −1
2
v02v
2
01 − v01v202
v02x1 − v01x2 .
Substituting x1 = 56.7m, v01 = 80.5 km/h = 22.4m/s, x2 = 24.4 m and v02 = 48.3 km/h = 13.4 m/s,
we find
tr =
13.42(56.7)− 22.42(24.4)
(22.4)(13.4)(13.4− 22.4) = 0.74 s
and
a = −1
2
(13.4)22.42 − (22.4)13.42
(13.4)(56.7)− (22.4)(24.4) = −6.2 m/s
2
.
The magnitude of the deceleration is therefore 6.2 m/s2. Although rounded off values are displayed
in the above substitutions, what we have input into our calculators are the “exact” values (such as
v02 = 16112 m/s).
		Main Menu
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		2.51 - 2.60
		2.51
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		2.53
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		2.59
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		2.61 - 2.70
		2.61
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		2.63
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		2.71 - 2.80
		2.71
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		2.81 - 2.90
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		2.83
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		2.89
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		2.91 - 2.100
		2.91
		2.92
		2.93
		2.94
		2.95
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		2.99
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		2.101 - 2.110
		2.101
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		2.105
		2.106
		2.107
		2.108
		2.109
		2.110
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_038.pdf
38. In this solution we elect to wait until the last step to convert to SI units. Constant acceleration is
indicated, so use of Table 2-1 is permitted. We start with Eq. 2-17 and denote the train’s initial velocity
as vt and the locomotive’s velocity as v� (which is also the final velocity of the train, if the rear-end
collision is barely avoided). We note that the distance ∆x consists of the original gap between them D
as well as the forward distance traveled during this time by the locomotive v�t. Therefore,
vt + v�
2
=
∆x
t
=
D + v�t
t
=
D
t
+ v� .
We now use Eq. 2-11 to eliminate time from the equation. Thus,
vt + v�
2
=
D
(v� − vt) /a + v�
leads to
a =
(
vt + v�
2
− v�
)(
v� − vt
D
)
= − 1
2D
(v� − vt)2 .
Hence,
a = − 1
2(0.676 km)
(
29
km
h
− 161 km
h
)2
= −12888 km/h2
which we convert as follows:
a =
(
−12888 km/h2
)(1000m
1 km
)(
1 h
3600 s
)2
= −0.994 m/s2
so that its magnitude is 0.994 m/s2. A graph is shown below for the case where a collision is just avoided
(x along the vertical axis is in meters and t along the horizontal axis is in seconds). The top (straight)
line shows the motion of the locomotive and the bottom curve shows the motion of the passenger train.
The other case
(where the colli-
sion is not quite
avoided) would
be similar except
that the slope of
the bottom curve
would be greater
than that of the
top line at the
point where they
meet.
0
200
400
600
800
x
10 20 30
t
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		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
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		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_039.pdf
39. We assume the periods of acceleration (duration t1) and deceleration (duration t2) are periods of constant
a so that Table 2-1 can be used. Taking the direction of motion to be +x then a1 = +1.22 m/s2 and
a2 = −1.22 m/s2. We use SI units so the velocity at t = t1 is v = 305/60 = 5.08 m/s.
(a) We denote ∆x as the distance moved during t1, and use Eq. 2-16:
v2 = v20 + 2a1∆x =⇒ ∆x =
5.082
2(1.22)
which yields ∆x = 10.59 ≈ 10.6 m.
(b) Using Eq. 2-11, we have
t1 =
v − v0
a1
=
5.08
1.22
= 4.17 s .
The deceleration time t2 turns out to be the same so that t1 + t2 = 8.33 s. The distances traveled
during t1 and t2 are the same so that they total to 2(10.59) = 21.18 m. This implies that for a
distance of 190 − 21.18 = 168.82 m, the elevator is traveling at constant velocity. This time of
constant velocity motion is
t3 =
168.82m
5.08m/s
= 33.21 s .
Therefore, the total time is 8.33 + 33.21 ≈ 41.5 s.
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		2.51
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		Chapter 3 Vectors
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		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_040.pdf
40. Neglect of air resistance justifies setting a = −g = −9.8 m/s2 (where down is our −y direction) for the
duration of the fall. This is constant acceleration motion, and we may use Table 2-1 (with ∆y replacing
∆x).
(a) Using Eq. 2-16 and taking the negative root (since the final velocity is downward), we have
v = −
√
v20 − 2g∆y = −
√
0− 2(9.8)(−1700) = −183
in SI units. Its magnitude is therefore 183 m/s.
(b) No, but it is hard to make a convincing case without more analysis. We estimate the mass of a
raindrop to be about a gram or less, so that its mass and speed (from part (a)) would be less than
that of a typical bullet, which is good news. But the fact that one is dealing with many raindrops
leads us to suspect that
this scenario poses an unhealthy situation. If we factor in air resistance,
the final speed is smaller, of course, and we return to the relatively healthy situation with which
we are familiar.
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		Chapter 10 Collisions
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		Chapter 13 Equilibrium and Elasticity
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		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
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		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
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		Chapter 35 Images
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		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_041.pdf
41. We neglect air resistance, which justifies setting a = −g = −9.8 m/s2 (taking down as the −y direction)
for the duration of the fall. This is constant acceleration motion, which justifies the use of Table 2-1
(with ∆y replacing ∆x).
(a) Starting the clock at the moment the wrench is dropped (vo = 0), then v2 = v2o − 2g∆y leads to
∆y = − (−24)
2
2(9.8)
= −29.4 m
so that it fell through a height of 29.4 m.
(b) Solving v = v0 − gt for time, we find:
t =
v0 − v
g
=
0− (−24)
9.8
= 2.45 s .
(c) SI units are used in the graphs, and the initial position is taken as the coordinate origin. In
the interest of saving space, we do not show the acceleration graph, which is a horizontal line at
−9.8m/s2.
......................................................................................................................................................................................................................................................................................................................................
1 2 3
t
0
−10
−20
−30
y
.......................................................................................................................................................................................................................................................................................
1 2 3
t
0
−10
−20
−30
v
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		Chapter 3 Vectors
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		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_042.pdf
42. We neglect air resistance, which justifies setting a = −g = −9.8 m/s2 (taking down as the −y direction)
for the duration of the fall. This is constant acceleration motion, which justifies the use of Table 2-1
(with ∆y replacing ∆x).
(a) Noting that ∆y = y − y0 = −30 m, we apply Eq. 2-15 and the quadratic formula (Appendix E) to
compute t:
∆y = v0t− 12gt
2 =⇒ t = v0 ±
√
v20 − 2g∆y
g
which (with v0 = −12 m/s since it is downward) leads, upon choosing the positive root (so that
t > 0), to the result:
t =
−12 +√(−12)2 − 2(9.8)(−30)
9.8
= 1.54 s .
(b) Enough information is now known that any of the equations in Table 2-1 can be used to obtain v;
however, the one equation that does not use our result from part (a) is Eq. 2-16:
v =
√
v20 − 2g∆y = 27.1 m/s
where the positive root has been chosen in order to give speed (which is the magnitude of the
velocity vector).
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		2.4
		2.5
		2.6
		2.7
		2.8
		2.9
		2.10
		2.11 - 2.20
		2.11
		2.12
		2.13
		2.14
		2.15
		2.16
		2.17
		2.18
		2.19
		2.20
		2.21 - 2.30
		2.21
		2.22
		2.23
		2.24
		2.25
		2.26
		2.27
		2.28
		2.29
		2.30
		2.31 - 2.40
		2.31
		2.32
		2.33
		2.34
		2.35
		2.36
		2.37
		2.38
		2.39
		2.40
		2.41 - 2.50
		2.41
		2.42
		2.43
		2.44
		2.45
		2.46
		2.47
		2.48
		2.49
		2.50
		2.51 - 2.60
		2.51
		2.52
		2.53
		2.54
		2.55
		2.56
		2.57
		2.58
		2.59
		2.60
		2.61 - 2.70
		2.61
		2.62
		2.63
		2.64
		2.65
		2.66
		2.67
		2.68
		2.69
		2.70
		2.71 - 2.80
		2.71
		2.72
		2.73
		2.74
		2.75
		2.76
		2.77
		2.78
		2.79
		2.80
		2.81 - 2.90
		2.81
		2.82
		2.83
		2.84
		2.85
		2.86
		2.87
		2.88
		2.89
		2.90
		2.91 - 2.100
		2.91
		2.92
		2.93
		2.94
		2.95
		2.96
		2.97
		2.98
		2.99
		2.100
		2.101 - 2.110
		2.101
		2.102
		2.103
		2.104
		2.105
		2.106
		2.107
		2.108
		2.109
		2.110
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_043.pdf
43. We neglect air resistance for the duration of the motion (between “launching” and “landing”), so a =
−g = −9.8 m/s2 (we take downward to be the −y direction). We use the equations in Table 2-1 (with
∆y replacing ∆x) because this is a =constant motion.
(a) At the highest point the velocity of the ball vanishes. Taking y0 = 0, we set v = 0 in v2 = v20 −2gy,
and solve for the initial velocity: v0 =
√
2gy. Since y = 50m we find v0 = 31 m/s.
(b) It will be in the air from the time it leaves the ground until the time it returns to the ground
(y = 0). Applying Eq. 2-15 to the entire motion (the rise and the fall, of total time t > 0) we have
y = v0t− 12gt
2 =⇒ t = 2v0
g
which (using our result from part (a)) produces t = 6.4 s. It is possible to obtain this without
using part (a)’s result; one can find the time just for the rise (from ground to highest point) from
Eq. 2-16 and then double it.
(c) SI units are understood in the x and v graphs shown. In the interest of saving space, we do not
show the graph of a, which is a horizontal line at −9.8m/s2.
.....
.....
.....
......
......
......
......
......
......
.......
.......
.......
.......
.......
........
........
.........
.........
..........
...........
............
.............
...............
....................
..................................
.................................................................................................................................................................................................................................................................................
2 4 6 8 t
0
20
40
60 y ............................................................................................................................................................................................................................................................................................................................................................................
2 4 6 8
t
0
−20
20
40
v
		Main Menu
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		2.1 - 2.10
		2.1
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		2.21 - 2.30
		2.21
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		2.31 - 2.40
		2.31
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		2.37
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		2.39
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		2.41 - 2.50
		2.41
		2.42
		2.43
		2.44
		2.45
		2.46
		2.47
		2.48
		2.49
		2.50
		2.51 - 2.60
		2.51
		2.52
		2.53
		2.54
		2.55
		2.56
		2.57
		2.58
		2.59
		2.60
		2.61 - 2.70
		2.61
		2.62
		2.63
		2.64
		2.65
		2.66
		2.67
		2.68
		2.69
		2.70
		2.71 - 2.80
		2.71
		2.72
		2.73
		2.74
		2.75
		2.76
		2.77
		2.78
		2.79
		2.80
		2.81 - 2.90
		2.81
		2.82
		2.83
		2.84
		2.85
		2.86
		2.87
		2.88
		2.89
		2.90
		2.91 - 2.100
		2.91
		2.92
		2.93
		2.94
		2.95
		2.96
		2.97
		2.98
		2.99
		2.100
		2.101 - 2.110
		2.101
		2.102
		2.103
		2.104
		2.105
		2.106
		2.107
		2.108
		2.109
		2.110
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling,
Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_044.pdf
44. There is no air resistance, which makes it quite accurate to set a = −g = −9.8 m/s2 (where downward
is the −y direction) for the duration of the fall. We are allowed to use Table 2-1 (with ∆y replacing
∆x) because this is constant acceleration motion; in fact, when the acceleration changes (during the
process of catching the ball) we will again assume constant acceleration conditions; in this case, we have
a2 = +25g = 245 m/s2.
(a) The time of fall is given by Eq. 2-15 with v0 = 0 and y = 0. Thus,
t =
√
2y0
g
=
√
2(145)
9.8
= 5.44 s .
(b) The final velocity for its free-fall (which becomes the initial velocity during the catching process)
is found from Eq. 2-16 (other equations can be used but they would use the result from part (a)).
v = −
√
v20 − 2g (y − y0) = −
√
2gy0 = −53.3 m/s
where the negative root is chosen since this is a downward velocity.
(c) For the catching process, the answer to part (b) plays the role of an initial velocity (v0 = −53.3 m/s)
and the final velocity must become zero. Using Eq. 2-16, we find
∆y2 =
v2 − v20
2a2
=
−(−53.3)2
2(245)
= −5.80 m
where the negative value of ∆y2 signifies that the distance traveled while arresting its motion is
downward.
		Main Menu
		Chapter 1 Measurement
		Chapter 2 Motion Along a Straight Line
		2.1 - 2.10
		2.1
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		2.6
		2.7
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		2.11 - 2.20
		2.11
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		2.17
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		2.21 - 2.30
		2.21
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		2.23
		2.24
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		2.27
		2.28
		2.29
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		2.31 - 2.40
		2.31
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		2.33
		2.34
		2.35
		2.36
		2.37
		2.38
		2.39
		2.40
		2.41 - 2.50
		2.41
		2.42
		2.43
		2.44
		2.45
		2.46
		2.47
		2.48
		2.49
		2.50
		2.51 - 2.60
		2.51
		2.52
		2.53
		2.54
		2.55
		2.56
		2.57
		2.58
		2.59
		2.60
		2.61 - 2.70
		2.61
		2.62
		2.63
		2.64
		2.65
		2.66
		2.67
		2.68
		2.69
		2.70
		2.71 - 2.80
		2.71
		2.72
		2.73
		2.74
		2.75
		2.76
		2.77
		2.78
		2.79
		2.80
		2.81 - 2.90
		2.81
		2.82
		2.83
		2.84
		2.85
		2.86
		2.87
		2.88
		2.89
		2.90
		2.91 - 2.100
		2.91
		2.92
		2.93
		2.94
		2.95
		2.96
		2.97
		2.98
		2.99
		2.100
		2.101 - 2.110
		2.101
		2.102
		2.103
		2.104
		2.105
		2.106
		2.107
		2.108
		2.109
		2.110
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_045.pdf
45. Taking the +y direction downward and y0 = 0, we have y = v0t + 12gt
2 which (with v0 = 0) yields
t =
√
2y/g.
(a) For this part of the motion, y = 50 m so that
t =
√
2(50)
9.8
= 3.2 s .
(b) For this next part of the motion, we note that the total displacement is y = 100 m. Therefore, the
total time is
t =
√
2(100)
9.8
= 4.5 s .
The difference between this and the answer to part (a) is the time required to fall through that
second 50 m distance: 4.5− 3.2 = 1.3 s.
		Main Menu
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		2.51 - 2.60
		2.51
		2.52
		2.53
		2.54
		2.55
		2.56
		2.57
		2.58
		2.59
		2.60
		2.61 - 2.70
		2.61
		2.62
		2.63
		2.64
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		2.71 - 2.80
		2.71
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		2.73
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		2.81 - 2.90
		2.81
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		2.83
		2.84
		2.85
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		2.88
		2.89
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		2.91 - 2.100
		2.91
		2.92
		2.93
		2.94
		2.95
		2.96
		2.97
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		2.99
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		2.101 - 2.110
		2.101
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		2.104
		2.105
		2.106
		2.107
		2.108
		2.109
		2.110
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8
Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_046.pdf
46. We neglect air resistance, which justifies setting a = −g = −9.8 m/s2 (taking down as the −y direction)
for the duration of the motion. We are allowed to use Table 2-1 (with ∆y replacing ∆x) because this is
constant acceleration motion. The ground level is taken to correspond to y = 0.
(a) With y0 = h and v0 replaced with −v0, Eq. 2-16 leads to
v =
√
(−v0)2 − 2g (y − y0) =
√
v20 + 2gh .
The positive root is taken because the problem asks for the speed (the magnitude of the velocity).
(b) We use the quadratic formula to solve Eq. 2-15 for t, with v0 replaced with −v0,
∆y = −v0t− 12gt
2 =⇒ t =
−v0 +
√
(−v0)2 − 2g∆y
g
where the positive root is chosen to yield t > 0. With y = 0 and y0 = h, this becomes
t =
√
v20 + 2gh− v0
g
.
(c) If it were thrown upward with that speed from height h then (in the absence of air friction) it would
return to height h with that same downward speed and would therefore yield the same final speed
(before hitting the ground) as in part (a). An important perspective related to this is treated later
in the book (in the context of energy conservation) .
(d) Having to travel up before it starts its descent certainly requires more time than in part (b). The
calculation is quite similar, however, except for now having +v0 in the equation where we had put
in −v0 in part (b). The details follow:
∆y = v0t− 12gt
2 =⇒ t = v0 +
√
v20 − 2g∆y
g
with the positive root again chosen to yield t > 0. With y = 0 and y0 = h, we obtain
t =
√
v20 + 2gh+ v0
g
.
		Main Menu
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		2.51 - 2.60
		2.51
		2.52
		2.53
		2.54
		2.55
		2.56
		2.57
		2.58
		2.59
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		2.61 - 2.70
		2.61
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		2.63
		2.64
		2.65
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		2.69
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		2.71 - 2.80
		2.71
		2.72
		2.73
		2.74
		2.75
		2.76
		2.77
		2.78
		2.79
		2.80
		2.81 - 2.90
		2.81
		2.82
		2.83
		2.84
		2.85
		2.86
		2.87
		2.88
		2.89
		2.90
		2.91 - 2.100
		2.91
		2.92
		2.93
		2.94
		2.95
		2.96
		2.97
		2.98
		2.99
		2.100
		2.101 - 2.110
		2.101
		2.102
		2.103
		2.104
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		2.106
		2.107
		2.108
		2.109
		2.110
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_047.pdf
47. We neglect air resistance, which justifies setting a = −g = −9.8 m/s2 (taking down as the −y direction)
for the duration of the motion. We are allowed to use Table 2-1 (with ∆y replacing ∆x) because this is
constant acceleration motion. The ground level is taken to correspond to the origin of the y axis.
(a) Using y = v0t− 12gt2, with y = 0.544 m and t = 0.200 s, we find
v0 =
y + 12gt
2
t
=
0.544 + 12 (9.8)(0.200)
2
0.200
= 3.70 m/s .
(b) The velocity at y = 0.544 m is
v = v0 − gt = 3.70− (9.8)(0.200) = 1.74 m/s .
(c) Using v2 = v20 − 2gy (with different values for y and v than before), we solve for the value of y
corresponding to maximum height (where v = 0).
y =
v20
2g
=
3.72
2(9.8)
= 0.698 m .
Thus, the armadillo goes 0.698− 0.544 = 0.154 m higher.
		Main Menu
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		2.1
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		2.6
		2.7
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		2.11 - 2.20
		2.11
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		2.13
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		2.17
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		2.19
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		2.21 - 2.30
		2.21
		2.22
		2.23
		2.24
		2.25
		2.26
		2.27
		2.28
		2.29
		2.30
		2.31 - 2.40
		2.31
		2.32
		2.33
		2.34
		2.35
		2.36
		2.37
		2.38
		2.39
		2.40
		2.41 - 2.50
		2.41
		2.42
		2.43
		2.44
		2.45
		2.46
		2.47
		2.48
		2.49
		2.50
		2.51 - 2.60
		2.51
		2.52
		2.53
		2.54
		2.55
		2.56
		2.57
		2.58
		2.59
		2.60
		2.61 - 2.70
		2.61
2.62
		2.63
		2.64
		2.65
		2.66
		2.67
		2.68
		2.69
		2.70
		2.71 - 2.80
		2.71
		2.72
		2.73
		2.74
		2.75
		2.76
		2.77
		2.78
		2.79
		2.80
		2.81 - 2.90
		2.81
		2.82
		2.83
		2.84
		2.85
		2.86
		2.87
		2.88
		2.89
		2.90
		2.91 - 2.100
		2.91
		2.92
		2.93
		2.94
		2.95
		2.96
		2.97
		2.98
		2.99
		2.100
		2.101 - 2.110
		2.101
		2.102
		2.103
		2.104
		2.105
		2.106
		2.107
		2.108
		2.109
		2.110
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_048.pdf
48. We neglect air resistance, which justifies setting a = −g = −9.8 m/s2 (taking down as the −y direction)
for the duration of the motion. We are allowed to use Table 2-1 (with ∆y replacing ∆x) because this is
constant acceleration motion. The ground level is taken to correspond to the origin of the y axis. The
total time of fall can be computed from Eq. 2-15 (using the quadratic formula).
∆y = v0t− 12gt
2 =⇒ t = v0 +
√
v20 − 2g∆y
g
with the positive root chosen. With y = 0, v0 = 0 and y0 = h = 60 m, we obtain
t =
√
2gh
g
=
√
2h
g
= 3.5 s .
Thus, “1.2 s earlier” means we are examining where the rock is at t = 2.3 s:
y − h = v0(2.3)− 12g(2.3)
2 =⇒ y = 34 m
where we again use the fact that h = 60 m and v0 = 0.
		Main Menu
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		Chapter 2 Motion Along a Straight Line
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		2.6
		2.7
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		2.21
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		2.31
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		2.39
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		2.41 - 2.50
		2.41
		2.42
		2.43
		2.44
		2.45
		2.46
		2.47
		2.48
		2.49
		2.50
		2.51 - 2.60
		2.51
		2.52
		2.53
		2.54
		2.55
		2.56
		2.57
		2.58
		2.59
		2.60
		2.61 - 2.70
		2.61
		2.62
		2.63
		2.64
		2.65
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		2.67
		2.68
		2.69
		2.70
		2.71 - 2.80
		2.71
		2.72
		2.73
		2.74
		2.75
		2.76
		2.77
		2.78
		2.79
		2.80
		2.81 - 2.90
		2.81
		2.82
		2.83
		2.84
		2.85
		2.86
		2.87
		2.88
		2.89
		2.90
		2.91 - 2.100
		2.91
		2.92
		2.93
		2.94
		2.95
		2.96
		2.97
		2.98
		2.99
		2.100
		2.101 - 2.110
		2.101
		2.102
		2.103
		2.104
		2.105
		2.106
		2.107
		2.108
		2.109
		2.110
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_049.pdf
49. The speed of the boat is constant, given by vb = d/t. Here, d is the distance of the boat from the bridge
when the key is dropped (12m) and t is the time the key takes in falling. To calculate t, we put the
origin of the coordinate system at the point where the key is dropped and take the y axis to be positive
in the downward direction. Taking the time to be zero at the instant the key is dropped, we compute
the time t when y = 45m. Since the initial velocity of the key is zero, the coordinate of the key is given
by y = 12gt
2. Thus
t =
√
2y
g
=
√
2(45m)
9.8m/s2
= 3.03 s .
Therefore, the speed of the boat is
vb =
12m
3.03 s
= 4.0 m/s .
		Main Menu
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		2.21
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		2.41
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		2.49
		2.50
		2.51 - 2.60
		2.51
		2.52
		2.53
		2.54
		2.55
		2.56
		2.57
		2.58
		2.59
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		2.61 - 2.70
		2.61
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		2.63
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		2.71 - 2.80
		2.71
		2.72
		2.73
		2.74
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		2.77
2.78
		2.79
		2.80
		2.81 - 2.90
		2.81
		2.82
		2.83
		2.84
		2.85
		2.86
		2.87
		2.88
		2.89
		2.90
		2.91 - 2.100
		2.91
		2.92
		2.93
		2.94
		2.95
		2.96
		2.97
		2.98
		2.99
		2.100
		2.101 - 2.110
		2.101
		2.102
		2.103
		2.104
		2.105
		2.106
		2.107
		2.108
		2.109
		2.110
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_050.pdf
50. With +y upward, we have y0 = 36.6 m and y = 12.2 m. Therefore, using Eq. 2-18 (the last equation in
Table 2-1), we find
y − y0 = vt+ 12gt
2 =⇒ v = −22 m/s
at t = 2.00 s. The term speed refers to the magnitude of the velocity vector, so the answer is |v| =
22.0 m/s.
		Main Menu
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		2.41
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		2.51 - 2.60
		2.51
		2.52
		2.53
		2.54
		2.55
		2.56
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		2.58
		2.59
		2.60
		2.61 - 2.70
		2.61
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		2.63
		2.64
		2.65
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		2.71 - 2.80
		2.71
		2.72
		2.73
		2.74
		2.75
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		2.81 - 2.90
		2.81
		2.82
		2.83
		2.84
		2.85
		2.86
		2.87
		2.88
		2.89
		2.90
		2.91 - 2.100
		2.91
		2.92
		2.93
		2.94
		2.95
		2.96
		2.97
		2.98
		2.99
		2.100
		2.101 - 2.110
		2.101
		2.102
		2.103
		2.104
		2.105
		2.106
		2.107
		2.108
		2.109
		2.110
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_051.pdf
51. We first find the velocity of the ball just before it hits the ground. During contact with the ground its
average acceleration is given by
aavg =
∆v
∆t
where ∆v is the change in its velocity during contact with the ground and ∆t = 20.0 × 10−3 s is the
duration of contact. Now, to find the velocity just before contact, we put the origin at the point where
the ball is dropped (and take +y upward) and take t = 0 to be when it is dropped. The ball strikes the
ground at y = −15.0 m. Its velocity there is found from Eq. 2-16: v2 = −2gy. Therefore,
v = −
√
−2gy = −
√
−2(9.8)(−15.0) = −17.1 m/s
where the negative sign is chosen since the ball is traveling downward at the moment of contact. Con-
sequently, the average acceleration during contact with the ground is
aavg =
0− (−17.1)
20.0× 10−3 = 857 m/s
2
.
The fact that the result is positive indicates that this acceleration vector points upward. In a later
chapter, this will be directly related to the magnitude and direction of the force exerted by the ground
on the ball during the collision.
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		2.71 - 2.80
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		2.81 - 2.90
		2.81
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		2.83
		2.84
		2.85
		2.86
		2.87
		2.88
		2.89
		2.90
		2.91 - 2.100
		2.91
		2.92
		2.93
		2.94
		2.95
		2.96
		2.97
		2.98
		2.99
		2.100
2.101 - 2.110
		2.101
		2.102
		2.103
		2.104
		2.105
		2.106
		2.107
		2.108
		2.109
		2.110
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_052.pdf
52. The y axis is arranged so that ground level is y = 0 and +y is upward.
(a) At the point where its fuel gets exhausted, the rocket has reached a height of
y′ =
1
2
at2 =
(4.00)(6.00)2
2
= 72.0 m .
From Eq. 2-11, the speed of the rocket (which had started at rest) at this instant is
v′ = at = (4.00)(6.00) = 24.0 m/s .
The additional height ∆y1 the rocket can attain (beyond y′) is given by Eq. 2-16 with vanishing
final speed: 0 = v′ 2 − 2g∆y1. This gives
∆y1 =
v′ 2
2g
=
(24.0)2
2(9.8)
= 29.4 m .
Recalling our value for y′, the total height the rocket attains is seen to be 72.0 + 29.4 = 101 m.
(b) The time of free-fall flight (from y′ until it returns to y = 0) after the fuel gets exhausted is found
from Eq. 2-15:
−y′ = v′t− 1
2
gt2 =⇒ −72.0 = (24.0)t− 9.80
2
t2 .
Solving for t (using the quadratic formula) we obtain t = 7.00 s. Recalling the upward acceleration
time used in part (a), we see the total time of flight is 7.00 + 6.00 = 13.0 s.
		Main Menu
		Chapter 1 Measurement
		Chapter 2 Motion Along a Straight Line
		2.1 - 2.10
		2.1
		2.2
		2.3
		2.4
		2.5
		2.6
		2.7
		2.8
		2.9
		2.10
		2.11 - 2.20
		2.11
		2.12
		2.13
		2.14
		2.15
		2.16
		2.17
		2.18
		2.19
		2.20
		2.21 - 2.30
		2.21
		2.22
		2.23
		2.24
		2.25
		2.26
		2.27
		2.28
		2.29
		2.30
		2.31 - 2.40
		2.31
		2.32
		2.33
		2.34
		2.35
		2.36
		2.37
		2.38
		2.39
		2.40
		2.41 - 2.50
		2.41
		2.42
		2.43
		2.44
		2.45
		2.46
		2.47
		2.48
		2.49
		2.50
		2.51 - 2.60
		2.51
		2.52
		2.53
		2.54
		2.55
		2.56
		2.57
		2.58
		2.59
		2.60
		2.61 - 2.70
		2.61
		2.62
		2.63
		2.64
		2.65
		2.66
		2.67
		2.68
		2.69
		2.70
		2.71 - 2.80
		2.71
		2.72
		2.73
		2.74
		2.75
		2.76
		2.77
		2.78
		2.79
		2.80
		2.81 - 2.90
		2.81
		2.82
		2.83
		2.84
		2.85
		2.86
		2.87
		2.88
		2.89
		2.90
		2.91 - 2.100
		2.91
		2.92
		2.93
		2.94
		2.95
		2.96
		2.97
		2.98
		2.99
		2.100
		2.101 - 2.110
		2.101
		2.102
		2.103
		2.104
		2.105
		2.106
		2.107
		2.108
		2.109
		2.110
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_053.pdf
53. The average acceleration during contact with the floor is given by aavg = (v2 − v1)/∆t, where v1 is its
velocity just before striking the floor, v2 is its velocity just as it leaves the floor, and ∆t is the duration
of contact with the floor (12× 10−3 s). Taking the y axis to be positively upward and placing the origin
at the point where the ball is dropped, we first find the velocity just before striking the floor, using
v21 = v
2
0 − 2gy. With v0 = 0 and y = −4.00 m, the result is
v1 = −
√
−2gy = −
√
−2(9.8)(−4.00) = −8.85 m/s
where the negative root is chosen because the ball is traveling downward. To find the velocity just after
hitting the floor (as it ascends without air friction to a height of 2.00 m), we use v2 = v22−2g(y−y0) with
v = 0, y = −2.00 m (it ends up two meters below its initial drop height), and y0 = −4.00 m. Therefore,
v2 =
√
2g(y − y0) =
√
2(9.8)(−2.00 + 4.00) = 6.26 m/s .
Consequently, the average acceleration is
aavg =
v2 − v1
∆t
=
6.26 + 8.85
12.0× 10−3 = 1.26× 10
3 m/s2 .
The positive nature of the result indicates that the acceleration vector points upward. In a later chapter,
this will be directly related to the magnitude and direction of the force exerted by the ground on the
ball during the collision.
		Main Menu
		Chapter 1 Measurement
		Chapter 2 Motion Along a Straight Line
		2.1 - 2.10
		2.1
		2.2
		2.3
		2.4
		2.5
		2.6
		2.7
		2.8
		2.9
		2.10
		2.11 - 2.20
		2.11
		2.12
		2.13
		2.14
		2.15
		2.16
		2.17
		2.18
		2.19
		2.20
		2.21 - 2.30
		2.21
		2.22
		2.23
		2.24
		2.25
		2.26
		2.27
		2.28
		2.29
		2.30
		2.31 - 2.40
		2.31
		2.32
		2.33
		2.34
		2.35
		2.36
		2.37
		2.38
		2.39
		2.40
		2.41 - 2.50
		2.41
2.42
		2.43
		2.44
		2.45
		2.46
		2.47
		2.48
		2.49
		2.50
		2.51 - 2.60
		2.51
		2.52
		2.53
		2.54
		2.55
		2.56
		2.57
		2.58
		2.59
		2.60
		2.61 - 2.70
		2.61
		2.62
		2.63
		2.64
		2.65
		2.66
		2.67
		2.68
		2.69
		2.70
		2.71 - 2.80
		2.71
		2.72
		2.73
		2.74
		2.75
		2.76
		2.77
		2.78
		2.79
		2.80
		2.81 - 2.90
		2.81
		2.82
		2.83
		2.84
		2.85
		2.86
		2.87
		2.88
		2.89
		2.90
		2.91 - 2.100
		2.91
		2.92
		2.93
		2.94
		2.95
		2.96
		2.97
		2.98
		2.99
		2.100
		2.101 - 2.110
		2.101
		2.102
		2.103
		2.104
		2.105
		2.106
		2.107
		2.108
		2.109
		2.110
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_054.pdf
54. The height reached by the player is y = 0.76 m (where we have taken the origin of the y axis at the floor
and +y to be upward).
(a) The initial velocity v0 of the player is
v0 =
√
2gy =
√
2(9.8)(0.76) = 3.86 m/s .
This is a consequence of Eq. 2-16 where velocity v vanishes. As the player reaches y1 = 0.76−0.15 =
0.61 m, his speed v1 satisfies v20 − v21 = 2gy1, which yields
v1 =
√
v20 − 2gy1 =
√
(3.86)2 − 2(9.80)(0.61) = 1.71 m/s .
The time t1 that the player spends ascending in the top ∆y1 = 0.15 m of the jump can now be
found from Eq. 2-17:
∆y1 =
1
2
(v1 + v) t1 =⇒ t1 = 2(0.15)1.71 + 0 = 0.175 s
which means that the total time spend in that top 15 cm (both ascending and descending) is
2(0.17) = 0.35 s = 350 ms.
(b) The time t2 when the player reaches a height of 0.15 m is found from Eq. 2-15:
0.15 = v0t2 − 12gt
2
2 = (3.86)t2 −
9.8
2
t22 ,
which yields (using the quadratic formula, taking the smaller of the two positive roots) t2 = 0.041 s
= 41 ms, which implies that the total time spend in that bottom 15 cm (both ascending and
descending) is 2(41) = 82 ms.
		Main Menu
		Chapter 1 Measurement
		Chapter 2 Motion Along a Straight Line
		2.1 - 2.10
		2.1
		2.2
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		2.4
		2.5
		2.6
		2.7
		2.8
		2.9
		2.10
		2.11 - 2.20
		2.11
		2.12
		2.13
		2.14
		2.15
		2.16
		2.17
		2.18
		2.19
		2.20
		2.21 - 2.30
		2.21
		2.22
		2.23
		2.24
		2.25
		2.26
		2.27
		2.28
		2.29
		2.30
		2.31 - 2.40
		2.31
		2.32
		2.33
		2.34
		2.35
		2.36
		2.37
		2.38
		2.39
		2.40
		2.41 - 2.50
		2.41
		2.42
		2.43
		2.44
		2.45
		2.46
		2.47
		2.48
		2.49
		2.50
		2.51 - 2.60
		2.51
		2.52
		2.53
		2.54
		2.55
		2.56
		2.57
		2.58
		2.59
		2.60
		2.61 - 2.70
		2.61
		2.62
		2.63
		2.64
		2.65
		2.66
		2.67
		2.68
		2.69
		2.70
		2.71 - 2.80
		2.71
		2.72
		2.73
		2.74
		2.75
		2.76
		2.77
		2.78
		2.79
		2.80
		2.81 - 2.90
		2.81
		2.82
		2.83
		2.84
		2.85
		2.86
		2.87
		2.88
		2.89
		2.90
		2.91 - 2.100
		2.91
		2.92
		2.93
		2.94
		2.95
		2.96
		2.97
		2.98
		2.99
		2.100
		2.101 - 2.110
		2.101
		2.102
		2.103
		2.104
		2.105
		2.106
		2.107
		2.108
		2.109
		2.110
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_055.pdf
55. We neglect air resistance, which justifies setting a = −g = −9.8 m/s2 (taking down as the −y direction)
for the duration of the motion. We are allowed to use Table 2-1 (with ∆y replacing ∆x) because this is
constant acceleration motion. The ground level is taken to correspond to the origin of the y axis. The
time drop 1 leaves the nozzle is taken as t = 0 and its time of landing on the floor t1 can be computed
from Eq. 2-15, with v0 = 0 and y1 = −2.00 m.
y1 = −12gt
2
1 =⇒ t1 =
√−2y
g
=
√
−2(−2.00)
9.8
= 0.639 s .
At that moment,the fourth drop begins to fall, and from the regularity of the dripping we conclude that
drop 2 leaves the nozzle at t = 0.639/3 = 0.213 s and drop 3 leaves the nozzle at t = 2(0.213) = 0.426 s.
Therefore, the time in free fall (up to the moment drop 1 lands) for drop 2 is t2 = t1 − 0.213 = 0.426 s
and the time in free fall (up to the moment drop 1 lands) for drop 3 is t3 = t1 − 0.426 = 0.213 s. Their
positions at that moment are
y2 = −12gt
2
2 = −
1
2
(9.8)(0.426)2 = −0.889 m
y3 = −12gt
2
3 = −
1
2
(9.8)(0.213)2 = −0.222 m ,
respectively. Thus, drop 2 is 89 cm below the nozzle and drop 3 is 22 cm below the nozzle when drop 1
strikes the floor.
		Main Menu
		Chapter 1 Measurement
		Chapter 2 Motion Along a Straight Line
		2.1 - 2.10
		2.1
		2.2
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		2.4
		2.5
		2.6
		2.7
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		2.11 - 2.20
		2.11
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		2.17
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		2.21 - 2.30
		2.21
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		2.23
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		2.31 - 2.40
		2.31
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		2.33
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		2.37
		2.38
		2.39
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		2.41 - 2.50
		2.41
		2.42
		2.43
		2.44
		2.45
		2.46
		2.47
		2.48
		2.49
		2.50
		2.51 - 2.60
		2.51
		2.52
		2.53
		2.54
		2.55
		2.56
		2.57
		2.58
		2.59
		2.60
		2.61 - 2.70
		2.61
		2.62
		2.63
		2.64
		2.65
		2.66
		2.67
		2.68
		2.69
		2.70
		2.71 - 2.80
		2.71
		2.72
		2.73
		2.74
		2.75
		2.76
		2.77
		2.78
		2.79
		2.80
		2.81 - 2.90
		2.81
		2.82
		2.83
		2.84
		2.85
		2.86
		2.87
		2.88
		2.89
		2.90
		2.91 - 2.100
		2.91
		2.92
		2.93
		2.94
		2.95
		2.96
		2.97
		2.98
		2.99
		2.100
		2.101 - 2.110
		2.101
		2.102
		2.103
		2.104
		2.105
		2.106
		2.107
		2.108
		2.109
		2.110
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_056.pdf
56. The graph shows y = 25 m to be the highest point (where the speed momentarily vanishes). The neglect
of “air friction” (or whatever passes for that on the distant planet) is certainly reasonable due to the
symmetry of the graph.
(a) To find the acceleration due to gravity gp on that planet, we use Eq. 2-15 (with +y up)
y − y0 = vt+ 12gpt
2 =⇒ 25− 0 = (0)(2.5) + 1
2
gp(2.5)2
so that gp = 8.0 m/s2.
(b) That same (max) point on the graph can be used to find the initial velocity.
y − y0 = 12 (v0 + v) t =⇒ 25− 0 =
1
2
(v0 + 0) (2.5)
Therefore, v0 = 20 m/s.
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		2.51 - 2.60
		2.51
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		2.53
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		2.55
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		2.91
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		2.93
		2.94
		2.95
		2.96
		2.97
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		2.101
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		2.104
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		2.106
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		2.109
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		Chapter 3 Vectors
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		Chapter 11 Rotation
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		Chapter 13 Equilibrium and Elasticity
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		Chapter 17 Waves—I
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		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_057.pdf
57. Taking +y to be upward and placing the origin at the point from which the objects are dropped, then the
location of diamond 1 is given by y1 = −12gt2 and the location of diamond 2 is given by y2 = −12g(t−1)2.
We are starting the clock when the first object is dropped. We want the time for which y2 − y1 = 10 m.
Therefore,
−1
2
g(t− 1)2 + 1
2
gt2 = 10 =⇒ t = (10/g) + 0.5 = 1.5 s .
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		2.51
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		2.53
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		2.55
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		2.91
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		Chapter 3 Vectors
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		Chapter 5 Force and Motion I
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		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_058.pdf
58. We neglect air resistance, which justifies setting a = −g = −9.8 m/s2 (taking down as the −y direction)
for the duration of the motion. We are allowed to use Table 2-1 (with ∆y replacing ∆x) because this is
constant acceleration motion. When something is thrown straight up and is caught at the level it was
thrown from (with a trajectory similar to that shown in Fig. 2-25), the time of flight t is half of its time
of ascent ta, which is given by Eq. 2-18 with ∆y = H and v = 0 (indicating the maximum point).
H = vta +
1
2
gt2a =⇒ ta =
√
2H
g
Writing these in terms of the total time in the air t = 2ta we have
H =
1
8
gt2 =⇒ t = 2
√
2H
g
.
We consider two throws, one to height H1 for total time t1 and another to height H2 for total time t2,
and we set up a ratio:
H2
H1
=
1
8gt
2
2
1
8gt
2
1
=
(
t2
t1
)2
from which we conclude that if t2 = 2t1 (as is required by the problem) then H2 = 22H1 = 4H1.
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		2.51 - 2.60
		2.51
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		2.71
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		2.81
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		2.83
		2.84
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		2.89
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		2.91 - 2.100
		2.91
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		2.93
		2.94
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		2.101 - 2.110
		2.101
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		2.104
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		2.106
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		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_059.pdf
59. We neglect air resistance, which justifies setting a = −g = −9.8 m/s2 (taking down as the −y direction)
for the duration of the motion. We are allowed to use Table 2-1 (with ∆y replacing ∆x) because this is
constant acceleration motion. We placing the coordinate origin on the ground. We note that the initial
velocity of the package is the same as the velocity of the balloon, v0 = +12 m/s and that its initial
coordinate is y0 = +80 m.
(a) We solve y = y0+v0t− 12gt2 for time, with y = 0, using the quadratic formula (choosing the positive
root to yield a positive value for t).
t =
v0 +
√
v20 + 2gy0
g
=
12 +
√
122 + 2(9.8)(80)
9.8
= 5.4 s
(b) If we wish to avoid using the result from part (a), we could use Eq. 2-16, but if that is not a
concern, then a variety of formulas from Table 2-1 can be used. For instance, Eq. 2-11 leads to
v = v0 − gt = 12− (9.8)(5.4) = −41 m/s. Its final speed is 41 m/s.
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		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_060.pdf
60. We neglect air resistance, which justifies setting a = −g = −9.8 m/s2 (taking down as the −y direction)
for the duration of the motion. We are allowed to use Eq. 2-15 (with ∆y replacing ∆x) because this is
constant acceleration motion. We use primed variables (except t) with the first stone, which has zero
initial velocity, and unprimed variables with the second stone (with initial downward velocity −v0, so
that v0 is being used for the initial speed). SI units are used throughout.
∆y′ = 0(t)− 1
2
gt2
∆y = (−v0) (t− 1)− 12g(t− 1)
2
Since the problem
indicates ∆y′ =
∆y = −43.9 m,
we solve the
first equation
for t (finding
t = 2.99 s) and
use this result to
solve the second
equation for the
initial speed of
the second stone:
21
0
20
40
y
2t
−43.9 = (−v0) (1.99)− 12(9.8)(1.99)
2
which leads to v0 = 12.3 m/s.
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		Chapter 3 Vectors
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		Chapter 5 Force and Motion I
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		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_061.pdf
61. We neglect air resistance, which justifies setting a = −g = −9.8 m/s2 (taking down as the −y direction)
for the duration of the motion of the shot ball. We are allowed to use Table 2-1 (with ∆y replacing
∆x) because the ball has constant acceleration motion. We use primed variables (except t) with the
constant-velocity elevator (so v′ = 20 m/s), and unprimed variables with the ball (with initial velocity
v0 = v′ + 10 = 30 m/s, relative to the ground). SI units are used throughout.
(a) Taking the time to be zero at the instant the ball is shot, we compute its maximum height y (relative
to the ground) with v2 = v20 − 2g(y− yo), where the highest point is characterized by v = 0. Thus,
y = yo +
v20
2g
= 76 m
where yo = y′o + 2 = 30 m (where y
′
o = 28 m is given in the problem) and v0 = 30 m/s relative to
the ground as noted above.
(b) There are a variety of approaches to this question. One is to continue working
in the frame of
reference adopted in part (a) (which treats the ground as motionless and “fixes” the coordinate
origin to it); in this case, one describes the elevator motion with y′ = y′o + v′t and the ball motion
with Eq. 2-15, and solves them for the case where they reach the same point at the same time.
Another is to work in the frame of reference of the elevator (the boy in the elevator might be
oblivious to the fact the elevator is moving since it isn’t accelerating), which is what we show here
in detail:
∆ye = v0et−
1
2
gt2 =⇒ t = v0e +
√
v02e − 2g∆ye
g
where v0e = 20 m/s is the initial velocity of the ball relative to the elevator and ∆ye = −2.0 m is
the ball’s displacement relative to the floor of the elevator. The positive root is chosen to yield a
positive value for t ; the result is t = 4.2 s.
		Main Menu
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		2.21
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		2.31 - 2.40
		2.31
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		2.39
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		2.41 - 2.50
		2.41
		2.42
		2.43
		2.44
		2.45
		2.46
		2.47
		2.48
		2.49
		2.50
		2.51 - 2.60
		2.51
		2.52
		2.53
		2.54
		2.55
		2.56
		2.57
		2.58
		2.59
		2.60
		2.61 - 2.70
		2.61
		2.62
		2.63
		2.64
		2.65
		2.66
		2.67
		2.68
		2.69
		2.70
		2.71 - 2.80
		2.71
		2.72
		2.73
		2.74
		2.75
		2.76
		2.77
		2.78
		2.79
		2.80
		2.81 - 2.90
		2.81
		2.82
		2.83
		2.84
		2.85
		2.86
		2.87
		2.88
		2.89
		2.90
		2.91 - 2.100
		2.91
		2.92
		2.93
		2.94
		2.95
		2.96
		2.97
		2.98
		2.99
		2.100
		2.101 - 2.110
		2.101
		2.102
		2.103
		2.104
		2.105
		2.106
		2.107
		2.108
		2.109
		2.110
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_062.pdf
62. We neglect air resistance, which justifies setting a = −g = −9.8 m/s2 (taking down as the −y direction)
for the duration of the stone’s motion. We are allowed to use Table 2-1 (with ∆x replaced by y) because
the ball has constant acceleration motion (and we choose yo = 0).
(a) We apply Eq. 2-16 to both measurements, with SI units understood.
v2B = v
2
0 − 2gyB =⇒
(
1
2
v
)2
+ 2g(yA + 3) = v20
v2A = v
2
0 − 2gyA =⇒ v2 + 2gyA = v20
We equate the two expressions that each equal v20 and obtain
1
4
v2 + 2gyA + 2g(3) = v2 + 2gyA =⇒ 2g(3) = 34v
2
which yields v =
√
2g(4) = 8.85 m/s.
(b) An object moving upward at A with speed v = 8.85 m/s will reach a maximum height y − yA =
v2/2g = 4.00 m above point A (this is again a consequence of Eq. 2-16, now with the “final” velocity
set to zero to indicate the highest point). Thus, the top of its motion is 1.00 m above point B.
		Main Menu
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		2.31
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		2.41 - 2.50
		2.41
		2.42
		2.43
		2.44
		2.45
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		2.47
		2.48
		2.49
		2.50
		2.51 - 2.60
		2.51
		2.52
		2.53
		2.54
		2.55
		2.56
		2.57
		2.58
		2.59
		2.60
		2.61 - 2.70
		2.61
		2.62
		2.63
		2.64
		2.65
		2.66
		2.67
		2.68
		2.69
		2.70
		2.71 - 2.80
		2.71
		2.72
		2.73
		2.74
		2.75
		2.76
		2.77
		2.78
		2.79
		2.80
		2.81 - 2.90
		2.81
		2.82
		2.83
		2.84
		2.85
		2.86
		2.87
		2.88
		2.89
		2.90
		2.91 - 2.100
		2.91
		2.92
		2.93
		2.94
		2.95
		2.96
		2.97
		2.98
		2.99
		2.100
		2.101 - 2.110
		2.101
		2.102
		2.103
		2.104
		2.105
		2.106
		2.107
		2.108
		2.109
		2.110
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and
the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_063.pdf
63. The object, once it is dropped (v0 = 0) is in free-fall (a = −g = −9.8 m/s2 if we take down as the −y
direction), and we use Eq. 2-15 repeatedly.
(a) The (positive) distance D from the lower dot to the mark corresponding to a certain reaction time
t is given by ∆y = −D = −12gt2, or D = gt2/2. Thus for t1 = 50.0ms
D1 =
(9.8m/s2)(50.0× 10−3 s)2
2
= 0.0123m = 1.23 cm .
(b) For t2 = 100ms
D2 =
(9.8m/s2)(100× 10−3 s)2
2
= 0.049m = 4D1 ;
for t3 = 150ms
D3 =
(9.8m/s2)(150× 10−3 s)2
2
= 0.11m = 9D1 ;
for t4 = 200ms
D4 =
(9.8m/s2)(200× 10−3 s)2
2
= 0.196m = 16D1 ;
and for t4 = 250ms
D5 =
(9.8m/s2)(250× 10−3 s)2
2
= 0.306m = 25D1 .
		Main Menu
		Chapter 1 Measurement
		Chapter 2 Motion Along a Straight Line
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		2.51 - 2.60
		2.51
		2.52
		2.53
		2.54
		2.55
		2.56
		2.57
		2.58
		2.59
		2.60
		2.61 - 2.70
		2.61
		2.62
		2.63
		2.64
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		2.71 - 2.80
		2.71
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		2.73
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		2.81 - 2.90
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		2.88
		2.89
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		2.91 - 2.100
		2.91
		2.92
		2.93
		2.94
		2.95
		2.96
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		2.99
		2.100
		2.101 - 2.110
		2.101
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		2.103
		2.104
		2.105
		2.106
		2.107
		2.108
		2.109
		2.110
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge
		Chapter 23 Electric Fieldsnull 
		Chapter 24 Gauss’ Law
		Chapter 25 Electric Potential
		Chapter 26 Capacitance
		Chapter 27 Current and Resistance
		Chapter 28 Circuits
		Chapter 29 Magnetic Fields
		Chapter 30 Magnetic Fields Due to Currents
		Chapter 31 Induction and Inductance
		Chapter 32 Magnetism of Matter: Maxwell’s Equation
		Chapter 33 Electromagnetic Oscillations and Alternating Current
		Chapter 34 Electromagnetic Waves
		Chapter 35 Images
		Chapter 36 Interference
		Chapter 37 Diffraction
		Chapter 38 Special Theory of Relativity
		Chapter 39 Photons and Matter Waves
		Chapter 40 More About Matter Waves
		Chapter 41 All About Atoms
		Chapter 42 Conduction of Electricity in Solids
		Chapter 43 Nuclear Physics
		Chapter 44 Energy from the Nucleus
		Chapter 45 Quarks, Leptons, and the Big Bang
Solu��o Halliday resnick Fundamentos de F�sica 6 ed/Sol. Halliday resnick 6 ed/chap02/p02_064.pdf
64. During free fall, we ignore the air resistance and set a = −g = −9.8 m/s2 where we are choosing down
to be the −y direction. The initial velocity is zero so that Eq. 2-15 becomes ∆y = −12gt2 where ∆y
represents the negative of the distance d she has fallen. Thus, we can write the equation as d = 12gt
2 for
simplicity.
(a) The time t1 during which the parachutist is in free fall is (using Eq. 2-15) given by
d1 = 50m =
1
2
gt21 =
1
2
(
9.80m/s2
)
t21
which yields t1 = 3.2 s. The speed of the parachutist just before he opens the parachute is given by
the positive root v21 = 2gd1, or
v1 =
√
2gh1 =
√
(2)(9.80m/s2)(50m) = 31m/s .
If the final speed is v2, then the time interval t2 between the opening of the parachute and the
arrival of the parachutist at the ground level is
t2 =
v1 − v2
a
=
31m/s− 3.0m/s
2m/s2
= 14 s .
This is a result of Eq. 2-11 where speeds are used instead of the (negative-valued) velocities (so that
final-velocity minus initial-velocity turns out to equal initial-speed minus final-speed); we also note
that the acceleration vector for this part of the motion is positive since it points upward (opposite
to the direction of motion – which makes it a deceleration). The total time of flight is therefore
t1 + t2 = 17 s.
(b) The distance through which the parachutist falls after the parachute is opened is given by
d =
v21 − v22
2a
=
(31m/s)2 − (3.0m/s)2
(2)(2.0m/s2)
≈ 240m .
In the computation, we have used Eq. 2-16 with both sides multiplied by −1 (which changes the
negative-valued ∆y into the positive d on the left-hand side, and switches the order of v1 and v2
on the right-hand side). Thus the fall begins at a height of h = 50 + d ≈ 290m.
		Main Menu
		Chapter 1 Measurement
		Chapter 2 Motion Along a Straight Line
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		2.51 - 2.60
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		2.91 - 2.100
		2.91
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		2.93
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		2.95
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		2.103
		2.104
		2.105
		2.106
		2.107
		2.108
		2.109
		2.110
		Chapter 3 Vectors
		Chapter 4 Motion in Two and Three Dimensions
		Chapter 5 Force and Motion I
		Chapter 6 Force and Motion II
		Chapter 7 Kinetic Energy and Work
		Chapter 8 Potential Energy and Conservation of Energy
		Chapter 9 System of Particles
		Chapter 10 Collisions
		Chapter 11 Rotation
		Chapter 12 Rolling, Torque, and Angular Momentum
		Chapter 13 Equilibrium and Elasticity
		Chapter 14 Gravitation
		Chapter 15 Fluids
		Chapter 16 Oscillations
		Chapter 17 Waves—I
		Chapter 18 Waves—II
		Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
		Chapter 20 The Kinetic Theory of Gases
		Chapter 21 Entropy and the Second Law of Thermodynamics
		Chapter 22 Electric Charge