All 44 Chapters Covered
SOLUTIONS
,CONTENTS
Preface ................................................................................................................. v
Part I Mechanics
Chapter 1 Units, Physical Quantities, and Vectors ............................................... 1-1
Chapter 2 Motion Along a Straight Line ................................................................ 2-1
Chapter 3 Motion in Two or Three Dimensions .................................................... 3-1
Chapter 4 Newton’s Laws of Motion ..................................................................... 4-1
Chapter 5 Applying Newton’s Laws ...................................................................... 5-1
Chapter 6 Work and Kinetic Energy...................................................................... 6-1
Chapter 7 Potential Energy and Energy Conservation ......................................... 7-1
Chapter 8 Momentum, Impulse, and Collisions .................................................... 8-1
Chapter 9 Rotation of Rigid Bodies....................................................................... 9-1
Chapter 10 Dynamics of Rotational Motion .......................................................... 10-1
Chapter 11 Equilibrium and Elasticity ................................................................... 11-1
Chapter 12 Fluid Mechanics ................................................................................. 12-1
Chapter 13 Gravitation .......................................................................................... 13-1
Chapter 14 Periodic Motion .................................................................................. 14-1
Part II Waves/Acoustics
Chapter 15 Mechanical Waves ............................................................................. 15-1
Chapter 16 Sound and Hearing ............................................................................ 16-1
Part III Thermodynamics
Chapter 17 Temperature and Heat ....................................................................... 17-1
Chapter 18 Thermal Properties of Matter ............................................................. 18-1
Chapter 19 The First Law of Thermodynamics..................................................... 19-1
Chapter 20 The Second Law of Thermodynamics ............................................... 20-1
© Copyright 2020 Pearson Education, Inc. All rights reserved. This material is protected under all copyright laws as they currently exist.
No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
iii
,iv Contents
Part IV Electromagnetism
Chapter 21 Electric Charge and Electric Field ...................................................... 21-1
Chapter 22 Gauss’s Law ....................................................................................... 22-1
Chapter 23 Electric Potential................................................................................. 23-1
Chapter 24 Capacitance and Dielectrics ............................................................... 24-1
Chapter 25 Current, Resistance, and Electromotive Force .................................. 25-1
Chapter 26 Direct-Current Circuits ........................................................................ 26-1
Chapter 27 Magnetic Field and Magnetic Forces ................................................. 27-1
Chapter 28 Sources of Magnetic Field .................................................................. 28-1
Chapter 29 Electromagnetic Induction .................................................................. 29-1
Chapter 30 Inductance .......................................................................................... 30-1
Chapter 31 Alternating Current ............................................................................. 31-1
Chapter 32 Electromagnetic Waves ..................................................................... 32-1
Part V Optics
Chapter 33 The Nature and Propagation of Light ................................................. 33-1
Chapter 34 Geometric Optics................................................................................ 34-1
Chapter 35 Interference ........................................................................................ 35-1
Chapter 36 Diffraction ........................................................................................... 36-1
Part VI Modern Physics
Chapter 37 Relativity ............................................................................................. 37-1
Chapter 38 Photons: Light Waves Behaving as Particles .................................... 38-1
Chapter 39 Particles Behaving as Waves ............................................................. 39-1
Chapter 40 Quantum Mechanics I: Wave Functions ............................................ 40-1
Chapter 41 Quantum Mechanics II: Atomic Structure........................................... 41-1
Chapter 42 Molecules and Condensed Matter ..................................................... 42-1
Chapter 43 Nuclear Physics.................................................................................. 43-1
Chapter 44 Particle Physics and Cosmology ........................................................ 44-1
© Copyright 2020 Pearson Education, Inc. All rights reserved. This material is protected under all copyright laws as they currently exist.
No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
, UNITS, PHYSICAL QUANTITIES, AND VECTORS
1
VP1.7.1. IDENTIFY: We know that the sum of three known vectors and a fourth unknown vector is zero. We
want to find the magnitude and direction of the unknown vector.
SET UP: The sum of their x-components and the sum of their y-components must both be zero.
Ax + Bx + C x + Dx = 0
Ay + By + C y + Dy = 0
The magnitude of a vector is w A = Ax2 + Ay2 and the angle θ it makes with the +x-axis is
Ay
θ = arctan .
Ax
EXECUTE: We use the results of Ex. 1.7. See Fig. 1.23 in the text.
Ax = 38.37 m, Bx = –46.36 m, Cx = 0.00 m, Ay = 61.40 m, By = –33.68 m, Cy = –17.80 m
Adding the x-components gives
38.37 m + (–46.36 m) + 0.00 m + Dx = 0 → Dx = 7.99 m
Adding the y-components gives
61.40 m + (–33.68 m) + (–17.80 m) + Dy = 0 → Dy = –9.92 m
D = Dx2 + Dy2 = (7.99 m) 2 + (–9.92 m) 2 = 12.7 m
Dy
glo θ = arctan = arctan[(–9.92 m)/(7.99 m)] = –51°
Dx
Since D has a positive x-component and a negative y-component, it points into the fourth quadrant
making an angle of 51° below the +x-axis and an angle of 360° – 51° = 309° counterclockwise with the
+x-axis.
EVALUATE: The vector D has the same magnitude as the resultant in Ex. 1.7 but points in the opposite
direction. This is reasonable because D must be opposite to the resultant of the three vectors in Ex. 1.7
to make the resultant of all four vectors equal to zero.
VP1.7.2. IDENTIFY: We know three vectors A , B , and C and we want to find the sum S where
S = A – B + C . The components of – B are the negatives of the components of B .
SET UP: The components of S are
S x = Ax − Bx + C x
S y = Ay − By + C y
The magnitude A of a vector A is A = Ax2 + Ay2 and the angle θ it makes with the +x-axis is
Ay
θ = arctan .
Ax
© Copyright 2020 Pearson Education, Inc. All rights reserved. This material is protected under all copyright laws as they currently exist.
No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
1-1
SOLUTIONS
,CONTENTS
Preface ................................................................................................................. v
Part I Mechanics
Chapter 1 Units, Physical Quantities, and Vectors ............................................... 1-1
Chapter 2 Motion Along a Straight Line ................................................................ 2-1
Chapter 3 Motion in Two or Three Dimensions .................................................... 3-1
Chapter 4 Newton’s Laws of Motion ..................................................................... 4-1
Chapter 5 Applying Newton’s Laws ...................................................................... 5-1
Chapter 6 Work and Kinetic Energy...................................................................... 6-1
Chapter 7 Potential Energy and Energy Conservation ......................................... 7-1
Chapter 8 Momentum, Impulse, and Collisions .................................................... 8-1
Chapter 9 Rotation of Rigid Bodies....................................................................... 9-1
Chapter 10 Dynamics of Rotational Motion .......................................................... 10-1
Chapter 11 Equilibrium and Elasticity ................................................................... 11-1
Chapter 12 Fluid Mechanics ................................................................................. 12-1
Chapter 13 Gravitation .......................................................................................... 13-1
Chapter 14 Periodic Motion .................................................................................. 14-1
Part II Waves/Acoustics
Chapter 15 Mechanical Waves ............................................................................. 15-1
Chapter 16 Sound and Hearing ............................................................................ 16-1
Part III Thermodynamics
Chapter 17 Temperature and Heat ....................................................................... 17-1
Chapter 18 Thermal Properties of Matter ............................................................. 18-1
Chapter 19 The First Law of Thermodynamics..................................................... 19-1
Chapter 20 The Second Law of Thermodynamics ............................................... 20-1
© Copyright 2020 Pearson Education, Inc. All rights reserved. This material is protected under all copyright laws as they currently exist.
No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
iii
,iv Contents
Part IV Electromagnetism
Chapter 21 Electric Charge and Electric Field ...................................................... 21-1
Chapter 22 Gauss’s Law ....................................................................................... 22-1
Chapter 23 Electric Potential................................................................................. 23-1
Chapter 24 Capacitance and Dielectrics ............................................................... 24-1
Chapter 25 Current, Resistance, and Electromotive Force .................................. 25-1
Chapter 26 Direct-Current Circuits ........................................................................ 26-1
Chapter 27 Magnetic Field and Magnetic Forces ................................................. 27-1
Chapter 28 Sources of Magnetic Field .................................................................. 28-1
Chapter 29 Electromagnetic Induction .................................................................. 29-1
Chapter 30 Inductance .......................................................................................... 30-1
Chapter 31 Alternating Current ............................................................................. 31-1
Chapter 32 Electromagnetic Waves ..................................................................... 32-1
Part V Optics
Chapter 33 The Nature and Propagation of Light ................................................. 33-1
Chapter 34 Geometric Optics................................................................................ 34-1
Chapter 35 Interference ........................................................................................ 35-1
Chapter 36 Diffraction ........................................................................................... 36-1
Part VI Modern Physics
Chapter 37 Relativity ............................................................................................. 37-1
Chapter 38 Photons: Light Waves Behaving as Particles .................................... 38-1
Chapter 39 Particles Behaving as Waves ............................................................. 39-1
Chapter 40 Quantum Mechanics I: Wave Functions ............................................ 40-1
Chapter 41 Quantum Mechanics II: Atomic Structure........................................... 41-1
Chapter 42 Molecules and Condensed Matter ..................................................... 42-1
Chapter 43 Nuclear Physics.................................................................................. 43-1
Chapter 44 Particle Physics and Cosmology ........................................................ 44-1
© Copyright 2020 Pearson Education, Inc. All rights reserved. This material is protected under all copyright laws as they currently exist.
No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
, UNITS, PHYSICAL QUANTITIES, AND VECTORS
1
VP1.7.1. IDENTIFY: We know that the sum of three known vectors and a fourth unknown vector is zero. We
want to find the magnitude and direction of the unknown vector.
SET UP: The sum of their x-components and the sum of their y-components must both be zero.
Ax + Bx + C x + Dx = 0
Ay + By + C y + Dy = 0
The magnitude of a vector is w A = Ax2 + Ay2 and the angle θ it makes with the +x-axis is
Ay
θ = arctan .
Ax
EXECUTE: We use the results of Ex. 1.7. See Fig. 1.23 in the text.
Ax = 38.37 m, Bx = –46.36 m, Cx = 0.00 m, Ay = 61.40 m, By = –33.68 m, Cy = –17.80 m
Adding the x-components gives
38.37 m + (–46.36 m) + 0.00 m + Dx = 0 → Dx = 7.99 m
Adding the y-components gives
61.40 m + (–33.68 m) + (–17.80 m) + Dy = 0 → Dy = –9.92 m
D = Dx2 + Dy2 = (7.99 m) 2 + (–9.92 m) 2 = 12.7 m
Dy
glo θ = arctan = arctan[(–9.92 m)/(7.99 m)] = –51°
Dx
Since D has a positive x-component and a negative y-component, it points into the fourth quadrant
making an angle of 51° below the +x-axis and an angle of 360° – 51° = 309° counterclockwise with the
+x-axis.
EVALUATE: The vector D has the same magnitude as the resultant in Ex. 1.7 but points in the opposite
direction. This is reasonable because D must be opposite to the resultant of the three vectors in Ex. 1.7
to make the resultant of all four vectors equal to zero.
VP1.7.2. IDENTIFY: We know three vectors A , B , and C and we want to find the sum S where
S = A – B + C . The components of – B are the negatives of the components of B .
SET UP: The components of S are
S x = Ax − Bx + C x
S y = Ay − By + C y
The magnitude A of a vector A is A = Ax2 + Ay2 and the angle θ it makes with the +x-axis is
Ay
θ = arctan .
Ax
© Copyright 2020 Pearson Education, Inc. All rights reserved. This material is protected under all copyright laws as they currently exist.
No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
1-1
