【英文原版书】Elementary Mechanics and Thermodynamics SOLUTIONS MANUAL - J. Norbury.pdf

SOLUTIONS MANUAL
for elementary mechanics &
thermodynamics
Professor John W. Norbury
Physics Department
University of Wisconsin-Milwaukee
. Box 413
Milwaukee, WI 53201
November 20, 2000
2
Contents
1 MOTION ALONG A STRAIGHT LINE 5
2 VECTORS 15
3 MOTION IN2&3DIMENSIONS 19
4 FORCE & MOTION - I 35
5 FORCE & MOTION - II 37
6 IC ENERGY & WORK 51
7 POTENTIAL ENERGY & CONSERVATION OF ENERGY 53
8 SYSTEMS OF PARTICLES 57
9 COLLISIONS 61
10 ROTATION 65
11 ROLLING, TORQUE & ANGULAR MOMENTUM 75
12 OSCILLATIONS 77
13 WAVES - I 85
14 WAVES - II 87
15 TEMPERATURE, HEAT & 1ST LAW OF THERMODY-
NAMICS 93
16 IC THEORY OF GASES 99
3
4 CONTENTS
17 Review of Calculus 103
Chapter 1
MOTION ALONG A
STRAIGHT LINE
5
6 CHAPTER 1. MOTION ALONG A STRAIGHT LINE
1. The following functions give the position as a function of time:
i) x = A
ii) x = Bt
iii) x = Ct2
iv) x = D cos ωt
v) x = E sin ωt
where A, B, C, D, E, ω are constants.
A) What are the units for A, B, C, D, E, ω?
B) Write down the velocity and acceleration equations as a function of
time. Indicate for what functions the acceleration is constant.
C) Sketch graphs of x, v, a as a function of time.
SOLUTION
A) X is always in m.
Thus we must have A in m; B in m sec
1, C in m sec
2.
ωt is always an angle,
is radius and cos
and sin
have no units.
Thus ω must be sec
1 or radians sec
1.
D and E must be m.
dx dv
B) v = dt and a = dt .Thus
i) v = 0 ii) v = B iii) v = Ct
iv) v =
ωD sin ωt v) v = ωE cos ωt
and notice that the units we worked out in part A) are all consistent
with v having units of m
sec
1. Similarly
i) a = 0 ii) a = 0 iii) a = C
iv) a =
ω2D cos ωt v) a =
ω2E sin ωt
7
C) i) ii) iii)
x x x
t t t
v v v
t t t
a a a
t t t
8 CHAPTER 1. MOTION ALONG A STRAIGHT LINE
iv) v)
1 1

x 0 x 0
- -
-1 -1
0 1 2 3 4 5 6 0 1 2 3 4 5 6
t t
1 1

v 0 v 0
- -
-1 -1
0 1 2 3 4 5 6 0 1 2