Solutions manual for mechanics and thermodynamics
.pdfSOLUTIONS MANUAL for elementary mechanics & thermodynamics
Professor John W. Norbury
Physics Department
University of Wisconsin-Milwaukee
P.O. Box 413
Milwaukee, WI 53201
November 20, 2000
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Contents
1 |
MOTION ALONG A STRAIGHT LINE |
5 |
2 |
VECTORS |
15 |
3 |
MOTION IN 2 & 3 DIMENSIONS |
19 |
4 |
FORCE & MOTION - I |
35 |
5 |
FORCE & MOTION - II |
37 |
6 |
KINETIC ENERGY & WORK |
51 |
7 |
POTENTIAL ENERGY & CONSERVATION OF ENERGY 53 |
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8 |
SYSTEMS OF PARTICLES |
57 |
9 |
COLLISIONS |
61 |
10 ROTATION |
65 |
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11 ROLLING, TORQUE & ANGULAR MOMENTUM |
75 |
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12 |
OSCILLATIONS |
77 |
13 |
WAVES - I |
85 |
14 |
WAVES - II |
87 |
15 TEMPERATURE, HEAT & 1ST LAW OF THERMODY- |
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NAMICS |
93 |
16 KINETIC THEORY OF GASES |
99 |
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3 |
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4 |
CONTENTS |
17 Review of Calculus |
103 |
Chapter 1
MOTION ALONG A STRAIGHT LINE
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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 !t
v)x = E sin !t
where A; B; C; D; E; ! are constants.
A)What are the units for A; B; C; D; E; !?
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.
!t is always an angle, µ is radius and cos µ and sin µ have no units. Thus ! must be sec°1 or radians sec°1.
D and E must be m.
B)v = dxdt and a = dvdt . Thus
i) v = 0 |
ii) v = B |
iii) v = Ct |
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iv) v = °!D sin !t |
v) v = !E cos !t |
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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 = °!2D cos !t |
v) a = °!2E sin !t |
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C) |
i) |
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CHAPTER 1. MOTION ALONG A STRAIGHT LINE |
iv) |
v) |
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9
2.The Øgures below show position-time graphs. Sketch the corresponding velocity-time and acceleration-time graphs.
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SOLUTION
The velocity-time and acceleration-time graphs are:
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10 |
CHAPTER 1. MOTION ALONG A STRAIGHT LINE |
3.If you drop an object from a height H above the ground, work out a formula for the speed with which the object hits the ground.
SOLUTION |
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v2 = v02 + 2a(y ° y0) |
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In the vertical direction we have: |
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v0 = 0, |
a = °g, |
y0 = H, |
y = 0. |
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Thus |
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v2 = 0 ° 2g(0 ° H) |
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2gH |
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p |
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2gH |
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