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Solutions manual for elementary mechanics and thermodynamics PDF

112 Pages·2000·0.56 MB·english
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SOLUTIONS 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 2 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 POTENTIALENERGY&CONSERVATIONOFENERGY 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 KINETIC 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 = Dcos!t v) x = Esin!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 msec¡1, C in msec¡2. !t is always an angle, (cid:181) is radius and cos(cid:181) and sin(cid:181) have no units. Thus ! must be sec¡1 or radians sec¡1. D and E must be m. B) v = dx and a = dv. Thus dt dt i) v = 0 ii) v = B iii) v = Ct iv) v = ¡!Dsin!t v) v = !Ecos!t 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 = ¡!2Dcos!t v) a = ¡!2Esin!t 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 0.5 0.5 x 0 x 0 -0.5 -0.5 -1 -1 0 1 2 3 4 5 6 0 1 2 3 4 5 6 t t 1 1 0.5 0.5 v 0 v 0 -0.5 -0.5 -1 -1 0 1 2 3 4 5 6 0 1 2 3 4 5 6 t t 1 1 0.5 0.5 a 0 a 0 -0.5 -0.5 -1 -1 0 1 2 3 4 5 6 0 1 2 3 4 5 6 t t 9 2. The flgures below show position-time graphs. Sketch the correspond- ing velocity-time and acceleration-time graphs. x x x t t t SOLUTION The velocity-time and acceleration-time graphs are: v v v tt tt tt a a a tt tt tt 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 v2 = v2+2a(y¡y ) 0 0 In the vertical direction we have: v = 0, a = ¡g, y = H, y = 0. 0 0 Thus v2 = 0¡2g(0¡H) = 2gH p ) v = 2gH

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