Archives: Solution Manual

PROBLEM 18.64 Determine the rate of change G H  of the angular momentum H G of the disk of Prob. 18.8 for an arbitrary value of  , knowing that the disk has an angular velocity  =  […]

PROBLEM 18.56 Determine the rate of change G H  of the angular momentum G H of the plate of Problem 18.2. PROBLEM 18.2 A thin rectangular plate of weight 15 lb rotates about its vertical diagonal AB with an […]

PROBLEM 18.50 Determine the kinetic energy imparted to the cube of Problem 18.21. PROBLEM 18.21 One of the sculptures displayed on a university campus consists of a hollow cube made of six aluminum sheets, each 1.5 1.5 m,  welded […]

PROBLEM 18.41 Determine the kinetic energy of the assembly of Problem 18.3. PROBLEM 18.3 Two uniform rods AB and CE, each of weight 3 lb and length 2 ft, are welded to each other at their midpoints. Knowing that this […]

PROBLEM 18.34 The coordinate axes shown represent the principal centroidal axes of inertia of a 3000-lb space probe whose radii of gyration are 1.375 ft, x k 1.425 ft, y k and 1.250 ft. z k The probe has no […]

PROBLEM 18.29 A circular plate of mass m is falling with a velocity 0 v and no angular velocity when its edge C strikes an obstruction. Assuming the impact to be perfectly plastic (0),e determine the angular velocity of the […]

PROBLEM 18.24 Solve Problem 18.23, assuming that the bent rod is hit at C . PROBLEM 18.23 A uniform rod of total mass m is bent into the shape shown and is suspended by a wire attached at B . […]

PROBLEM 18.16 For the assembly of Prob. 18.15, determine ( a ) the angular momentum B H of the assembly about point B , ( b ) the angle formed by B H and BA . PROBLEM 18.15: Two L-shaped […]

PROBLEM 18.7 (Continued) For each plate parallel to the xy plane: 1 5 mm  2 222 177 a  2 222 22 2 2 151 (2 ) 12 2 12 60 x I ma m ma ma   […]

CHAPTER 18 PROBLEM 18.1 A thin, homogeneous disk of mass m and radius r spins at the constant rate 1  about an axle held by a fork-ended vertical rod, which rotates at the constant rate 2.  Determine the […]

PROBLEM 17.CQ2 A solid steel sphere A of radius r and mass m is released from rest and rolls without slipping down an incline as shown. After traveling a distance d the sphere has a speed v. If a solid […]

PROBLEM 17.142 (Continued) Panel in down position ( ) (2 )[ (2 ) ] Itbbb   22 2 panel 1 4 4 12 10 12 5 tb   1 6 tb   Conservation of angular momentum about […]

PROBLEM 17.137 (Continued) Kinetics: (b) (c) Work Energy Equation Pos. 1 and 3: 0 OO M I     tTt tT F ma Omy     0 t O 2 2 12 31.91 90.7 2.8168 5.993 […]

PROBLEM 17.132 (Continued) Add Equations (1) and (2) to eliminate .Pdt 11 or AB BA mv mv mv v v v  (3) Condition of impact. 1. e 11BA vvevv  (4) Solving Equations (3) and (4) simultaneously, 1 0, […]

PROBLEM 17.127 (Continued) Coefficient of restitution. 4 () ev v   DAD D A L vvv      0.1875 (0.5)(3 0) D v       (2) Solving Eqs. (1) and (2) simultaneously. […]

PROBLEM 17.123 A slender rod AB is released from rest in the position shown. It swings down to a vertical position and strikes a second and identical rod CD which is resting on a frictionless surface. Assuming that the coefficient […]

PROBLEM 17.118 A uniformly loaded square crate is released from rest with its corner D directly above A; it rotates about A until its corner B strikes the floor, and then rotates about B. The floor is sufficiently rough to […]

PROBLEM 17.112 (Continued) moments about B: 00 0 t mv mv L mv L mL L I        22 211 224 422   L     22 00 mv L m […]

PROBLEM 17.106 (Continued) Substitute rolling Kinematics and Mass Moment Equations into Momentum Equation: cm 22 r2cosvr cm v rm  23 rm    23 cos 1 cvcr   3 rr  Substitute in the velocity at position […]

PROBLEM 17.100 (Continued) Principle of impulse and momentum. 1 Syst. Momenta  12  Syst. Ext. Imp.  2 Syst. Momenta Moments about A: 1222 22 ( ) ft 0 ( ) (0.95015 ft) ft 12 12 4lb 7 4lb […]

PROBLEM 17.94 (Continued) Kinetic energy.  / AB DCE AB G C r II mrv      222 22222 22 2 1 11 1 22 2 111 (0.0025)(5) (0.3)(5) (1.6)(0.0625) 0 3.859375 J T   11 […]

PROBLEM 17.89 (Continued) Solving the quadratic equation for , I 0.04965167 0.126590 0.050804 and 0.022179 3.46904 I   Reject the negative root. From Equation (10), 2(21)(0.050804) 0.378 0.050804 0.02592    18.83 rad/s   2 0.0508 kg […]

PROBLEM 17.83 (Continued) Moments about C: 2  .5359 rad/s 11 1/1 2 2 2/2 22 /1 1 /2 2 22 2 2 2 () () [0.0025 0.30 (1.6)(0.0625) ](5) [0.0025 0.30 (1.6)(0.4375) ] (0.30875)(5) 0.60875 AB DCE AB G […]

PROBLEM 17.76 (Continued) Moments about B: 2 (4 ) 1 4( ) (4 ) 12 ABC ABC Mt Qt r I Mt Qt r m r     2 4( ) 3ABC M tQtrmr   (2) 4 […]

PROBLEM 17.71 (Continued) (a) (0.150)(17.0077) 2.55115 m/sv 2.55 m/sv  Linear components: 0 P t mgt Qt mv  (3)(2.55115) (3)(9.81) 24 1.5 mv QmgP t    (b) Tension in cord C. 10.53 NQ  Copyright © McGraw-Hill […]

PROBLEM 17.64 (Continued) Moments about A: 0 AAB AA A A rT t rTt I   6 0.9 0.9 0 ( ) (0.75)(0.24) (169.837 10 )(133.333) 12 12 0.48193 lb s AB AB Tt Tt     […]

PROBLEM 17.58 Disk A, of weight 5 lb and radius 3in.,r is at rest when it is placed in contact with a belt which moves at a constant speed 50 ft/s.v Knowing that 0.20 k   between the disk […]

PROBLEM 17.48 Knowing that the maximum allowable couple that can be applied to a shaft is 15.5 kip  in., determine the maximum horsepower that can be transmitted by the shaft at (a) 180 rpm, (b) 480 rpm. SOLUTION 15.5 […]

PROBLEM 17.42 (Continued) By Eq. (2), 22 2 2 735 kg m 21.096 J 12 12 AB AB mL       222 7.2329 rad /s 2.6894 rad/s AB AB   By Eq. (1), (1m)(2.6894 rad/s) […]

PROBLEM 17.38 A long ladder of length l, mass m, and centroidal mass moment of inertia I is placed against a house at an angle    . Knowing that the ladder is released from rest, determine the angular […]

PROBLEM 17.32 Two uniform cylinders, each of weight W  14 lb and radius r  5 in., are connected by a belt as shown. Knowing that at the instant shown the angular velocity of cylinder B is 30 rad/s […]

PROBLEM 17.27 Greek engineers had the unenviable task of moving large columns from the quarries to the city. One engineer, Chersiphron, tried several different techniques to do this. One method was to cut pivot holes into the ends of the […]

PROBLEM 17.20 A 160-lb gymnast is executing a series of full-circle swings on the horizontal bar. In the position shown he has a small and negligible clockwise angular velocity and will maintain his body straight and rigid as he swings […]

PROBLEM 17.15 Gear A has a mass of 1 kg and a radius of gyration of 30 mm; gear B has a mass of 4 kg and a radius of gyration of 75 mm; gear C has a mass of […]

PROBLEM 17.8 (Continued)     12 5.886 2 36.983 N m BB k k UM     Principle of work and energy for cylinder B. 2 1122 : 0 36.983 0.0225 kB TU T   […]

CHAPTER 17 PROBLEM 17.1 A 200-kg flywheel is at rest when a constant 300 N m  couple is applied. After executing 560 revolutions, the flywheel reaches its rated speed of 2400 rpm. Knowing that the radius of gyration of […]

PROBLEM 16.F3 Two uniform disks and two cylinders are assembled as indicated. Disk A weighs 20 lb and disk B weighs 12 lb. Knowing that the system is released from rest, draw the FBD and KD for the whole system. […]

PROBLEM 16.164 (Continued) 12 32.2 ft/s    22 2 6 lb 1.5 ft (81.391 rad/s ) 0.23697 lb ft 0 since 0 ss DD I I a a    = = ⋅    = […]

PROBLEM 16.161 A cylinder with a circular hole is rolling without slipping on a fixed curved surface as shown. The cylinder would have a weight of 16 lb without the hole, but with the hole it has a weight of […]

PROBLEM 16.157 The uniform rod AB of weight W is released from rest when 70 . β = ° Assuming that the friction force between end A and the surface is large enough to prevent sliding, determine immediately after release […]

184 Perloff • Microeconomics: Theory and Applications with Calculus, Third Edition 5.6 The welfare loss from the tax is equal to area abc. If the ad valorem tax is levied on firms, then the supply curve will shift leftward. Also […]

PROBLEM 16.151* (a) Determine the magnitude and the location of the maximum bending moment in the rod of Problem 16.78. (b) Show that the answer to Part a is independent of the weight of the rod. SOLUTION Rod AB: 2 […]

174 Perloff • Microeconomics: Theory and Applications with Calculus, Third Edition 12. Suppose the demand curve for a good is Q = 9 − p and the supply curve is Q = 2p. The government imposes a specific tax of […]

170 ©2014 Pearson Education, Inc. Chapter 9 Properties and Applications of the Competitive Model  Chapter Outline 9.1 Zero Profit for Competitive Firms in the Long Run Zero Long-Run Profit with Free Entry Zero Long–Run Profit when Entry Is Limited […]

PROBLEM 16.145 (Continued) Rod eff / ( ) : 0 ( ) ( cos25 ) 22 A A RGR RC LL M M I ma ma a Σ=Σ =+ − ° (1.50cos25 ) C a a = ° (2) (a) […]

Chapter 8 Competitive Firms and Markets 163 ©2014 Pearson Education, Inc. If the government imposes a $1.00 tax, the minimum average cost of production and hence the equilibrium price increase by $1.00 (to $1.75), but the quantity produced by the […]

PROBLEM 16.141 (Continued) Rod AE: / , AE AE P AE u= =α αk a j  // 2 P P P AE P AE ′ =+ +×aaa ωv where // 2 2 10 10 sin30 (20) sin30 12 12 […]

Chapter 8 Competitive Firms and Markets 153 8. True or false, explain your answer. “If all firms in an industry have identical variable cost, but each pays a different one–time fee to enter the market, all firms will produce identical […]

PROBLEM 16.136 (Continued) Effective couples at mass centers. Disk AB: (0.2)(150) AB AB I= α 30 N m= ⋅ Rod BC: (0.08)(149.649) BC BC I=α 11.97192 N m= ⋅ Rod CD: (0.0260417)(239.719) CD CD I=α 6.24268 N m= ⋅ Summary […]

148 ©2014 Pearson Education, Inc. Chapter 8 Competitive Firms and Markets  Chapter Outline 8.1 Perfect Competition Price Taking Why a Firm’s Demand Curve Is Horizontal Large Number of Small Firms and Consumers Identical Products Full Information Negligible Transaction Costs […]