Archives: Solution Manual

PROBLEM 14.110 (Continued) 112 2 :TV T V 2 0 27 0.10352 2.5 A v  22 236.67 ft A v 15.38 ft/s A v  5.13 ft/s B v  Copyright © McGraw-Hill Education. Permission required for reproduction or […]

PROBLEM 14.104 In a rocket, the kinetic energy imparted to the consumed and ejected fuel is wasted as far as propelling the rocket is concerned. The useful power is equal to the product of the force available to propel the […]

PROBLEM 14.98 The rocket engines of a spacecraft are fired to increase its velocity by 450 ft/s. Knowing that 1200 lb of fuel is ejected at a relative velocity of 5400 ft/s, determine the weight of the spacecraft after the […]

PROBLEM 14.89 A toy car is propelled by water that squirts from an internal tank at a constant 6 ft/s relative to the car. The weight of the empty car is 0.4 lb and it holds 2 lb of water. […]

PROBLEM 14.81 (Continued) Input power  rate of supply of kinetic energy of the stream 2 in 2 3 11 () 2 1 2 1 2 A A A P mv t mv t Av      […]

PROBLEM 14.73 Prior to take-off the pilot of a 3000-kg twin-engine airplane tests the reversible-pitch propellers by increasing the reverse thrust with the brakes at point B locked. Knowing that point G is the center of gravity of the airplane, […]

PROBLEM 14.64 The stream of water shown flows at a rate of 550 liters/min and moves with a velocity of magnitude 18 m/s at both A and B. The vane is supported by a pin and bracket at C and […]

PROBLEM 14.55 (Continued) Conservation of energy. Before break:  22 0 22 2 2 0 11 (3 ) 3 22 33 [(1.3) (2.6) ] 12.675 22 Tmv mv mv v m m         […]

PROBLEM 14.50 Three small spheres A, B, and C, each of mass m, are connected to a small ring D of negligible mass by means of three inextensible, inelastic cords of length l. The spheres can slide freely on a […]

PROBLEM 14.44 In a game of pool, ball A is moving with the velocity 00 vvi when it strikes balls B and C, which are at rest side by side. Assuming frictionless surfaces and perfectly elastic impact (i.e., conservation of […]

PROBLEM 14.36 It is assumed that each of the two automobiles involved in the collision described in Problem 14.35 had been designed to safely withstand a test in which it crashed into a solid, immovable wall at the speed v0. […]

PROBLEM 14.27 Derive the relation OG m HrvH between the angular momenta O H and G H defined in Eqs. (14.7) and (14.24), respectively. The vectors r and v define, respectively, the position and velocity of the mass center G […]

PROBLEM 14.20 (Continued) Data: ft 59 ft, 46   PP yx ( ) From (2),a   P t66325.0359    s 611.2  P t s 61.2  P t  ()From (1), b    […]

PROBLEM 14.13 A system consists of three particles A, B, and C. We know that 3 A m  kg, 2 B m  kg, and 4 C m kg and that the velocities of the particles expressed in m/s […]

PROBLEM 14.7 (Continued) (c) Container slides and stops only after 2nd coupling 12 360 65 100vv 15.54 km/hv  23.60 km/hv  Copyright © McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 14.8 Two identical cars A and B […]

CHAPTER 14 PROBLEM 14.1 A 30-g bullet is fired with a horizontal velocity of 450 m/s and becomes embedded in block B which has a mass of 3 kg. After the impact, block B slides on 30-kg carrier C until […]

PROBLEM 13.78 The pendulum shown is released from rest at A and swings through 90° before the cord touches the fixed peg B. Determine the smallest value of a for which the pendulum bob will describe a circle about the […]

PROBLEM 13.72 (Continued) Forces at B. 0 2 2 ( ) (10) 6.6667 lb. 3 5 sin 13 5 5 in. ft 12 (0.031056)(205.72) 5/12 15.3332 lb sB B n Fk mv ma α ρ ρ  = −= = […]

PROBLEM 13.67 Cornhole is a game that requires you to toss beanbags through a hole in a wooden board. People with limited arm mobility often have difficulty enjoying this favorite tailgating activity. An adapted launching device attaches to a wheelchair […]

PROBLEM 13.62 An elastic cable is to be designed for bungee jumping from a tower 130 ft high. The specifications call for the cable to be 85 ft long when unstretched, and to stretch to a total length of 100 […]

PROBLEM 13.55 A force P is slowly applied to a plate that is attached to two springs and causes a deflection 0 .x In each of the two cases shown, derive an expression for the constant , e k in […]

PROBLEM 13.39 The sphere at A is given a downward velocity 0 v of magnitude 5 m/s and swings in a vertical plane at the end of a rope of length 2ml= attached to a support at O. Determine the […]

PROBLEM 13.31 A 5–kg collar A is at rest on top of, but not attached to, a spring with stiffness k1 = 400 N/m; when a constant 150–N force is applied to the cable. Knowing A has a speed of […]

PROBLEM 13.25 Four 3–kg packages are held in place by friction on a conveyor which is disengaged from its drive motor. When the system is released from rest, package 1 leaves the belt at A just as package 4 comes […]

PROBLEM 13.18 The subway train shown is traveling at a speed of 30 mi/h when the brakes are fully applied on the wheels of cars A, causing it to slide on the track, but are not applied on the wheels […]

PROBLEM 13.9 A package is projected up a 15° incline at A with an initial velocity of 8 m/s. Knowing that the coefficient of kinetic friction between the package and the incline is 0.12, determine (a) the maximum distance d […]

CHAPTER 13 PROBLEM 13.1 A 400–kg satellite is placed in a circular orbit 6394 km above the surface of the earth. At this elevation the acceleration of gravity is 2 4.09 m/s . Knowing that its orbital speed is 20 […]

PROBLEM 12.F2 Two blocks weighing WA and WB are at rest on a conveyor that is initially at rest. The belt is suddenly started in an upward direction so that slipping occurs between the belt and the boxes. Assuming the […]

PROBLEM 12.133* (Continued) and and at  Note: implies that the slider remains at its initial radial position. With Eq. (2) implies  (b) Substituting the given values into Eq. (1) Now Then so that At Now At 0 dr […]

PROBLEM 12.128 A small 200-g collar C can slide on a semicircular rod which is made to rotate about the vertical AB at the constant rate of 6 rad/s. Determine the minimum required value of the coefficient of static friction […]

PROBLEM 12.121 Show that the angular momentum per unit mass h of a satellite describing an elliptic orbit of semimajor axis a and eccentricity about a planet of mass M can be expressed as SOLUTION By Eq. At A, At […]

PROBLEM 12.113 (Continued) Then 2 4 3 3 2 1or 2 28 3 8 6332 10 m 3 10,131.4 m/s 1666.63 s BA BA BA A A BA AA BA AA A A A ht t h r v h […]

PROBLEM 12.107 (Continued) (b) From Part (a), we have 2 sun 11 2() AA A B GM r v rr     Then, for any other elliptic orbit about the sun, we have   211 2 12 […]

PROBLEM 12.101 It was observed that as the Voyager I spacecraft reached the point of its trajectory closest to the planet Saturn, it was at a distance of 3 185 10km from the center of the planet and had a […]

(b) Acceleration of B relative to the rod. At () 96 0, ( ) 8 ft/s 96 in./s, 9.6 rad/s 10 A AA v tv r      2() 0 BB Br rr a    […]

PROBLEM 12.84 The periodic time (see Prob. 12.83) of an earth satellite in a circular polar orbit is 120 minutes. Determine (a) the altitude h of the satellite, (b) the time during which the satellite is above the horizon for […]

PROBLEM 12.75 (Continued) Since the particle moves under a central force, 0.   a Magnitude of acceleration. 2 22 0 2 0 rvr aaa r   Tangential component of acceleration. 2 000 2 00 0 sin 2 tvr […]

PROBLEM 12.68 The 3-kg collar B slides on the frictionless arm .AA  The arm is attached to drum D and rotates about O in a horizontal plane at the rate 0.75 , t    where   […]

PROBLEM 12.62 (Continued) We must determine the values of  which maximize the above expression. Thus    2 2 2 2 sin sin (cos )( cos ) cos 0 sin sin B B B g v gg vv […]

PROBLEM 12.57 A turntable A is built into a stage for use in a theatrical production. It is observed during a rehearsal that a trunk B starts to slide on the turntable 10 s after the turntable begins to rotate. […]

PROBLEM 12.50 (Continued) At B: 2 : B nnB v Fma N m    or 22 22,555 m /s 54 kg 1200 m B N or 1014.98 N B N :|| tt B t FmaWPma   or […]

PROBLEM 12.43* (Continued) max max ( ) 16.9443 lb () 17lb DA DE T T   Eq. (1) max 2 2 () (32.2 ft/s )(0.5 ft) ( ) (16.9443sin 20 17sin 30 ) lb 1.2 lb DA T v […]

PROBLEM 12.36 A 450-g tetherball A is moving along a horizontal circular path at a constant speed of 4 m/s. Determine (a) the angle  that the cord forms with pole BC, (b) the tension in the cord. SOLUTION First […]

PROBLEM 12.31 A 10-lb block B rests as shown on a 20-lb bracket A. The coefficients of friction are 0.30 s   and 0.25 k   between block B and bracket A, and there is no friction in […]

PROBLEM 12.24 An airplane has a mass of 25 Mg and its engines develop a total thrust of 40 kN during take-off. If the drag D exerted on the plane has a magnitude 2 2.25 , D v where v […]

PROBLEM 12.19 (Continued) Now AsA FN   or 0.2[( ) cos 25 sin 25 ] AAB Fmmg P  0: sin 25 cos 25 0 xAABA FTFFW P      or 0.2[( ) cos 25 sin […]

PROBLEM 12.14 (Continued) Block B 350 1 :350lb2 32.2 2 yBB A Fma T a       (2) (a) Multiply Eq. (1) by 2 and add Eq. (2) in order to eliminate T: 200 350 1 […]

Copyright © McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 12.7 (Continued) (b) From Kinematics: x x vdv adx vdv dx a   2 1 0 2.5 1 27000 3 33ln3 27000 | v x v mvdv dx […]

CHAPTER 12 PROBLEM 12.1 Astronauts who landed on the moon during the Apollo 15, 16 and 17 missions brought back a large collection of rocks to the earth. Knowing the rocks weighed 139 lb when they were on the moon, […]

PROBLEM 11.193 (Continued) Multiply Eq. (1) by sin 30° and Eq. (2) by cos 30° and subtract 2 2 sin 30 ( 10)cos30 0 (109.95 )sin 30 (12.654 16.1 10)cos30 0 13.943 44.016 8.6603 0 xy ttt tt   […]