Archives
978-0073380308 Chapter 1 Solution Manual Part 1
Solutions Manual Engineering Mechanics: Dynamics 2nd Edition Gary L. Gray The Pennsylvania State University Francesco Costanzo The Pennsylvania State University Michael E. Plesha University of Wisconsin–Madison Version: May 12, 2012 The McGraw-Hill Companies, Inc. Copyright © 2002–2012 Gary L. Gray, […]
978-0073380308 Chapter 1 Solution Manual Part 2
Dynamics 2e 11 Problem 1.6 The magnitude of the velocity vector of the car is jEvj D 80 ft=s . If the vector Ev forms an angle D0:09 rad with the horizontal direction, determine the Cartesian representation of Ev relative […]
978-0073380308 Chapter 1 Solution Manual Part 3
Dynamics 2e 21 Problem 1.16 Two Coast Guard patrol boats P1 and P2 are stationary while monitoring the motion of a surface vessel A . The velocity of Awith respect to P1is expressed by EvAD.23 O{16O|1/ft=s; whereas the acceleration of […]
978-0073380308 Chapter 10 Solution Manual Part 1
Dynamics 2e 2059 Chapter 10 Solutions Problem 10.1 The radar dish can rotate about the vertical ´ axis at rate !1 and about the horizontal y axis (not shown in the figure) at rate P ✓ . The distance between […]
978-0073380308 Chapter 10 Solution Manual Part 10
Dynamics 2e 2149 Problem 10.41 The uniform bar AB of length L and mass m is attached to the T-bar support by a frictionless pin at A . The mass of the T-bar is negligible, and it rotates freely in […]
978-0073380308 Chapter 10 Solution Manual Part 11
Dynamics 2e 2159 we are viewing the bar AB in the plane of the angle ˇ , the spring force Fs has a component .Fs/k in that plane and a component .Fs/? perpendicular to that plane. Fortunately, the work of […]
978-0073380308 Chapter 10 Solution Manual Part 12
Dynamics 2e 2169 Problem 10.49 The thin uniform disk of radius R and mass m is mounted on the horizontal shaft, such that the mass center of the disk is on the axis of rotation. Due to an error in […]
978-0073380308 Chapter 10 Solution Manual Part 13
Dynamics 2e 2179 Problem 10.54 The L-shaped bar OCD is pin-connected at O to the vertical bar AB . The segments OC and CD are uniform, and each has mass m and length L . The bar AB rotates about […]
978-0073380308 Chapter 10 Solution Manual Part 14
Dynamics 2e 2189 Problem 10.58 The uniform sphere of mass m and radius R can spin freely relative to the shaft AB , whose mass is negligible. The shaft AB precesses about the vertical axis with constant angular speed !0 […]
978-0073380308 Chapter 10 Solution Manual Part 15
Dynamics 2e 2199 Problem 10.65 The shaft AB rotates with angular speed !0.t/ about the vertical axis. The uniform thin disk CD of radius R is rigidly attached to the end of the hori- zontal arm OG , which is […]
978-0073380308 Chapter 10 Solution Manual Part 16
2210 Solutions Manual Substituting Eqs. (??) and (??) into Eq. (??), we obtain vAO{DP ˇpd2Ch2O{Cd.` R/ pd2Ch2P ˇh!ACR!dO|h.` R/ pd2Ch2P ˇCd! AO k: Equating components and solving the resulting three scalar equations for vA,!A, and P ˇ, we obtain vADdR!d […]
978-0073380308 Chapter 10 Solution Manual Part 2
Dynamics 2e 2069 Problem 10.7 The bent arm rotates with angular speed !arm and angular accel- eration ˛arm in the directions shown. The wheel of radius R with center at A rotates relative to the bent arm as it rolls […]
978-0073380308 Chapter 10 Solution Manual Part 3
Dynamics 2e 2079 D⇣R ``P ✓2⌘⇣cos ✓O{Csin ✓O k⌘C⇣`R ✓C2P `P ✓⌘⇣sin ✓O{Ccos ✓O k⌘ Dh⇣R ``P ✓2⌘cos ✓C⇣`R ✓C2P `P ✓⌘sin ✓iO{ Ch⇣R ``P ✓2⌘sin ✓C⇣`R ✓C2P `P ✓⌘cos ✓iO k; Substituting everything into the expression for EaB, we […]
978-0073380308 Chapter 10 Solution Manual Part 4
Dynamics 2e 2089 0:9063vAD0:5917!ABx 3:000!AB´;(8) 0:4226vAD2:269!ABx C3:000!ABy 20:00: (9) These three equations contain four unknowns, that is !ABx , !ABy , !AB´ , and vA . Fortunately, there is one thing that we have not taken into account—any rotation of […]
978-0073380308 Chapter 10 Solution Manual Part 5
Dynamics 2e 2099 positive direction defined by a positive rotation of the angle ˇ . The collar A is constrained to rotate in the direction OuD=C , so we can write it as E!AD!AOuD=C D!A⇣cos ✓O|Csin ✓O k⌘D0:9063!AO|C0:4226!AO k: (6) […]
978-0073380308 Chapter 10 Solution Manual Part 6
Dynamics 2e 2109 Problem 10.25 Rod AB is attached to the collar at B by a ball joint and to the slider at A by a clevis joint. Collar A slides along the fixed bar OD , which lies in […]
978-0073380308 Chapter 10 Solution Manual Part 7
Dynamics 2e 2119 ˛ABy Dhh2L2 AB R2!2 d L2 AB L2 AB d2h23=2 ; AB R2!2 d of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the permission […]
978-0073380308 Chapter 10 Solution Manual Part 8
Dynamics 2e 2129 0D.R `/ ˛AB´ C!ABx!ABy Ch˛ABx C!ABy !AB´Cd!2 ABx C!2 AB´; 0Dh⇣!2 ABx C!2 ABy ⌘C.R `/ ˛ABy !ABx !AB´d˛ABx C!ABy !AB´: We obtain the fourth equation by writing that the angular acceleration of bar AB must be […]
978-0073380308 Chapter 10 Solution Manual Part 9
Dynamics 2e 2139 Problem 10.37 The angled bar CDE is rigidly attached to the horizontal shaft AB , which can rotate freely in the bearings at A and B . The system is released from rest when the segment DE […]
978-0073380308 Chapter 2 Solution Manual Part 1
Chapter 2 Solutions Problem 2.1 If Evavg is the average velocity of a point P over a given time interval, is jEvavgj , the magnitude of the average velocity, equal to the average speed of Pover the time interval in […]
978-0073380308 Chapter 2 Solution Manual Part 10
120 Solutions Manual Problem 2.78 As we will see in Chapter 3, the acceleration of a particle of mass m suspended by a linear spring with spring constant k and unstretched length L0 (when the spring length is equal to […]
978-0073380308 Chapter 2 Solution Manual Part 11
130 Solutions Manual Problem 2.85 The spool of paper used in a printing process is unrolled with velocity vp and acceleration ap . The thickness of the paper is h, and the outer radius of the spool at any instant […]
978-0073380308 Chapter 2 Solution Manual Part 12
140 Solutions Manual Problem 2.92 An airplane flying horizontally at elevation hD60 m and at a constant speed v0D120 km=h drops a package P when passing over point O . Determine the time it takes for the package to hit […]
978-0073380308 Chapter 2 Solution Manual Part 13
150 Solutions Manual Problem 2.102 Suppose that you can throw a projectile at a large enough v0 so that it can hit a target a distance R downrange. Given that you know v0 and R , determine the general expressions […]
978-0073380308 Chapter 2 Solution Manual Part 14
160 Solutions Manual Problem 2.110 The jaguar A leaps from O at speed v0 and angle ˇ relative to the incline to intercept the panther B at C . The distance along the incline from O to C is R […]
978-0073380308 Chapter 2 Solution Manual Part 15
170 Solutions Manual Problem 2.116 With reference to Probs. 2.113 and 2.115, assume that an experiment is conducted so that the measured value of xI is 10% smaller than what is predicted in the absence of viscous drag. Find the […]
978-0073380308 Chapter 2 Solution Manual Part 16
180 Solutions Manual Problem 2.124 Consider the four points whose positions are given by the vectors ErAD 2O{C0O km , ErBD2O{C1O km , ErCD2O{C2O km , and ErDD2O{C3O km . Knowing that the magnitude of these vectors is constant and […]
978-0073380308 Chapter 2 Solution Manual Part 17
190 Solutions Manual of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the permission of McGraw-Hill, is prohibited. CR ✓r.sin ✓O{Ccos ✓O|/P ✓2r.cos ✓O{Csin ✓O| /: (7) Collecting […]
978-0073380308 Chapter 2 Solution Manual Part 18
200 Solutions Manual Problem 2.141 A particle P is moving along the curve C , whose equation is given by y2x2.x 1/.2x 3/ D4x2Cy22x2; at a constant speed vc . For any position on the curve C for which the […]
978-0073380308 Chapter 2 Solution Manual Part 19
210 Solutions Manual Problem 2.151 The position of the piston C , as a function of the crank angle and the lengths of the crank AB and connecting rod BC , is given by yCDRcos C Lp1.R sin =L/2 […]
978-0073380308 Chapter 2 Solution Manual Part 2
40 Solutions Manual Problem 2.11 The position of a car as a function of time t, with t>0and expressed in seconds, is Er.t/ DŒ.5:98t2C0:139t30:0149t4/O{C.0:523t2C0:0122t 30:00131t4/O|çft: Determine the velocity, speed, and acceleration of the car for tD15 s. of McGraw-Hill, and […]
978-0073380308 Chapter 2 Solution Manual Part 20
220 Solutions Manual Problem 2.160 Particles A and B are moving in the plane with the same constant speed v , and their paths are tangent at P . Do these particles have zero acceleration at P ? If not, […]
978-0073380308 Chapter 2 Solution Manual Part 21
230 Solutions Manual Problem 2.168 A water jet is ejected from the nozzle of a fountain with a speed v0D12 m=s . Letting ˇD33ı , determine the rate of change of the speed of the water particles as soon as […]
978-0073380308 Chapter 2 Solution Manual Part 22
240 Solutions Manual of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the permission of McGraw-Hill, is prohibited. From the problem figure, we have that ds Dqdx2Cdy2:(5) Since […]
978-0073380308 Chapter 2 Solution Manual Part 23
250 Solutions Manual Problem 2.186 At a given instant, the merry-go-round is rotating with an angular velocity !D18 rpm . When the child is 0:45 m away from the spin axis, determine the second derivative with respect to time of […]
978-0073380308 Chapter 2 Solution Manual Part 24
260 Solutions Manual Problem 2.196 A micro spiral pump consists of a spiral channel attached to a stationary plate. This plate has two ports, one for fluid inlet and another for outlet, the outlet being farther from the center of […]
978-0073380308 Chapter 2 Solution Manual Part 25
270 Solutions Manual P of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the permission of McGraw-Hill, is prohibited. where we have used the following numerical data: RrD187;500 […]
978-0073380308 Chapter 2 Solution Manual Part 26
280 Solutions Manual Problem 2.211 The collar is mounted on the horizontal arm shown, which is originally rotating with the angular velocity !0 . Assume that after the cord is cut, the collar slides along the arm in such a […]
978-0073380308 Chapter 2 Solution Manual Part 27
290 Solutions Manual Problem 2.218 Reference frame A is translating relative to reference frame B with velocity EvA=B and acceleration EaA=B . A particle C appears to be stationary relative to frame A . What can you say about the […]
978-0073380308 Chapter 2 Solution Manual Part 28
300 Solutions Manual Problem 2.226 During practice, a player P punts a ball B with a speed v0D25 ft=s , at an angle ✓D60ı , and at a height h from the ground. Then the player sprints along a straight […]
978-0073380308 Chapter 2 Solution Manual Part 29
310 Solutions Manual Problem 2.233 At the instant shown, EvBD5O{m=s . If ✓D25ı , determine the speed of A relative to B in order for A to travel only in the vertical direction while sliding over B. Solution Using the […]
978-0073380308 Chapter 2 Solution Manual Part 3
50 Solutions Manual where, referring to the problem statement, x.t/ Dx0⇥sin.2⇡!t/ 3sin.⇡!t /⇤:(5) of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the permission of McGraw-Hill, is prohibited. […]
978-0073380308 Chapter 2 Solution Manual Part 30
320 Solutions Manual Problem 2.242 The gun tackle shown is operated with the help of a horse. If the horse moves to the right at a constant speed of 7ft=s , determine the velocity and acceleration of B when the […]
978-0073380308 Chapter 2 Solution Manual Part 31
330 Solutions Manual Problem 2.252 A crate A is being pulled up an inclined ramp by a winch. The rate of winding of the cord is controlled so as to hoist the crate up the incline with a constant speed […]
978-0073380308 Chapter 2 Solution Manual Part 32
Problem 2.261 Referring to the problem of a robot arm catching an egg (Prob. 2.260), the strategy is that the arm and the egg must have the same velocity and the same position at the same time for the arm […]
978-0073380308 Chapter 2 Solution Manual Part 33
350 Solutions Manual Problem 2.271 A golfer chips the ball on a flat, level part of a golf course as shown. Letting ˛D23ı , ˇD41ı , and the initial speed be v0D6m=s , determine the x and y coordinates of […]
978-0073380308 Chapter 2 Solution Manual Part 34
360 Solutions Manual Problem 2.278 An airplane is being tracked by a radar station at A . At the instant tD0 , the following data is recorded: rD15 km , D80ı , ✓D15ı , PrD350 km=h , P D0:002 rad=s […]
978-0073380308 Chapter 2 Solution Manual Part 35
370 Solutions Manual of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the permission of McGraw-Hill, is prohibited. Recall that we have vsD800 m=s , vaD2 3vs , […]
978-0073380308 Chapter 2 Solution Manual Part 36
380 Solutions Manual Problem 2.291 A skater is spinning with her arms completely stretched out and with an angular velocity !D60 rpm . Letting rbD0:55 ft , and `D2:2 ft and neglecting the change in ! as the skater lowers […]
978-0073380308 Chapter 2 Solution Manual Part 37
390 Solutions Manual of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the permission of McGraw-Hill, is prohibited. where we have used the data vmax D2m=s and R0D3cm […]
978-0073380308 Chapter 2 Solution Manual Part 38
400 Solutions Manual Problem 2.305 Block B is released from rest at the position shown, and it has a constant acceleration downward a0D5:7 m=s2 . Determine the velocity and acceleration of block A at the instant that B touches the […]
978-0073380308 Chapter 2 Solution Manual Part 4
60 Solutions Manual Problem 2.27 Find the x and y components of the acceleration in Example 2.3 (except for the plots) by differentiating the first of Eqs. (3) and the last of Eqs. (1) with respect to time and then […]
978-0073380308 Chapter 2 Solution Manual Part 5
70 Solutions Manual of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the permission of McGraw-Hill, is prohibited. where, in obtaining the last of Eqs. (6), we have […]
978-0073380308 Chapter 2 Solution Manual Part 6
80 Solutions Manual Problem 2.40 The following four problems refer to a car traveling between two stop signs, in which the car’s velocity is assumed to be given by v.t/ DŒ9 9cos.2t=5/çm=s for 0t5⇡s. Determine the time at which the […]
978-0073380308 Chapter 2 Solution Manual Part 7
90 Solutions Manual Problem 2.50 Approximately 1 h 15 min into the movie King Kong (the one directed by Peter Jackson), there is a scene in which Kong is holding Ann Darrow (played by the actress Naomi Watts) in his […]
978-0073380308 Chapter 2 Solution Manual Part 8
100 Solutions Manual Problem 2.60 Referring to Example 2.8 on p. 56, and defining terminal velocity as the velocity at which a falling object stops accelerating, determine the skydiver’s terminal velocity without performing any integrations. Solution of McGraw-Hill, and must […]
978-0073380308 Chapter 2 Solution Manual Part 9
110 Solutions Manual Problem 2.70 Heavy rains cause a particular stretch of road to have a coefficient of friction that changes as a function of location. Specifically, mea- surements indicate that the friction coefficient has a 3% decrease per meter. […]
978-0073380308 Chapter 3 Solution Manual Part 1
406 Solutions Manual Chapter 3 Solutions Problem 3.1 Two curling stones A and B , with masses m and 4m , respectively, and initially at rest on the start line, are pushed by two identical forces Fover the distance d. […]
978-0073380308 Chapter 3 Solution Manual Part 10
496 Solutions Manual Problem 3.61 Continue Prob. 3.60 and using mathematical software, numerically solve the equations of motion. Use the same parameters and initial conditions that were used in Example 3.10, and compare your results with those presented in that […]
978-0073380308 Chapter 3 Solution Manual Part 11
506 Solutions Manual of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the permission of McGraw-Hill, is prohibited. where we have separated the variables t and Px , […]
978-0073380308 Chapter 3 Solution Manual Part 12
516 Solutions Manual P of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the permission of McGraw-Hill, is prohibited. where, in the last of Eqs. (6), we have […]
978-0073380308 Chapter 3 Solution Manual Part 13
526 Solutions Manual Problem 3.77 The wedge-shaped cart B is moving up and to the left with accel- eration aB . The coefficient of static friction between the crate and the cart is insufficient to prevent slipping between the two. […]
978-0073380308 Chapter 3 Solution Manual Part 14
536 Solutions Manual Problem 3.84 The package handling system is designed to launch the small pack- age of mass m from A , using a compressed linear spring of constant k . After launch, the package slides along the track […]
978-0073380308 Chapter 3 Solution Manual Part 15
546 Solutions Manual Problem 3.89 A pendulum with cord length LD6ft and a bob weighing 3lb is released from rest at an angle ✓i . Once the pendulum has swung to the vertical position (i.e., ✓D0 ), its cord runs […]
978-0073380308 Chapter 3 Solution Manual Part 16
556 Solutions Manual Problem 3.94 Consider a collar with mass m that is free to slide with no friction along a rotating arm, which has negligible mass. The system is initially rotating with an angular velocity !0 while the collar […]
978-0073380308 Chapter 3 Solution Manual Part 17
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the permission of McGraw-Hill, is prohibited. 566 Solutions Manual Let be the angle such that tan Ds , […]
978-0073380308 Chapter 3 Solution Manual Part 18
576 Solutions Manual of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the permission of McGraw-Hill, is prohibited. Lis such that P LD(0for tD0, 4ft=s for t1s:(6) For […]
978-0073380308 Chapter 3 Solution Manual Part 19
586 Solutions Manual Problem 3.117 Two identical balls, each of mass m , are connected by a string of neg- ligible mass and length 2l . A short string is attached to the middle of the string connecting the two […]
978-0073380308 Chapter 3 Solution Manual Part 2
416 Solutions Manual Problem 3.10 A hammer hits a mass m on the end of a metal bar. In Chapter 5, we will see that this imparts an instantaneous initial velocity v0 at xD0 to the mass. Treating the bar […]
978-0073380308 Chapter 3 Solution Manual Part 20
596 Solutions Manual Problem 3.122 A simple elevator consists of a 15;000 kg car A connected to a 12;000 kg counterweight B . Suppose that a failure occurs when the car is at rest and 50 m above its buffer, […]
978-0073380308 Chapter 3 Solution Manual Part 21
606 Solutions Manual Problem 3.127 The double pendulum shown consists of two particles with masses m1D7:5 kg and m2D12 kg connected by two inextensible cords of length L1D1:4 m and L2D2 m and negligible mass. If the system is released […]
978-0073380308 Chapter 3 Solution Manual Part 22
616 Solutions Manual of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the permission of McGraw-Hill, is prohibited. where, since PyB>0 , PyB coincides with vB , the […]
978-0073380308 Chapter 3 Solution Manual Part 23
626 Solutions Manual Problem 3.137 In the ride shown, a person A sits in a seat that is attached by a cable of length L to a freely moving trolley B of mass mB . The total mass of the […]
978-0073380308 Chapter 3 Solution Manual Part 24
636 Solutions Manual Problem 3.142 Two particles A and B , with masses mA and mB , respectively, are a distance r0 apart. Particle B is fixed in space, and A is initially at rest. Using Eq. (1.5) on p. […]
978-0073380308 Chapter 3 Solution Manual Part 25
646 Solutions Manual of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the permission of McGraw-Hill, is prohibited. We now turn to the determination of the radius of […]
978-0073380308 Chapter 3 Solution Manual Part 26
Dynamics 2e 657 Problem 3.155 A crate of mass m is thrown horizontally with speed vc onto an inextensible conveyor belt that is moving to the right at a constant speed vb . Treating the crate as a particle, knowing […]
978-0073380308 Chapter 3 Solution Manual Part 3
426 Solutions Manual of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the permission of McGraw-Hill, is prohibited. To determine the locomotive’s stopping distance, we recall that RxDPxd […]
978-0073380308 Chapter 3 Solution Manual Part 4
436 Solutions Manual of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the permission of McGraw-Hill, is prohibited. Computation. Substituting Eq. (3) into Eq. (1), and Eq. (4) […]
978-0073380308 Chapter 3 Solution Manual Part 5
446 Solutions Manual of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the permission of McGraw-Hill, is prohibited. where v is the speed of the weight so that […]
978-0073380308 Chapter 3 Solution Manual Part 6
456 Solutions Manual of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the permission of McGraw-Hill, is prohibited. We recall that RyDPyd Py=dy. Therefore, Eq. (5) can be […]
978-0073380308 Chapter 3 Solution Manual Part 7
466 Solutions Manual Problem 3.40 A 6lb collar is constrained to travel along a rectilinear and friction- less bar of length LD5ft . The springs attached to the collar are identical and are unstretched when the collar is at B […]
978-0073380308 Chapter 3 Solution Manual Part 8
476 Solutions Manual of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the permission of McGraw-Hill, is prohibited. Computation. Because T1 and T2 are equal, we see that […]
978-0073380308 Chapter 3 Solution Manual Part 9
486 Solutions Manual Problem 3.54 A partial cross section of an amusement park ride is shown. While the ride spins up to the angular speed !c , there is a small platform at F on which the person P stands. […]
978-0073380308 Chapter 4 Solution Manual Part 1
Dynamics 2e 667 Chapter 4 Solutions Problem 4.1 A rocket lifts off with an acceleration a . During liftoff, in terms of absolute values, is the work done on an astronaut by gravity larger than, equal to, or smaller than […]
978-0073380308 Chapter 4 Solution Manual Part 10
Dynamics 2e 757 Problem 4.68 Spring scales work by measuring the displacement of a spring that supports both the platform and the object, of mass m , whose weight is being measured. Neglect the mass of the platform on which […]
978-0073380308 Chapter 4 Solution Manual Part 11
Dynamics 2e 767 of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the permission of McGraw-Hill, is prohibited. Computation. Substituting Eqs. (6) into Eqs. (2), we have T1D0and […]
978-0073380308 Chapter 4 Solution Manual Part 12
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the permission of McGraw-Hill, is prohibited. Dynamics 2e 777 Computation. Substituting Eqs. (6) into Eqs. (2), we have T1D0and […]
978-0073380308 Chapter 4 Solution Manual Part 13
Dynamics 2e 787 Problem 4.87 Consider the simple catapult shown in the figure with an 800 lb counter– weight A and a 150 lb projectile B . If the system is released from rest as shown, determine the speed of […]
978-0073380308 Chapter 4 Solution Manual Part 14
Dynamics 2e 797 of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the permission of McGraw-Hill, is prohibited. Kinematic Equations. Denoting by Lthe length of the cable, we […]
978-0073380308 Chapter 4 Solution Manual Part 15
Dynamics 2e 807 Problem 4.100 The weights B in the pulley systems shown are identical and are being lifted at the same constant speed v . Assume there are no energy losses in the pulleys. Is the power developed by […]
978-0073380308 Chapter 4 Solution Manual Part 16
Dynamics 2e 817 Problem 4.110 The motor B is used to raise and lower the crate C by a pulley system. At the instant shown, the cable is being retracted by the motor with the constant speed vcD5ft=s. The weight […]
978-0073380308 Chapter 4 Solution Manual Part 17
Dynamics 2e 827 Problem 4.117 Strength of materials tells us that if a load P is applied at the free end of a cantilevered beam, then the tip displacement ı is given by ıDPL3=.3EIcs/ , where L is the length […]
978-0073380308 Chapter 4 Solution Manual Part 18
838 Solutions Manual of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the permission of McGraw-Hill, is prohibited. )v2Dq.k1Ck2/ı2 1=m C2gı1.sin ✓kcos ✓/; (7) where we have account […]
978-0073380308 Chapter 4 Solution Manual Part 2
Dynamics 2e 677 Problem 4.10 Consider a 1500 kg car whose speed is increased by 45 km=h over a distance of 50 m while traveling up an incline with a 15% grade. Modeling the car as a particle, determine the […]
978-0073380308 Chapter 4 Solution Manual Part 3
Dynamics 2e 687 Problem 4.18 Two identical cars travel at a speed of 60 mph , one along a newly asphalt-paved straight and horizontal road and the other on a straight and horizontal dirt road. If brakes are applied and […]
978-0073380308 Chapter 4 Solution Manual Part 4
Dynamics 2e 697 Problem 4.25 An F/A-18 Hornet takes off from an aircraft carrier, using two separate propul- sion systems: its two jet engines and a steam-powered catapult. During launch, a fully loaded Hornet weighing about 50;000 lb goes from […]
978-0073380308 Chapter 4 Solution Manual Part 5
Dynamics 2e 707 Problem 4.31 Car bumpers are designed to limit the extent of damage to the car in the case of low-velocity collisions. Consider a 1420 kg passenger car impacting a concrete barrier while traveling at a speed of […]
978-0073380308 Chapter 4 Solution Manual Part 6
Dynamics 2e 717 Problem 4.41 Each of the two rubber tubes of the wrist rocket has an unstretched length L0D1ft . They are symmetrically pulled back so that `D3ft and then are released from rest. The pellet P that is […]
978-0073380308 Chapter 4 Solution Manual Part 7
Dynamics 2e 727 of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the permission of McGraw-Hill, is prohibited. Next, substituting the first two of Eqs. (2), Eqs. (3), […]
978-0073380308 Chapter 4 Solution Manual Part 8
Dynamics 2e 737 Problem 4.55 The arm AB can rotate freely about the pin at A . The spring with stiffness kD500 N=m is designed so that the system is in static equilibrium when ✓D0ı . Let LD18:2 cm , […]
978-0073380308 Chapter 4 Solution Manual Part 9
Dynamics 2e 747 Problem 4.62 While the stiffness of an elastic cord can be nearly constant over a large range of deformation, as a bungee cord is stretched, it tends to get less stiff as it gets longer. Assume a […]
978-0073380308 Chapter 5 Solution Manual Part 1
Chapter 5 Solutions Problem 5.1 An airplane performs a turn at constant speed and elevation so as to change its course by 180ı . Let A and B designate the beginning and endpoints of the turn. Assuming that the change […]
978-0073380308 Chapter 5 Solution Manual Part 10
940 Solutions Manual of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the permission of McGraw-Hill, is prohibited. Computation. Substituting (where appropriate) Eqs. (3)–(7) into Eqs. (1) and […]
978-0073380308 Chapter 5 Solution Manual Part 11
950 Solutions Manual Problem 5.66 An 8600 lb Ford Excursion A traveling with a speed vAD55 mph collides head-on with a 1990 lb Smart Fortwo B traveling in the oppo- site direction with a speed vBD35 mph . Determine the […]
978-0073380308 Chapter 5 Solution Manual Part 12
960 Solutions Manual of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the permission of McGraw-Hill, is prohibited. where V is the potential energy of the system, and […]
978-0073380308 Chapter 5 Solution Manual Part 13
970 Solutions Manual Problem 5.79 A golfer strikes a stationary ball B with a putter. At the time of impact, the putter’s head A is traveling horizontally with a speed v AD1:2 m=s . Model the impact as an unconstrained […]
978-0073380308 Chapter 5 Solution Manual Part 14
980 Solutions Manual of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the permission of McGraw-Hill, is prohibited. which is a system of four equations in the four […]
978-0073380308 Chapter 5 Solution Manual Part 15
990 Solutions Manual of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the permission of McGraw-Hill, is prohibited. We denote by ErA and ErB the final positions of […]
978-0073380308 Chapter 5 Solution Manual Part 16
1000 Solutions Manual Problem 5.95 Ball B is stationary when it is hit by an identical ball A as shown, with ˇD45ı . The preimpact speed of ball Ais v0D1m=s. Determine the postimpact velocity of ball A if the COR […]
978-0073380308 Chapter 5 Solution Manual Part 17
Problem 5.101 A 1:34 lb ball is dropped on a 10 lb incline with ˛D33ı . The ball’s release height is h1D5ft , and the height of the impact point relative to the ground is h2D0:3 ft . Assume that […]
978-0073380308 Chapter 5 Solution Manual Part 18
1020 Solutions Manual A ball is dropped from rest from a height h0D1:5 m. The impact between the ball and the floor has a COR eD0:92 . Find the formula that allows you to compute the rebound height hi of […]
978-0073380308 Chapter 5 Solution Manual Part 19
Problem 5.115 Particles A and B have masses mAD3kg and mBD1:3 kg , respectively. At the instant shown, the .x; y; ´/ coordinates of A and B are .3; 2; 0/ m and .3; 0; 4/ m , respectively. In […]
978-0073380308 Chapter 5 Solution Manual Part 2
860 Solutions Manual Problem 5.11 Consider an elevator that moves with an operating speed of 2:5 m=s . Suppose that a person who boards the elevator on the ground floor gets off on the fifth floor. Assuming that the elevator […]
978-0073380308 Chapter 5 Solution Manual Part 20
We now proceed to compute the moment of the forces acting on P with respect to O . Referring to the FBD to the right, consistently with the calculation carried out so far, we treat this problem as a projectile […]
978-0073380308 Chapter 5 Solution Manual Part 21
Problem 5.129 A collar with mass mD2kg is mounted on a rotating arm of negligible mass that is initially rotating with an angular velocity !0D1rad=s . The collar’s initial distance from the ´ axis is r0D 0:5 m and dD1 […]
978-0073380308 Chapter 5 Solution Manual Part 22
1060 Solutions Manual A disk A with mass m moves on a frictionless horizontal surface. The disk is attached to point O with an elastic cord. The disk follows the trajectory shown between ¿ and ¡ . The coordinates of […]
978-0073380308 Chapter 5 Solution Manual Part 23
Problem 5.142 Explorer 7 was launched on October 13, 1959, with an apogee altitude above the Earth’s surface of 1073 km and a perigee altitude of 573 km above the Earth’s surface. Its orbital period was 101:4 min. Using this […]
978-0073380308 Chapter 5 Solution Manual Part 24
Problem 5.149 The optimal way (from an energy standpoint) to transfer from one circular orbit about a primary body B to another circular orbit is via the so-called Hohmann transfer, which involves transferring from one circular orbit to another using […]
978-0073380308 Chapter 5 Solution Manual Part 25
Problem 5.155 One option when traveling to Mars from the Earth is to use a Hohmann transfer orbit like that described in Probs. 5.148–5.152. Assuming that the Sun is the primary gravitational influence and ignoring the gravitational influence of Earth […]
978-0073380308 Chapter 5 Solution Manual Part 26
1100 Solutions Manual A test is conducted in which an 80 kg person sitting in a 15 kg cart is propelled by the jets emitted by two household fire extinguishers with a combined initial mass of 18 kg . The […]
978-0073380308 Chapter 5 Solution Manual Part 27
1110 Solutions Manual obtain FRD270:4 kN: To determine the reaction moment at the base of the of the turbine’s support, we now consider the turbine’s FBD shown on the right. In this FBD, we have indicated the force acting on […]
978-0073380308 Chapter 5 Solution Manual Part 28
Problem 5.179 A Pelton impulse wheel, as shown in Fig. P5.136(a), is typically found in hydroelectric power plants and consists of a wheel with a series of buckets attached at the periphery. As shown in Fig. P5.136(b), water jets impinge […]
978-0073380308 Chapter 5 Solution Manual Part 29
Problem 5.185 A 31;000 lb truck A and a 3970 lb sports car B collide at an inter- section. At the moment of the collision, the truck and the sports car are traveling with speeds v AD60 mph and v […]
978-0073380308 Chapter 5 Solution Manual Part 3
870 Solutions Manual Problem 5.21 A 30;000 lb airplane is flying on a horizontal trajectory with a speed v0D650 mph when, at point A , it maneuvers so that at point B it is on a steady climb with ✓D40ı […]
978-0073380308 Chapter 5 Solution Manual Part 30
Using the results in Eqs. (1) and (3), letting mD722 kg denote the mass of the probe in our problem, the change in kinetic energy of the probe at aphelion is TjD1 2mv2 aphelion 1 2m.vcirc/2 Jupiter , which, using […]
978-0073380308 Chapter 5 Solution Manual Part 4
880 Solutions Manual of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the permission of McGraw-Hill, is prohibited. Balance Principles. Letting subscripts 2and 3denote quantities at times t2and […]
978-0073380308 Chapter 5 Solution Manual Part 5
890 Solutions Manual of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the permission of McGraw-Hill, is prohibited. Kinematic Equations. The laptop is released from rest. At t2 […]
978-0073380308 Chapter 5 Solution Manual Part 6
900 Solutions Manual of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the permission of McGraw-Hill, is prohibited. Using Eqs. (2) and (3), and recalling that mAD80;000 lb=g […]
978-0073380308 Chapter 5 Solution Manual Part 7
910 Solutions Manual Problem 5.46 Two persons A and B weighing 140 and 180 lb , respectively, jump off a floating platform (in the same direction) with a velocity relative to the platform that is completely horizontal and with magnitude […]
978-0073380308 Chapter 5 Solution Manual Part 8
920 Solutions Manual Computation. Substituting Eqs. (2)–(5) into Eq. (1), we obtain an equation in the only unknown vA2 whose solution is vA2 Dp2gh: (6) Since Ais moving in the positive xdirection in ¡, we then have EvA2 Dp2gh O{: […]
978-0073380308 Chapter 5 Solution Manual Part 9
930 Solutions Manual of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the permission of McGraw-Hill, is prohibited. Force Laws. All forces are accounted for on the FBD. […]
978-0073380308 Chapter 6 Solution Manual Part 1
2nd Edition Gary L. Gray The Pennsylvania State University Francesco Costanzo The Pennsylvania State University Michael E. Plesha University of Wisconsin–Madison Version: May 30, 2012 The McGraw-Hill Companies, Inc. Solutions Manual Engineering Mechanics: Dynamics Copyright © 2002–2012 Gary L. Gray, […]
978-0073380308 Chapter 6 Solution Manual Part 10
the spool. Since EvD=O D EvD EvO and OutD O{ , using the second of Eqs. (2) and the last of Eqs. (4), Eq. (5) becomes P `DvO1Cr RO{vOO{O{)P `Dr RvO:(6) Using vOD3m=s, rD1m, and RD2:2 m, we conclude that […]
978-0073380308 Chapter 6 Solution Manual Part 11
Expanding the cross products and equation coefficients, we obtain the following two scalar equations LAB .!AB C!BC /sin LCD !BC sin D LCD !CD sin ; (9) dAD!BC CLAB .!AB !BC /cos CLCD!BC cos DLCD!CD cos ; (10) for the […]
978-0073380308 Chapter 6 Solution Manual Part 12
Problem 6.84 For the slider-crank mechanism shown, let RD20 mm , LD80 mm , and HD38 mm. Determine the angular velocity of the crank OA when D20ı and the slider is moving downward at 15 m=s. Solution Using the given […]
978-0073380308 Chapter 6 Solution Manual Part 13
Problem 6.92 Let LD4ft , let point A travel parallel to the guide shown, and let Cbe the midpoint of the bar. If, when D0ı , A is accelerating to the right with aAD27 ft=s2 and EaCDE 0, determine P […]
978-0073380308 Chapter 6 Solution Manual Part 14
Problem 6.98 One way to convert rotational motion into linear motion and vice versa is by the use of a mechanism called the Scotch yoke, which consists of a crank C that is connected to a slider B by a […]
978-0073380308 Chapter 6 Solution Manual Part 15
Problem 6.105 A bar of length LD2:5 m is falling so that, when D34ı , vAD3m=s and aAD8:7 m=s2 . At this instant, determine the angular acceleration of the bar AB and the acceleration of point D, where Dis the […]
978-0073380308 Chapter 6 Solution Manual Part 16
Substituting in the solutions for !AB and !W, the angular acceleration of the wheel becomes E˛WD 984Cp2RaBC479 C202p2v2 343R2O k: This solutions manual, in any print or electronic form, remains the property of McGraw-Hill, Inc. It may be used and/or […]
978-0073380308 Chapter 6 Solution Manual Part 17
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the permission of McGraw-Hill, is prohibited. 1310 Solutions Manual CRP 2.Hsin /H2CR22HR cos .H cos R/2HR sin H2CR22HR […]
978-0073380308 Chapter 6 Solution Manual Part 18
Problem 6.124 A flood gate is controlled by the hydraulic cylinder AB . If the length of the cylinder is increased with a constant time rate of 2:5 ft=s , determine the angular acceleration of the gate when D0ı . […]
978-0073380308 Chapter 6 Solution Manual Part 19
Since point Ccan only move in the vertical direction, aCx D0, which implies L!2 BC sin R!2 AB cos L˛BC cos D0 )˛BC DL!2 BC sin R!2 AB cos Lcos Dtan R!AB sin Lcos 2 R!2 AB cos […]
978-0073380308 Chapter 6 Solution Manual Part 2
Problem 6.7 Letting RAD203 mm , RBD107 mm , RCD165 mm , and RDD140 mm , determine the angular acceleration of gears B , C , and D when gear A has an angular acceleration with magnitude j˛Aj D 47 […]
978-0073380308 Chapter 6 Solution Manual Part 20
Problem 6.134 Using polar coordinates, obtain the acceleration of point P of the the mini- example on p. 497; that is, obtain Eq. (6.56). Solution The polar coordinate system shown in the figure on the right rotates with the disk […]
978-0073380308 Chapter 6 Solution Manual Part 21
Problem 6.142 Bar AB is pinned to the fixed support at A , and the pin P is fixed to the disk at radius Ri . The disk with outer radius Ro rolls without slipping over the horizontal flat surface […]
978-0073380308 Chapter 6 Solution Manual Part 22
Problem 6.149 Bar AB rotates about point A with angular speed !1 and angular acceleration ˛1 , both in the directions shown. The curved bar BC is pinned to bar AB at B and rotates with angular speed !2 and […]
978-0073380308 Chapter 6 Solution Manual Part 23
2 2 0.10 0.05 0.00 0.05 0.10 rad v bar m s v bar 2 2 1.0 0.5 abar ms 0.0 0.5 1.0 rad 2 a bar 0 2 3 2 2 0.5 0.4 0.3 abar ms 0.2 0.1 0.0 […]
978-0073380308 Chapter 6 Solution Manual Part 24
Solving these two equations gives !CD DR!AB hCRD.R= h/!AB 1CR= h and PrB=C D0: (5) If Q is the contact point in common between the gear and the bar at this instant, the velocity of the bar at this instant […]
978-0073380308 Chapter 6 Solution Manual Part 25
Problem 6.161 At the instant shown, the wheel D rolls without slipping over a flat surface with an angular velocity !DD14 rad=s and an angular acceleration ˛DD1:1 rad=s2 . The X Y Z frame shown is inertial, whereas the xy´ […]
978-0073380308 Chapter 6 Solution Manual Part 26
Problem 6.169 At the instant shown, bar AB rotates with a constant angular velocity !AB D24 rad=s . Letting LD0:75 m and HD0:85 m, determine the angular acceleration of bar BC when bars AB and CD are as shown, i.e., […]
978-0073380308 Chapter 6 Solution Manual Part 27
where we have used the fact that PxDvCand P D!C. To find the acceleration of D, we can relate the acceleration of Dto that of Ousing EaDD EaOC EaDrel C2E ˝ EvDrel CP E ˝ ErD=O CE ˝E ˝ ErD=O […]
978-0073380308 Chapter 6 Solution Manual Part 3
Problem 6.16 The bent rod rotates about an axis connecting points Aand E. All bends in the rod are 90ı angles, and the given dimensions are hD21 cm , `D14:5 cm , dD21 cm , and bD7:6 cm . Express […]
978-0073380308 Chapter 6 Solution Manual Part 4
Problem 6.21 The rectangular block is attached to a rod that runs through the block along a diagonal. The rod is mounted in bearings at A and B that allow it to rotate about its own axis. The given dimensions […]
978-0073380308 Chapter 6 Solution Manual Part 5
Problem 6.28 The wheel A , with diameter dD5cm , is mounted on the shaft of the motor shown and is rotating with a constant angular speed !AD250 rpm . The wheel B , with center at the fixed point […]
978-0073380308 Chapter 6 Solution Manual Part 6
Problem 6.35 A bicycle has wheels 700 mm in diameter and a gear set with the dimensions given in the table below. Crank Sprocket C1 C2 C3 No. of Cogs 26 36 48 Radius (mm) 52.6 72.8 97.0 Cassette (9 […]
978-0073380308 Chapter 6 Solution Manual Part 7
Problem 6.43 A bar of length LD2:5 m is pin-connected to a roller at A . The roller is moving along a horizontal rail as shown with vAD5m=s . If, at a certain instant, D33ı and P D0:4 rad=s , […]
978-0073380308 Chapter 6 Solution Manual Part 8
Problem 6.52 A ball of radius RAD3in: is rolling without slip in a stationary spherical bowl of radius RBD8in: Assume that the ball’s mo- tion is planar. Express your answers using the component system shown. If the speed of the […]
978-0073380308 Chapter 6 Solution Manual Part 9
Problem 6.61 As the circular cam, whose center is at A rotates, it causes the follower B to move back and forth. The cam angle is , the radius of the cam is R , and the angular speed […]
978-0073380308 Chapter 7 Solution Manual Part 1
2nd Edition Gary L. Gray The Pennsylvania State University Francesco Costanzo The Pennsylvania State University Michael E. Plesha University of Wisconsin–Madison Version: July 6, 2012 The McGraw-Hill Companies, Inc. Solutions Manual Engineering Mechanics: Dynamics Copyright © 2002–2012 Gary L. Gray, […]
978-0073380308 Chapter 7 Solution Manual Part 10
Problem 7.47 The cutting arm of the paper cutter is pinned about a fixed axis at O , and its angle relative to the horizontal is measured by . A linear elastic torsional spring at O with constant kt […]
978-0073380308 Chapter 7 Solution Manual Part 11
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the permission of McGraw-Hill, is prohibited. 1516 Solutions Manual 3 2mgL D1 12 mL2˛TC1 12 mL2˛TC1 4mL2˛TCmL2˛T: ˛Tis found […]
978-0073380308 Chapter 7 Solution Manual Part 12
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the permission of McGraw-Hill, is prohibited. 1526 Solutions Manual AyDg.2mAB CmD/6g .3mAB C2mD/2L2 20mAB L2CmD5h2C12hL C24L2 C1 2ŒmAB LCmD.hC2L/ […]
978-0073380308 Chapter 7 Solution Manual Part 13
Computation. Substituting the force laws, the kinematic equations, and the expression for the mass moment of inertia into the Newton-Euler equations, we obtain the following system of three equations in the three unknowns N,aQx , and ˛c PkNDmaQx h 2˛c; […]
978-0073380308 Chapter 7 Solution Manual Part 15
Problem 7.74 The uniform thin rod AB couples the slider A , which moves along a frictionless guide, to the wheel B , which rolls without slip over a horizon- tal surface. While not required, the use of computer algebra […]
978-0073380308 Chapter 7 Solution Manual Part 16
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the permission of McGraw-Hill, is prohibited. 1566 Solutions Manual TD“kk2 GCRcos Ck2 Gsin 2Ck2 G#mg: Recalling that EaGD […]
978-0073380308 Chapter 7 Solution Manual Part 17
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the permission of McGraw-Hill, is prohibited. 1576 Solutions Manual FL 2cos NL 2sin D 1 12mL2R ; whose […]
978-0073380308 Chapter 7 Solution Manual Part 18
which can be rearranged to obtain the following equation of motion m 1Ck2 r2!RxCkx Dmg sin CkL0: G Computer Solution This equation of motion can now be integrated using mD200 kg , rD0:8 m, kGD0:65 m, D38ı , kD500 N=m […]
978-0073380308 Chapter 7 Solution Manual Part 19
1596 Solutions Manual Problem 7.93 The uniform ball of radius and mass m is gently placed in the bowl B with inner radius R and is released. The angle measures the position of the center of the ball […]
978-0073380308 Chapter 7 Solution Manual Part 2
Kinematic Equations. Since the system is translating with the trolley, there is no rotation and the y components of acceleration are zero, which implies aGy D0; aDy D0; ˛AB D0; and ˛CD0: In addition, since the composite body is translating, […]
978-0073380308 Chapter 7 Solution Manual Part 20
Problem 7.97 An SUV is pushing a large drum to the right with force P , using its front bumper. The drum has mass m and radius of gyration kG . The static and kinetic friction coefficients between the drum […]
978-0073380308 Chapter 7 Solution Manual Part 21
ΑBC “ !1#!L R“2“Cos#Θ$ !! L R“2#Cos#Θ$2“3%2 ΩAB 2; Parameters “&ΩAB &5700. 2Π 60.0 ,R& 48.5 1000. ,L& 141.0 1000. ,d& 36.4 1000. ,mD&0.439, (D&0.00144, mC&0.434‘; PlotBx“Plot#Bx%.Parameters,(Θ, 0, 2 Π), AxesLabel &(“Θ“, “Bx“)$ PlotBy“Plot*By%.Parameters,(Θ, 0, 2 Π), AxesLabel &+“Θ“, “By“,– […]
978-0073380308 Chapter 7 Solution Manual Part 22
which is a system of nine equations for the nine unknowns Ax , Ay , Bx , By , Cx , Cy , Dx , Dy , and ˛b . Solving this system of equations using WrD2500 lb , WbD100 […]
978-0073380308 Chapter 7 Solution Manual Part 23
Problem 7.110 A bowling ball is thrown onto a lane with a forward spin !0 and forward velocity v0 . The mass of the ball is m , its radius is r , its radius of gyration is given by […]
978-0073380308 Chapter 7 Solution Manual Part 24
Force Laws. The spring force can be expressed as FsDk.ıCı0/; where ı0is given and ıis the contribution to the stretch due when > 0. Kinematic Equations. Noticing that points B and D can move only in the vertical direction […]
978-0073380308 Chapter 7 Solution Manual Part 25
Kinematic Equations. Relating the acceleration of Dto that of A, we have EaDD EaAC E˛AB ErD=A !2 AB ErD=A D RxAO{CR O kL 2.sin O{cos O|/P 2L 2.sin O{cos O|/ DRxAL 2R cos CL 2P 2sin „ ƒ‚ […]
978-0073380308 Chapter 7 Solution Manual Part 26
Problem 7.124 Bars AB and BC are uniform with masses mAB D2kg and mBC D1kg , respectively. Their lengths are LD1:25 m and HD0:75 m. Bar BC is pin-connected to a fixed support at C that is a distance ıD0:2 […]
978-0073380308 Chapter 7 Solution Manual Part 3
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the permission of McGraw-Hill, is prohibited. 1436 Solutions Manual NBDPh `1 2CWd 2)NBD146:0 lb, aGx DgP WdD4:293 ft=s2; where […]
978-0073380308 Chapter 7 Solution Manual Part 4
Now that we have determined .Fm/to , we can add lift to our model so that the Newton-Euler equations become XFxWTDmaGx ; XFyWLCF fC2Fmmg DmaGy ; XMGW2FmdF f.` d / T .h ı/ DIG˛p: Applying the unchanged force laws and […]
978-0073380308 Chapter 7 Solution Manual Part 5
Problem 7.22 The stationary excavator is vertically lifting the load at A with acceleration a0D2:5 m=s2 . If `D4 m, wD3:65 m, dD 0:82 m, the mass of the load at A is mAD8300 kg , and the total mass […]
978-0073380308 Chapter 7 Solution Manual Part 6
Problem 7.26 The system shown lies in the vertical plane. The trolley A is moving to the right with a constant acceleration aA . Attached to the trolley by a pin is a thin uniform bar AB of mass m […]
978-0073380308 Chapter 7 Solution Manual Part 7
Problem 7.31 The uniform disk of radius RD0:8 ft and weight WD20 lb is pin- connected to the link AB and is pulled on its periphery by a force P via a rope that is wrapped around the disk. The […]
978-0073380308 Chapter 7 Solution Manual Part 8
Problem 7.37 The composite body lies in the vertical plane and is rotating with angular speed !bD11 rad=s at the instant shown. The mass of the disk D is mbD4kg , the mass of the bar AB is mAB D1:5 […]
978-0073380308 Chapter 7 Solution Manual Part 9
Problem 7.42 The driveway gate is hinged at its right end and can swing freely in the horizontal plane. The gate is pushed open by the force P that always acts perpendicular to the plane of the gate at point […]
978-0073380308 Chapter 8 Solution Manual Part 1
Chapter 8 Solutions Problem 8.1 A conveyor is moving cans at a constant speed v0 when, to pro- ceed to the next step in packaging, the cans are transferred onto a stationary surface at A . The cans each have […]
978-0073380308 Chapter 8 Solution Manual Part 10
Force Laws. Due to the choice of datum, V1DWAB .1 2lCLld/WBD Œd .L l/=2çWcıD125:2 ftlb .120:0 lb/ı; (4) V2D0; (5) where we have used the following numerical data: WAB D20 lb , lD11:6 ft , LD15:7 ft , dD2:58 ft […]
978-0073380308 Chapter 8 Solution Manual Part 11
Using the (full precision) values of IG and IQ in Eqs. (3), and recalling that mSD4:2 kg , mAB D7kg , gD9:81 m=s2,RD0:6 m, LD1:75 m, and ✓1D69ı, we can evaluate vB2 to obtain vB2 D2:205 m=s; As far as […]
978-0073380308 Chapter 8 Solution Manual Part 12
1768 Solutions Manual Force Laws. To evaluate the potential energy of the spring, we need to intergrate the expression of the moment with respect to ✓ . To do so, we refer to the figure on the right, and we […]
978-0073380308 Chapter 8 Solution Manual Part 13
1778 Solutions Manual The uniform thin pin-connected bars AB , BC , and CD have masses mAB D2:3 kg , mBC D3:2 kg , and mCD D5:0 kg , respectively. In addition, RD0:75 m, LD1:2 m, and HD1:55 m. When […]
978-0073380308 Chapter 8 Solution Manual Part 14
Problem 8.77 The rear-wheel-drive car can go from rest to 60 mph in tD8 s. Assume that the wheels are all identical and that their geometric centers coincide with their mass centers. Let Mrear be the average moment applied to […]
978-0073380308 Chapter 8 Solution Manual Part 15
Problem 8.84 A uniform disk of mass mD20 kg and radius RD0:75 m is being pulled to the left with a constant horizontal force P by the cord wrapped around it. Assume that the disk starts from rest and that […]
978-0073380308 Chapter 8 Solution Manual Part 16
Problem 8.90 A uniform disk W of radius RWD7mm and mass mWD0:15 kg is connected to point O via the rotating arm OC . Disk W also rolls without slip over the stationary cylinder S of radius RSD15 mm . […]
978-0073380308 Chapter 8 Solution Manual Part 17
1818 Solutions Manual a Cartesian coordinate system with origin at the center of pulley D and with axes x and y. We have labeled P the point on the spool at which the cord comes off the spool. We recall […]
978-0073380308 Chapter 8 Solution Manual Part 18
1828 Solutions Manual !DriO| , respectively. Since the cord is inextensible and the cord does not slip relative to the pulleys, we must have EvBDEvQD!DroO| and EvEDEvHD!DriO| . We now observe that EvADvCy O| because pulley P moves with the […]
978-0073380308 Chapter 8 Solution Manual Part 19
Since the ballast is modeled as a particle at a distance B from the spin axis, applying the parallel axis theorem, we have IGCDmCb2DmC m2 B`2 4.mBCmC/2:(4) Since B is modeled as a uniform bar and its mass center E […]
978-0073380308 Chapter 8 Solution Manual Part 2
Computation. Substituting Eqs. (2)–(5) into Eq. (1), we have 0D3 2mgL C17 24 mL2!2 b2 )!b2 D6rg 17L:(6) Recalling that gD32:2 ft=s2and LD5ft, we can evaluate the above expression to obtain !b2 D3:693 rad=s: This solutions manual, in any print […]
978-0073380308 Chapter 8 Solution Manual Part 20
1848 Solutions Manual Some pipe sections are gently nudged from rest down an incline and roll without slipping all the way to a step of height b . Assume that each pipe section does not slide or rebound against the […]
978-0073380308 Chapter 8 Solution Manual Part 21
1858 Solutions Manual Consider the impact-relevant FBD of a car involved in a collision. Assume that, at the time of impact, the car was stationary. In addition, assume that the impulsive force F , with line of action ` , […]
978-0073380308 Chapter 8 Solution Manual Part 22
Computation. Substituting Eqs. (6) and (5) into Eqs. (1), (2), and (4), and taking into account Eq. (3), we have v0cos ˇDvC Gx; Œ.`=2/ dçv0sin ˇD1 12 `2!C bŒ.`=2/ dçvC Gy ; vC Gy C!C bŒ.`=2/ dçDev0sin ˇ; (7) which […]
978-0073380308 Chapter 8 Solution Manual Part 23
Force Laws. Due to our choice of datum, V1DmgŒ.d Cı/ sin ˇChçand V2Dmgh: (6) Kinematic Equations. The ring is released from rest, so !r1 D0: (7) Computation. Substituting Eqs. (4)–(7) into Eq. (3), we have mgŒ.d Cı/ sin ˇChçDmr2!2 r2 […]
978-0073380308 Chapter 8 Solution Manual Part 24
Problem 8.132 A uniform thin ring A and a uniform disk B roll without slip as shown. Letting TA and TB be the kinetic energies of A and B , respectively, if the two objects have the same mass and […]
978-0073380308 Chapter 8 Solution Manual Part 25
Problem 8.139 Consider Prob. 8.87 on p. 631 in which an eccentric wheel B is spun from rest under the action of a known torque M . In that problem, it was said that the wheel was in the horizontal […]
978-0073380308 Chapter 8 Solution Manual Part 3
Problem 8.17 A door AB weighing 80 lb is pinned at A and swings in the horizontal plane. The spring CD has stiffness k and is unstretched when ✓D0ı . Let LD1:5 ft and hD0:5 ft. If the door is […]
978-0073380308 Chapter 8 Solution Manual Part 4
1688 Solutions Manual An electric motor drawing 15 kW and with an efficiency of 85 % lifts a 400 kg crate B with a constant speed vc . Pulley A has radius rpD15 cm , and the center of mass […]
978-0073380308 Chapter 8 Solution Manual Part 5
Problem 8.29 A 14 lb bowling ball is thrown onto a lane with a backspin angular speed !0D10 rad=s and forward velocity v0D17 mph . After a few seconds, the ball starts rolling without slip and moving forward with a […]
978-0073380308 Chapter 8 Solution Manual Part 6
Computation. Substituting Eqs. (2)–(5) into Eq. (1), we have kmgdR cos ✓=⇢D1 2m.k2 GC⇢2/.v2 G2=⇢2/mgd sin ✓)vG2 Ds2gd⇢.⇢sin ✓kRcos ✓/ k2 GC⇢2: Recalling that gD32:2 ft=s2 , dD10 ft , ⇢D4ft , ✓D30ı , kD0:25 , RD6ft , and kGD5ft […]
978-0073380308 Chapter 8 Solution Manual Part 7
1718 Solutions Manual A payload B of mass mBD50 kg is lifted via the pulley system shown by the application of a constant force FD300 N. The pulleys are identical and can be modeled as uniform disks of radius rpD10 […]
978-0073380308 Chapter 8 Solution Manual Part 8
1728 Solutions Manual A spool of mass msD150 kg and inner and outer radii ⇢D0:8 m and RD1:2 m, respectively, is connected to a counterweight A of mass mAD50 kg by a pulley system whose cord, at one end, is […]
978-0073380308 Chapter 8 Solution Manual Part 9
Computation. Substituting Eqs. (2)–(4) and the last three of Eqs. (5) in Eq. (1), we have mg.R `1 2h/ C.U1-2/nc D1 2mv2 G2 C1 24 m.h2Cb2/v2 .R `1 2h/2;(6) which can be solved for .U1-2/nc to obtain .U1-2/nc D1 2mv2 […]
978-0073380308 Chapter 9 Solution Manual Part 1
Dynamics 2e 1923 Chapter 9 Solutions Problem 9.1 Show that Eq. (9.15) is equivalent to Eq. (9.3) if CDpA2CB2and tan DA=B. where we have use the identity that if tan DA=B , then cos DB=pA2CB2 . Therefore, rewriting the expression […]
978-0073380308 Chapter 9 Solution Manual Part 10
Problem 9.55 A module with sensitive electronics is mounted on a panel that vibrates due to excitation from a nearby diesel generator. To prevent fatigue failure, the module is placed on vibration-absorbing mounts. The displacement of the panel is measured […]
978-0073380308 Chapter 9 Solution Manual Part 11
Dynamics 2e 2019 Problem 9.59 Consider a simple viscously damped harmonic oscillator governed by Eq. (9.45), and analyze the case in which the damping coefficient c is negative. Calculate the general expression for the response (without taking into account specific […]
978-0073380308 Chapter 9 Solution Manual Part 13
Dynamics 2e 2039 Problem 9.68 A delicate instrument of mass m must be isolated from excessive vibration of the ground, which is described by the function u.t/ D Asin !0t . To do so, we need to design a vibration […]
978-0073380308 Chapter 9 Solution Manual Part 14
Dynamics 2e 2049 Problem 9.74 When the electric motor is resting on the beam, the static de- flection of the beam is ısD15 mm . The motor is not perfectly balanced, so when it is operating the unbalanced mass is […]
978-0073380308 Chapter 9 Solution Manual Part 15
Dynamics 2e 2059 Computation. Substituting the kinematics relations into the force laws and then substituting the force laws into Eqs. (1) and (2), we obtain ok1 o of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or […]
978-0073380308 Chapter 9 Solution Manual Part 2
Dynamics 2e 1933 Problem 9.9 A block of mass mD3kg is in equilibrium when a hammer hits it, imparting a velocity v0 of 2m=s to it. If k is 120 N=m , determine the amplitude of the ensuing vibration and […]
978-0073380308 Chapter 9 Solution Manual Part 3
Dynamics 2e 1943 Problem 9.17 For the silicon nanowire in Example 9.2, use the lumped mass model shown, in which a point mass m is connected to a rod of negligible mass and length L that is pinned at O […]
978-0073380308 Chapter 9 Solution Manual Part 4
Dynamics 2e 1953 Problem 9.22 Grandfather clocks keep time by advancing the hands a set amount per oscillation of the pendulum. Therefore, the pendulum needs to have a very accurate period for the clock to keep time accurately. As a […]
978-0073380308 Chapter 9 Solution Manual Part 5
Dynamics 2e 1963 Problem 9.28 The U-tube manometer lies in the vertical plane and contains a fluid of density that has been displaced a distance y and oscillates in the tube. If the cross- sectional area of the tube […]
978-0073380308 Chapter 9 Solution Manual Part 6
Problem 9.32 Suppose that the equation of motion of a forced harmonic oscillator is given by RxC!2 nxD.F0=m/ cos !0t . Obtain the expression for the response of the oscillator, and compare it to the response presented in Eq. (9.36) […]
978-0073380308 Chapter 9 Solution Manual Part 7
Problem 9.38 Revisit Example 9.6 and discuss whether it is possible to obtain the equation of motion of the system via the energy method. Solution No, it is not possible since the system is not conservative and the energy method […]
978-0073380308 Chapter 9 Solution Manual Part 8
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the permission of McGraw-Hill, is prohibited. 1990 Solutions Manual Computation. Solving Eq. (1) for Tand substituting the result into […]
978-0073380308 Chapter 9 Solution Manual Part 9
Problem 9.49 For identical systems, one with damping and the other without, would you expect the period of damped vibration to be greater, less than, or equal to the period of undamped vibration? Explain your answer. Solution Equation (9.62) tells […]