Archives: Solution Manual

Now that we have determined .Fm/to , we can add lift to our model so that the Newton-Euler equations become XFxWTDmaGx ; XFyWLCF fC2Fmmg DmaGy ; XMGW2FmdF f.` d / T .h ı/ DIG˛p: Applying the unchanged force laws and […]

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 NBDPh `1 2CWd 2)NBD146:0 lb, aGx DgP WdD4:293 ft=s2; where […]

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, […]

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, […]

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 […]

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., […]

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´ […]

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 […]

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 […]

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 […]

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 […]

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 […]

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 […]

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 . […]

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 /H2CR22HR cos .H cos R/2HR sin  H2CR22HR […]

Substituting in the solutions for !AB and !W, the angular acceleration of the wheel becomes E˛WD 984Cp2RaBC479 C202p2v2 343R2O k: This solutions manual, in any print or electronic form, remains the property of McGraw-Hill, Inc. It may be used and/or […]

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 […]

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 […]

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 […]

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 […]

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 […]

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 `DvO1Cr RO{vOO{O{)P `Dr RvO:(6) Using vOD3m=s, rD1m, and RD2:2 m, we conclude that […]

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 […]

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 […]

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 , […]

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 […]

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 […]

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 […]

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 […]

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 […]

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, […]

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 […]

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 […]

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 […]

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 […]

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 […]

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 […]

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 […]

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 […]

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 […]

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 […]

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 […]

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 […]

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 […]

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 […]

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 […]

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 […]

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 […]

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 […]

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 […]