Archives: Solution Manual

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 […]

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 […]

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 […]

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 […]

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 […]

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 […]

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 […]

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 bŒ.`=2/ dçvC Gy ; vC Gy C!C bŒ.`=2/ dçDev0sin ˇ; (7) which […]

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 ` , […]

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 […]

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 […]

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 […]

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 […]

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 . […]

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 […]

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 […]

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 […]

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 […]

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 […]

Force Laws. Due to the choice of datum, V1DWAB .1 2lCLld/WBD Œd .L l/=2çWcıD125:2 ftlb .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 […]

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 […]

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 […]

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 […]

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 […]

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 […]

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 […]

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 […]

Computation. Substituting Eqs. (2)–(5) into Eq. (1), we have 0D3 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 […]

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 […]

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 […]

Kinematic Equations. Relating the acceleration of Dto that of A, we have EaDD EaAC E˛AB  ErD=A !2 AB ErD=A D RxAO{CR O kL 2.sin O{cos O|/P 2L 2.sin O{cos O|/ DRxAL 2R cos CL 2P 2sin  „ ƒ‚ […]

Force Laws. The spring force can be expressed as FsDk.ıCı0/; where ı0is given and ıis the contribution to the stretch due when  > 0. Kinematic Equations. Noticing that points B and D can move only in the vertical direction […]

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 […]

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 […]

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“,– […]

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 […]

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 […]

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 […]

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 […]

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“kk2 GCRcos Ck2 Gsin  2Ck2 G#mg: Recalling that EaGD […]

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 […]

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 PkNDmaQx h 2˛c; […]

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 L2CmD5h2C12hL C24L2 C1 2ŒmAB LCmD.hC2L/ […]

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 […]

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 […]

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 […]

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 […]

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 […]

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 […]

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 […]