Archives: Solution Manual
Mechanical Engineering Chapter 18 Homework Gof Rolls Without Slipping determine Its Angular Velocity
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Mechanical Engineering Chapter 18 Homework If it is allowed to fall freely, determine the angle
952 18–41. The spool has a mass of 20 kg and a radius of gyration of kO=160 mm . If the 15-kg block A is released from rest, determine the distance the block must fall in order for the spool […]
Mechanical Engineering Chapter 18 Homework Mexerts Constant Force The Ropeif The 100kg
932 18–21. SOLUTION Ans.s=0.304 ft 0+(0.3)(s)=1 2a0.3 32.2 b(1.40)2+1 2c(0.06)2a0.3 32.2 bd(70)2 T1+©U1–2=T2 vG=(0.02)70 =1.40 ft>s A yo-yo has a weight of 0.3 lb and a radius of gyration If it is released from rest, determine how far it must […]
Mechanical Engineering Chapter 18 Homework The Block Fig Does Positive Work
912 18–1. SOLUTION Q.E.D.=1 2IIC v2 =1 2 A mr2 G>IC +IG B v2However mr2 G>IC +IG=IIC =1 2m(vrG>IC)2+1 2IGv2 T=1 2my2 G+1 2IGv2where yG=vrG>IC At a given instant the body of mass mhas an angular velocity and its mass […]
Mechanical Engineering Chapter 17 Homework The Disk Mass And Radius Rolls Without
902 17–111. 4 (0.4) m 3p SOLUTION For roll A. c(1) +©MA=IAa;T(0.09) =1 2(8)(0.09)2aA For roll B a(2) (3) +c©Fy=m(aG)y;T–8(9.81) =-8aB +©MO=©(Mk)O;8(9.81)(0.09) =1 2(8)(0.09)2aB+8aB(0.09) Kinematics: (4) also, (5) A +T B aO=aA(0.09) A +T B aB=aO+0.09aB caB Td=caO Td+caB(0.09) Td+[0] […]
Mechanical Engineering Chapter 17 Homework Since The Roller Required The Verge Slipping
891 *17–100. A force of F = 10 N is applied to the 10-kg ring as shown. If slipping does not occur, determine the ring’s initial angular acceleration, and the acceleration of its mass center, G. Neglect the thickness of […]
Mechanical Engineering Chapter 17 Homework The lightweight turbine consists of a rotor which
871 17–81. Ans: Ax=0 A =289 N y a = > 2 23.1 rad s SOLUTION a Solving, Ans. Ans. Ans.a=23.1 rad>s2 Ay=289 N Ax=0 ; +aFn=m(aG)n;Ax=0 +caFt=m(aG)t; 1400 –245.25 –Ay=25(1.5a) +aMA=IAa; 1.5(1400 –245.25) =c1 3(25)(3)2da Determine the angular acceleration […]
Mechanical Engineering Chapter 17 Homework If the bar is released from rest when it is vertical at
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Mechanical Engineering Chapter 17 Homework Fig Ausing This Result And Writing The
831 17–41. The smooth 180-lb pipe has a length of 20 ft and a negligible diameter. It is carried on a truck as shown. If the truck accelerates at a = 5 ft > s 2 , determine the normal […]
Mechanical Engineering Chapter 17 Homework Determine how far the door moves in 2 s
811 17–21. SOLUTION Ans. Ans.=4.45 kg #m2 =1 12 (3)(2)2+3(1.781 –1)2+1 12 (5)(0.52+12)+5(2.25 –1.781)2 IG=©IG+md2 y=©ym ©m=1(3) +2.25(5) 3+5=1.781 m =1.78 m 1m 0.5 m G 2m y O T he pendulum consists of the 3-kg slender rod and the […]
Mechanical Engineering Chapter 17 Homework Steel Has Specific Weight Of
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Mechanical Engineering Chapter 16 Homework Peg The Gear Slides Freely Along The
781 16–143. SOLUTION Gear Motion:The IC of the gear is located at the point where the gear and the gear rack mesh, Fig. a.Thus, Then, vB=vrB>IC =20(0.3) =6m>s: v=vO rO>IC =3 0.15 =20 rad>s Since the gear rolls on the […]
Mechanical Engineering Chapter 16 Homework The collar consists of two pin-connected slider
770 16–133. SOLUTION Reference Frame: The xyz rotating reference frame is attached to the impeller and coincides with the XYZ fixed reference frame at the instant considered, Fig. a.Thus, the motion of the xyz frame with respect to the XYZ […]
Mechanical Engineering Chapter 16 Homework The wheel rolls without slipping such that
750 *16–116. The disk has an angular acceleration a = 8 rad > s 2 and angular velocity v =3 rad>s at the instant shown. If it does not slip at A, determine the acceleration of point B. C A […]
Mechanical Engineering Chapter 16 Homework Ms Ans applying The Relative Acceleration
730 16–97. SOLUTION 5 0.1–x = 0.75 x x=0.01304 m vS= 0.75 0.01304 =57.5 rad>s d Ans. vA=57.5(0.05 –0.01304) =2.125 m>s vOA = 2.125 0.2=10.6 rad>s d Ans. If the hub gear H and ring gear R have angular velocities […]
Mechanical Engineering Chapter 16 Homework In each case show graphically how
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Mechanical Engineering Chapter 16 Homework About Fixed Axis For Link Ab Refer
690 *16–60. The slider block C moves at 8 m > s down the inclined groove. Determine the angular velocities of links AB and BC, at the instant shown. SOLUTION Rotation About Fixed Axis. For link AB, refer to Fig. […]
Mechanical Engineering Chapter 16 Homework Here, since acts in the positive rotational sense of
670 16–41. SOLUTION Here , and ,,,. Ans. Ans.–3=-0.3[sin 50°(a)+cos 50°(8.70)2]a=-50.5 rad>s2 –2=-0.3 sin 50°(v)v=8.70 rad>s u=50°u $=au #=vu #=vvy=-2m>s, ay=-3m>s2 y ## =ay=-0.3 A sin uu $+cos uu #2 B y #=vy=-0.3 sin uu v2m/s a3m/s 2 # y=0.3 […]
Mechanical Engineering Chapter 16 Homework Determine the angular velocity of the propeller in
650 16–21. The motor turns the disk with an angular velocity of v = ( 5t 2+ 3t ) rad > s, where t is in seconds. Determine the magnitudes of the velocity and the n and t components of […]
Mechanical Engineering Chapter 16 Homework The disk is driven by a motor such that the angular
630 16–1. SOLUTION Ans. Ans.aA=2(4)2+(8.45)2=9.35 m>s2 an=v2r=(3.25)2(0.8) =8.45 m>s2 az=ar=5(0.8) =4m>s2 vA=vr=3.25(0.8) =2.60 m>s a=5 rad>s2 v=3.25 rad>s t=0.5 s a=dv dt =10 t v=(5 t2+2) rad>s The angular velocity of the disk is defined by where tis in seconds. […]
Mechanical Engineering Chapter 15 Homework Assume that air has a constant density of
612 *15–132. Sand is deposited from a chute onto a conveyor belt which is moving at 0.5 m > s. If the sand is assumed to fall vertically onto the belt at A at the rate of 4 kg > […]
Mechanical Engineering Chapter 15 Homework Neglect the weight of the nozzle and the water within it
594 15–114. 30 60 45 The fire boat discharges two streams of seawater, each at a flow of and with a nozzle velocity of 50 ms. needed to secure the boat. The density of seawater is .rsw =1020 kg>m3 >0.25 […]
Mechanical Engineering Chapter 15 Homework If the attached cord is pulled down through the hole with a constant
574 15–95. Determine the angular momentum H p of the 6-lb particle about point P. SOLUTION Position and Velocity Vector. The coordinates of points A, B and P are A(–8, 8, 12) ft, B(0, 18, 0) ft and P(–8, 0, […]
Mechanical Engineering Chapter 15 Homework By considering the x and y motion of the marble from A to B
554 15–78. Using a slingshot, the boy fires the 0.2-lb marble at the concrete wall, striking it at B. If the coefficient of restitution between the marble and the wall is , determine the speed of the marble after it […]
Mechanical Engineering Chapter 15 Homework determine the maximum compression of the spring due
534 15–59. SOLUTION Conservation of Linear Momentum: The linear momentum of the system is conserved along the xaxis (line of impact). The initial speeds of the truck and car are and . By referring to Fig. a, (1) 5 A […]
Mechanical Engineering Chapter 15 Homework As Original Position Determine The Final Position
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Mechanical Engineering Chapter 15 Homework When the sand bag is dropped, the thrust
494 *15–20. The 200-lb cabinet is subjected to the force F=20(t+1) lb where t is in seconds. If the cabinet is initially moving to the left with a velocity of 20 ft > s, determine its speed when t=5 s. […]
Mechanical Engineering Chapter 15 Homework Impulse And Momentum 12 solving Eqs1 And 2
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Mechanical Engineering Chapter 14 Homework Solving For The Positive Root 02687
456 Ans: v=5.94 m>s N=8.53 N *14–80. When s=0 , the spring on the firing mechanism is unstretched. If the arm is pulled back such that s=100 mm and released, determine the speed of the 0.3-kg ball and the normal […]
Mechanical Engineering Chapter 14 Homework The Car And Its Contents Have Weight
437 14–61. SOLUTION Equations of Motion: By referring to the free-body diagram of the dragster shown in Fig. a, Kinematics: The velocity of the dragster can be determined from Power: Ans.= C 400(103)t D W P=F#v=20(103)(20 t) v=0+20 t=(20 t)m>s […]
Mechanical Engineering Chapter 14 Homework The 1000lb Elevator Hoisted The Pulley System
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Mechanical Engineering Chapter 14 Homework Work And Energy Which Acts The Direction
397 14–21. SOLUTION Block A: Block B: Use the system of both blocks. NA,NB,T, and Rdo no work. When , Also, 2vA=-vB |¢sA|=1ft|¢sB|=2ft 2¢sA=-¢sB 2sA+sB=l (0 +0) +60 sin 60°|¢sA|–40 sin 30°|¢sB|–3|¢sA|–3.464|¢sB|=1 2a60 32.2 bv2 A+1 2a40 32.2 bv2 B […]
Mechanical Engineering Chapter 14 Homework If it is originally at rest, determine the distance
377 14–1. SOLUTION Equation of Motion: Since the crate slides, the friction force developed between the crate and its contact surface is . Applying Eq. 13–7, we have Principle of Work and Energy: The horizontal component of force Fwhich acts […]
Mechanical Engineering Chapter 13 Homework Take The Earths Radius And
361 13–117. SOLUTION From Eq. 13–19, For and , Eliminating C, from Eqs. 13–28 and 13–29, 2a b2=2GMs h2 From Eq. 13–31, Thus, Q.E.D.T2=a4p2 GMsba3 4p2a3 T2h2=GMs h2 b2=T2h2 4p2a2 T= p h(2a)(b) 1 ra =-C+GMs h2 1 rp =C+GMs […]
Mechanical Engineering Chapter 13 Homework Needed Cause The Motion And The Normal
345 13–101. The ball of mass mis guided along the vertical circular path using the arm OA.If the arm has a constant angular velocity ,determine the angle at which the ball starts to leave the surface of the semicylinder. Neglect […]
Mechanical Engineering Chapter 13 Homework Determine The Force Must Exert The 05kg
325 Ans: u=37.7° SOLUTION Equation of Motion. The FBD of the bob at an arbitrary position u is shown in Fig. a. Here, it is required that T=0. ΣFt=mat; –2(9.81) cos =2at u at=–9.81 cos u ΣFn=man; 2(9.81) sin u=2 […]
Mechanical Engineering Chapter 13 Homework A girl having a mass of 25 kg sits at the edge of
305 13–61. At the instant the boy’s center of mass Gis momentarily at rest. Determine his speed and the tension in each of the two supporting cords of the swing when The boy has a weight of 60 lb. Neglect […]
Mechanical Engineering Chapter 13 Homework Neglect Friction Solution 15 Block F Sin
285 13–41. Block Ahas a mass and is attached to a spring having a stiffness kand unstretched length . If another block B, having a mass , is pressed against Aso that the spring deforms a distance d, determine the […]
Mechanical Engineering Chapter 13 Homework Mon The Cable Shown The Graph determine The
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Mechanical Engineering Chapter 13 Homework Block Weighs Lb Neglect The Mass The
245 13–1. The 6-lb particle is subjected to the action of its weight and forces and where tis in seconds. Determine the distance the ball is from the origin 2safter being released from rest. F3=5–2ti6lb,5t2i–4tj–1k6lb, F2=F1=52i+6j–2tk6lb, SOLUTION Equating components: Since […]
Mechanical Engineering Chapter 12 Homework Two Planes And Are Flying The Same
221 *12–212. SOLUTION The length lof cord is Taking the time derivative: (1) xC=6 ft/s 1 2[(8)2+xB 2]–1/2 2 xBxB+xC=0 ## # When AB = 50 ft, From Eq. (1) Ans.xB=-6.0783 =6.08 ft>s; 1 2[(8)2+(49.356)2]–1/2 2(49.356)(xB)+6=0 # # xB=2(50)2–(8)2=49.356 ft […]
Mechanical Engineering Chapter 12 Homework No portion of this material may be reproduced
233 *12–224. At the instant shown, car Ahas a speed of , which is being increased at the rate of as the car enters an expressway. At the same instant, car Bis decelerating at while traveling forward at . Determine […]
Mechanical Engineering Chapter 12 Homework The Peg Constrained Move The Slots The
181 SOLUTION Velocity. Using the chain rule, the first and second time derivatives of r can be determined. r=200(2 –cos ) u r # = # =5 #6 > 200 (sin u) u 200 (sin u) u mm s r […]
Mechanical Engineering Chapter 12 Homework No portion of this material may be reproduced, in any form or by any means
161 *12–152. A particle Ptravels along an elliptical spiral path such that its position vector ris defined by where tis in seconds and the arguments for the sine and cosine are given in radians.When determine the coordinate direction angles and […]
Mechanical Engineering Chapter 12 Homework The velocity of the train along the track can be determined by
141 12–133. A particle travels around a circular path having a radius of 50 m. If it is initially traveling with a speed of 10 m s and its speed then increases at a rate of determine the magnitude of […]
Mechanical Engineering Chapter 12 Homework If it then starts to increase its speed at where tis in
121 SOLUTION r=4(t–sin t) i+(2 t2–3)j v= dr dt =4(1 –cos t)i+(4 t)j v 0 t=1= 1.83879i + 4j v =2 + = > (1.83879)2 (4)2 4.40 m s Ans. u=tan–1 a 1.83879 b 4 =65.312° a u a=4 sin […]
Mechanical Engineering Chapter 12 Homework Also What The Corresponding Angle Which Should
101 *12–96. It is observed that the skier leaves the ramp Aat an angle with the horizontal. If he strikes the ground at B, determine his initial speed and the time of flight .tAB vA uA=25° SOLUTION Solving, Ans. Ans.tAB […]
Mechanical Engineering Chapter 12 Homework Here The Angle That The Tangent Makes
8 1 SOLUTION The total distance traveled is STot =SAB +SBC +SCA =20 a 2b 2 p + 202+302+(30 +20) =117.47 m The total time taken is tTot =tAB +tBC +tCA =5+8+10 =23 s Thus, the average speed is (vsp)avg […]
Mechanical Engineering Chapter 12 Homework Ans Using The Initial Time Function Can
6 1 SOLUTION v9s Graph. The v–s function can be determined by integrating v dv=a ds . For 0…s6100 ft , a–8 s–0 6–8 100 –0 = , a= e 1 f > – 50 s+8 ft s2 using the […]
Mechanical Engineering Chapter 12 Homework Draw The At Graph And Determine The
4 1 12–41. SOLUTION Thus Thus, When t = 2.145, v = vmax = 10.7 ft>s and h = 11.4 ft. Ans.t=t1+t2=7.48 s t2=5.345 s t1=2.138 s vmax =10.69 ft>s h=11.429 ft Ans: t=7.48 s. When t=2.14 s , v=vmax […]