Archives: Solution Manual

s g Solution 2.38 2 g tv dv akv dt dv dt kv =− =− = (see Art. C.10): − =1 0 g thv k () () − =  == = =  1 00 1tan g g gtan […]

Solution 2.1 0t, s –100 0 6 0t, s –100 200 2 0 a, m/s 6 2 2 20 100 50 See plots 40 100 0 : 40 100 0, 2.5 s A t 2.5 s, 20(2.5) 100(2.5) 50 75 […]

Solution 1.1 () 2 180 lb 801 N lb : 801 N 9.81 /s =   == Wmg m 5.59 slugs 4.4482 N 81.6 kg =  = m m Solution 1.2 () () () 2 2 1500 kg […]

Problem 21.63 The stepped disk weighs 20 lb and its moment of inertia is I=0.6 slug-ft2. It rolls on the horizontal surface. The disk is initially stationary with the spring unstretched, and at t=0 a constant force F=10 lb is […]

Problem 21.80 The moments of inertia of gears Aand Bare IA=0.014 slug-ft2and IB=0.100 slug-ft2. Gear Ais attached to a torsional spring with constant k= 2 ft-lb/rad. What is the frequency of angular vibrations of the gears relative to their equilibrium […]

Problem 21.1 In Active Example 21.1, suppose that the pulley has radius R=100 mm and its moment of inertia is I=0.005 kg-m2. The mass m=2 kg, and the spring constant is k=200 N/m. If the mass is displaced downward from […]

Problem 21.34 The mass of each slender bar is 1 kg. If the frequency of small vibrations of the system is 0.935 Hz, what is the mass of the object A? 350 mm 280 mm A 0.280 m, m=1 kg, […]

Problem 20.104 The inertia matrix of a rigid body in terms of a body-fixed coordinate system with its origin at the center of mass is [I]=41−1 12 0 −10 6 kg-m2. If the rigid body’s angular velocity is ω=10i−5j+ 10k(rad/s), […]

Problem 20.92 A 3-kg slender bar is rigidly attached to a 2-kg thin circular disk. In terms of the body-fixed coordinate system shown, the angular velocity of the composite object is ω=100i−4j+6k(rad/s). What is the object’s angular momentum about its […]

Problem 20.1 The airplane’s angular velocity relative to an earth-fixed reference frame, expressed in terms of the body-fixed coordinate system shown, is ω=0.62i+ 0.45j−0.23k(rad/s). The coordinates of point Aof the airplane are (3.6, 0.8, −1.2) m. What is the velocity […]

Problem 20.60* By substituting the components of HOfrom Eqs. (20.9) into the equation MO=dHOx dt i+dHOy dt j+dHOz dt k+||×HO derive Eqs. (20.12). Solution: M0=dHOx dt i+dHOy dt j+dHOz dt k +      ijk xyz HOx […]

Problem 19.38 The 8-kg slender bar is released from rest with θ=60◦. The horizontal surface is smooth. What is the bar’s angular velocity when θ=30◦. 2 m Solution: The bar’s potential energy is No horizontal force acts on the bar, […]

Problem 19.100 The ring gear is fixed. The mass and moment of inertia of the sun gear are mS= 22 slugs and IS=4400 slug-ft2. The mass and moment of inertia of each planet gear are mP=2.7 slugs and IP=65 slug-ft2. […]

Problem 19.68 The mass of the ship is 544,000 kg, and the moment of inertia of the vessel about its center of mass is 4 ×108kg-m2. Wind causes the ship to drift sideways at 0.1 m/s and strike the stationary […]

Problem 19.1 The moment of inertia of the rotor of 0.8 N-m on it. (a) How much work has the motor done on the rotor when the rotor has rotated through four revolu- tions? (b) What is the rotor’s angular […]

Problem 18.80 The mass of the object is 10 kg. Its moment of inertia about L1is 10 kg-m2. What is its moment of inertia about L2? (The three axes are in the same plane.) LL 1L2 0.6 m 0.6 m […]

Problem 18.54 The 2-kg slender bar and 5-kg block are released from rest in the position shown. What minimum coefficient of static friction between the block and the horizontal surface would be necessary for the block not to move when […]

Problem 18.112 A 2-kg box is subjected to a 40-N horizontal force. Neglect friction. (a) If the box remains on the floor, what is its accel- eration? (b) Determine the range of values of cfor which the box will remain […]

Problem 18.31 Points Band C lie in the x–yplane. The yaxis is vertical. The center of mass of the 18- kg arm BC is at the midpoint of the line from B 0.4k(rad/s). If you want to program the robot […]

Problem 18.1 A horizontal force F=30 lb is applied to the 230-lb refrigerator as shown. Friction is negligible. (a) What is the magnitude of the refrigerator’s accel- eration? (b) What normal forces are exerted on the refrigerator by the floor […]

Problem 17.166 In Problem 17.165, bar AB rotates with a constant angular velocity of 6 rad/s in the counterclockwise direction. Determine the acceleration of point D. y D C 8 in 12 in 4 in6 in8 in Solution: Use the […]

Problem 17.143 In Active Example 17.10, suppose that the merry-go-round has counterclockwise angular velocity ωand counterclockwise angular acceleration α. The person Ais standing still on the ground. Determine her acceleration relative to your reference frame at the instant shown. y […]

Problem 17.116 The large gear is fixed. The angu- lar velocity and angular acceleration of the bar AB are ωAB =2 rad/s and αAB =4 rad/s2. Determine the angu- lar acceleration of the bars CD and DE. 4 in 16 […]

17.71 is in the position shown here, use instantaneous centers to determine the horizontal velocity of B. A B 1 rad/s O Solution: The strategy is to determine the intersection of lines perpendicular to the motions at Aand B. The […]

Problem 17.96 The angular velocity and angular acceleration of bar AB are ωAB =4 rad/s and αAB = −6 rad/s2. Determine the angular accelerations of bars BC and CD. C 1 m 2 m AB D 1 m 1 m […]

Problem 17.42 The upper grip and jaw of the pli- ers ABC is stationary. The lower grip DEF is rotating at 0.2 rad/s in the clockwise direction. At the instant shown, what is the angular velocity of the lower jaw […]

Problem 17.1 In Active Example 17.1, suppose that at a given instant the hook His moving downward at 2 m/s. What is the angular velocity of gear Aat that instant? A 50 mm B 200 mm 100 mm Solution: The […]

Problem 16.116* It has been suggested that a heavy chain could be used to gradually stop an airplane that rolls past the end of the runway. A hook attached to the end of the chain engages the plane’s nose wheel, […]

Problem 16.41 The masses mA=mB. The surface is smooth. At t=0,A is stationary, the spring is unstretched, and Bis given a velocity v0toward the right. (a) In the subsequent motion, what is the velocity of the common center of mass […]

Problem 16.1 The 20-kg crate is stationary at time t=0. It is subjected to a horizontal force given as a function of time (in newtons) by F=10 +2t2. (a) Determine the magnitude of the linear impulse exerted on the crate […]

Problem 16.82 If the coefficient of restitution is the same for both impacts, show that the cue ball’s path after two banks is parallel to its original path. Solution: The strategy is to treat the two banks as two successive […]

Problem 15.118 The driver of a 3000-lb car moving at 40 mi/h applies an increasing force on the brake pedal. The magnitude of the resulting frictional force exerted on the car by the road is f=250 +6slb, where sis the […]

Problem 15.84 The mass of the ball is m=2 kg and the string’s length is L=1 m. The ball is released from rest in position 1. When the string is vertical, it hits the fixed peg shown. (a) Use conservation […]

Problem 15.44 The 2400-lb car is traveling 40 mi/h at position 1. If the combined effect of the aerodynamic drag on the car and the tangential force exerted on its wheels by the road is that they exert no net […]

Problem 15.1 In Active Example 15.1, what is the velocity of the container when it has reached the position s=2m? s A Problem 15.2 The mass of the Sikorsky UH-60A heli- copter is 9300 kg. It takes off vertically with […]

Problem 14.106* The 1/4-lb slider Ais pushed along the circular bar by the slotted bar. The circular bar lies in the vertical plane. The angular position of the slotted bar is θ=10t2rad. Determine the polar components of the total force […]

Problem 14.71 The circular disk lies in the horizontal plane and rotates with a constant counterclockwise angu- lar velocity of 4 rad/s. The 0.5-kg slider Ais supported horizontally by the smooth slot and the string attached at B. Determine the […]

Problem 14.33 The crane’s trolley at Amoves to the right with constant acceleration, and the 800-kg load moves without swinging. (a) What is the acceleration of the trolley and load? (b) What is the sum of the tensions in the […]

Problem 14.1 In Active Example 14.1, suppose that the coefficient of kinetic friction between the crate and the inclined surface is µk=0.12. Determine the dis- tance the crate has moved down the inclined surface at t=1s. 20⬚ Solution: There are […]

Problem 13.155 In Example 13.15, determine the velocity of the cam follower when θ=135◦(a) in terms of polar coordinates and (b) in terms of cartesian coordinates. rFollower y x u (a) θ=135◦,ω=dθ/dt =4rad/s, and α=0. r=0.15(1+0.5 cos θ)−1 =0.232 m. […]

Problem 13.131 If y=100 mm, dy dt =200 mm/s, and d2y dt2=0, what are the velocity and acceleration of Pin terms of normal and tangential components? P y dt =−y xdy dt =vx=−0.0707 m/s. The velocity of point Pis vp=ivx+jvy, […]

Problem 13.89 If y=150 mm, dy dt =300 mm/s, and d2y dt2=0, what are the magnitudes of the velocity and acceleration of point P? P y Solution: The equation for the location of the point Pis R2= x2+y2, from which […]

Problem 13.49 A sky diver jumps from a helicopter and is falling straight down at 30 m/s when her parachute opens. From then on, her downward acceleration is approximately a=g−cv2, where g=9.81 m/s2and cis a constant. After an initial “transient” […]

Problem 13.1 In Example 13.2, suppose that the vehi- cle is dropped from a height h=6m. (a) What is the downward velocity 1 s after it is released? (b) What is its downward velocity just before it reaches the ground? […]

Problem 12.1 The value of πis 3.1415962654….. If Cis the circumference of a circle and ris its radius, Solution: C=2πr ⇒r To four significant digits we have r C=0.1592 Problem 12.2 The base of natural logarithms is e= 2.718281828 … […]

Problem 11.33 The homogenous bar has weight W, and the spring is unstretched when the bar is vertical (˛D0). (a) Use potential energy to show that the bar is in equi- librium when ˛D0. (b) Show that the equilibrium position […]

Problem 11.1 Determine the reactions at A. Strategy: Subject the beam to three virtual motions: (1) a horizontal displacement υx; (2) a vertical displace- ment υy; and (3) a rotation υ about A. 300 N 2 m A 800 N-m […]

Problem 10.31 Model the ladder rung as a simply supported (pin-supported) beam and assume that the 750-N load exerted by the person’s shoe is uniformly distributed. Draw the shear force and bending moment diagrams. 200 mm 100 mm 375 mm […]

Problem 10.1 In Active Example 10.1, suppose that the distance from point Ato point Cis increased from 1 4Lto 1 2L. Draw a sketch of the beam with Cin its new position. Determine the internal forces amd moment at C. […]

Problem 10.85 The width of the gate (the dimension into the page) is 2 m and there is water of depth dD1m on one side. Atmospheric pressure patm D1ð105Pa and the mass density of the water is D1000 kg/m3. Determine […]