1. The motor M pulls on the cables with a force F that has a magnitude which varies as shown on the graph. If the 15-kg crate is originally resting on the floor such that the cable tension is zero when the motor is turned on, determine the speed of the crate when t = 6s.
2. A stunt driver in car A travels in free flight off the edge of a ramp at C. At the point of maximum height he strikes car B. If the direct collision is perfectly plastic (e = 0), determine the required ramp speed vC at the end of the ramp C, and the approximate distance s where both cars strike the ground. Each car has a mass of 3.5 Mg. Neglect the size of the cars in the calculation.
3. A toboggan and rider, having a total mass of 150 kg, enter horizontally tangent to a 90° circular curve with a velocity VA and the angle of "descent," measured from the horizontal in a vertical x — z plane, at which the toboggan exits at B. Neglect friction in the calculation. The radius rB equals 57 m.
4. The projectile having a mass of m = 3 kg is fired from a cannon with a muzzle velocity of vO = 500 m/s. Determine the projectile's angular momentum about point O at the instant it is at the maximum height of its trajectory.
5. The two handcars A and B each have a mass of 80 kg. Both cars are initially at rest. Both cars start from rest before the man jumps. If the man C has a mass of 70 kg and jumps from A with a horizontal relative velocity of vC/A = 2 m/s and lands on B, determine the velocity of each car after the jump. Neglect the effects of rolling resistance.
6. Determine the velocities of blocks A and B 2 s after they are released from rest. Neglect the mass of the pulleys and cables.
7. A 0.6-kg brick is thrown into a 25-kg wagon which is initially at rest. If, upon entering, the brick has a velocity of 10 m/s as shown, determine the final velocity of the wagon.
8. A 30-lb block is initially moving along a smooth horizontal surface with a speed of v1 = 6 ft/s to the left. If it is acted upon by a force F, which varies in the manner shown, determine the velocity of the block in 15 s. The argument for the cosine is in radians.
9. A man wearing ice skates throws an 8-kg block with an initial velocity of 2 m/s, measured relative to himself, in the direction shown. If he is originally at rest and completes the throw in 1.5 s while keeping his legs rigid, determine the horizontal velocity of the man just after releasing the block. What is the average vertical reaction of both his skates on the ice during the throw? The man has a mass of 70 kg. Neglect friction and the motion of his arms.
10. Plates A and B each have a mass of 4 kg and are restricted to move along the frictionless guides. If the coefficient of restitution between the plates is e = 0.7, determine (a) the speed of both plates just after collision and (b) the maximum deflection of the spring. Plate A has a velocity of 4 m/s just before striking B. Plate B is originally at rest.
11. A girl having a weight of 40 lb slides down the smooth slide onto the surface of a 20-lb wagon. Determine the speed of the wagon at the instant the girl stops sliding on it. If someone ties the wagon to the slide at B, determine the horizontal impulse the girl will exert at C in order to stop her motion. Neglect friction and assume that the girl starts from rest at the top of the slide, A.
12. A hockey puck is traveling to the left with a velocity of v1 = 10 m/s when it is struck by a hockey stick and given a velocity of v2 = 20 m/s as shown. Determine the magnitude of the net impulse exerted by the hockey stick on the puck. The puck has a mass of 0.2 kg.
13. A rifle has a mass of 2.5 kg. If it is loosely gripped and a 1.5-g bullet is fired from it with a muzzle velocity of 1400 m/s, determine the recoil velocity of the rifle just after firing.
14. The two blocks A and B each have a mass of 500 g. The blocks are fixed to the horizontal rods and their initial velocity is 2 m/s in the direction shown. If a couple moment of M = 0.8 N • m is applied about CD of the frame, determine the speed of the block in 4 s. The mass of the supporting frame is negligible and its free to rotate about CD.
15. A boy, having a weight of 90 lb, jumps off a wagon with a relative velocity of vb/w = 6 ft/s. If the angle of jump is 30°, determine the horizontal velocity (vw)2 of the wagon just after the jump. Originally both the wagon and the boy are at rest. Also, compute the total average impulsive force that all four wheels of the wagon exert on the ground of the boy jumps off in t = 0.8s. The wagon has a weight of 20 lb.
16. A golf ball having a mass of 40 g is struck such that it has an initial velocity of 200 m/s as shown. Determine the horizontal and vertical components of the impulse given to the ball.
17. The drop hammer H has a weight of 900 lb and falls from rest. H has a weight of 900 lb and falls from rest h = 3 ft onto a forged anvil plate P that has a weight of 500 lb. The plate is mounted on a set of springs which have a combined stiffness of kT = 500 lb/ft. Determine (a) the velocity of P and H just after collision and (b) the maximum compression in the springs caused by the impact. The coefficient of restitution between the hammer and the plate is e = 0.6. Neglect friction along the vertical guide posts A and B.
18. A basket and its contents weigh 10 lb. A 20-lb monkey grabs the other end of the rope and very quickly (almost instantaneously) accelerates by pulling hard on the rope until he is moving with a constant speed of vm/r = 2 ft/s measured relative to the rope. The monkey then continues climbing at this constant rate relative to the rope for 3 seconds. How fast is the basket rising at the end of the 3 seconds? Neglect the mass of the pulley and the rope.
19. In cases of emergency, the gas actuator can be used to move a 75-kg block B by exploding a charge C near a pressurized cylinder of negligible mass. As a result of the explosion, the cylinder fractures and the released gas forces the front part ofthe cylinder, A, to move B and the floor is = 0.5, determine the impulse that the actuator must impart to B.
20. Two coins A and B have the initial velocities shown just before they collide at point O. If they have weights of WA = 13.2(10-3) lb and WB = 6.6(10-3) lb and the surface upon which they slide is smooth, determine their speed just after impact. The coefficient of restitution is e = 0.65.