65601. The 2-kg shaft CA passes through a smooth journal bearing at B. Initially, the springs, which are coiled loosely around the shaft, are unstretched when no force is applied to the shaft. In this position s = sª = 250 and the shaft is originally at rest. If a horizontal force of F = 5 kN is applied, determine the speed of the shaft at the instant s = 50 mm, sª = 450 mm. The ends of the springs are attached to the bearing at B and the caps at C and A.
65602. A boy twirls a 15-lb bucket of water in a vertical circle. If the radius of curvature of the path is 4 ft, determine the minimum speed the bucket must have when it is overhead at A so no water spills out.
65603. Determine the acceleration of block A when the system is released. The coefficient of friction and the weight of each block are indicated in the figure. Neglect the mass of the pulleys and cords.
65604. A tobbogan and rider have a total mass of 100 kg and travel down along the (smooth) slope defined by the equation y = 0.2x2. At the instant x = 8 m, the toboggan's speed is 4 m/s. At this point, determine the rate of increase in speed and the normal force which the toboggan exerts on the slope. Neglect the size of the toboggan and rider for the calculation.
65605. A block having a mass of 2 kg is placed on a a spring scale located in an elevator that is moving downward. If the scale reading, which measures the force in the spring, is 20 N, determine the acceleration of the elevator. Neglect the mass of the scale.
65606. The pendulum bob B has a weight of 5 lb and is released from rest in the position shown, =0°. Determine the tension in string BC just after the bob is released, = 0°, and also at the instant the bob reaches point D, = 45°.
65607. A truck T has a weight of 8,000 lb and is traveling along a portion of a road defined by the lemniscate r2 = 0.2(106) cos 2 , where r is measured in feet and is in radians. If the truck maintains a constant speed of vr = 4 ft/s, determine the magnitude of the resultant frictional force which must be exerted by all the wheels to maintain the motion when = 0.
65608. A smooth can C, having a mass of 2 kg, is lifted from a feed at A to a ramp at B by a forked rotating rod. If the rod maintains a constant angular motion of = 0.5 rad/s, determine the force which the rod exerts on the can at the instant = 30°. Neglect the effects of friction in the calculation. The ramp from A to B is circular, having a radius of 700 min.
65609. The spool, which has a weight of 2lb, slides along the smooth horizontal spiral rod, r = (2) ft, where is in radians. If its angular rate of rotation is constant and equals = 4 rad/s, determine the tangential force P needed to cause the motion and the normal force that the spool exerts on the rod at the instant = 90°.
65610. Each of the three barges has a mass of 30 Mg, whereas the tugboat has a mass of 12 Mg. As the barges are being pulled forward with a constant velocity of 4 m/s, the tugboat must overcome the frictional resistance of the water, which is 2 kN for each barge and 1.5 kN for the tugboat. If the cable between A and B breaks, determine the acceleration of the tugboat.
65611. A particle having a mass of 1.5 kg, moves along a three-dimensional path defined by the equations r = 94 + 3t) m, = (t2 + 2) rad, and z = (6 - t3) m, where t is in seconds, and the z-axis is vertical. Determine the r, , and z components of force which the path exerts on the particle when t = 2 s.
65612. Rod OA rotates counterclockwise with a constant angular rate of = 5 rad/s. The double collar B is pin-connected together such that one collar slides over the rotating rod and the other slides over the horizontal curved rod, of which the shape is a limacon described by the equation r - 1.5(2 - cos ) ft. If both collars weigh 0.75 lb, determine the normal force which the curved path exerts on one of the collars, and the force that OA exerts on the other collar at the instant = 90°.
65613. The 30-lb crate is being hoisted upward with a constant acceleration of 6 ft/s2. If the uniform beam AB has a weight of 200 lb, determine the components of reaction at A. Neglect the size and mass of the pulley at B.
65614. The 300-kg bar B, originally at rest, is being towed over a series of small rollers. Computer the force in the cable when t = 5s, if the motor M is drawing in the cable for a short time at a rate of v = (0.4t2) m/s, where t is in seconds (0 t 6 s). How far does the bar move in 5 s? Neglect the mass of the cable, pulley P, and the rollers.
65615. A 1.5-lb brick is released from rest A and slides down the inclined roof. If the coefficient of friction between the roof and the brick is = 0.3, determine the speed at which the brick strikes the gutter G.
65616. A ball having a mass of 2 kg slides without friction within a vertical circular slot. If it is released from rest when = 10°, determine the force it exerts on the slot when it arrives at points A and B.
65617. 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.
65618. 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.
65619. 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.
65620. 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.
65621. 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.
65622. Determine the velocities of blocks A and B 2 s after they are released from rest. Neglect the mass of the pulleys and cables.
65623. 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.
65624. 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.
65625. 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.
65626. 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.
65627. 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.
65628. 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.
65629. 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.
65630. 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.
65631. 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.
65632. 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.
65633. 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.
65634. 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.
65635. 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.
65636. 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.
65637. The roller-coaster car has a speed of 15 ft/s when it is at the crest of a vertical parabolic track. Compute the velocity and the normal force it exerts on the track when it reaches point B. Neglect friction and the mass of the wheels. The total weight of the car and the passengers is 350 lb.
65638. A motor hoists a 50-kg crate at constant speed to a height of h = 6 m in 3 s. If the indicated power of the motor is 4 kw, determine the motor's efficiency.
65639. A truck has a weight of 25,000 lb and an engine which transmits a power of 350hp. Assuming that the wheels do not slip on the ground, determine the angle of the largest incline the truck can climb at a constant speed of v = 50 ft/s.
65640. The book A having a weight of 1.5 lb slides on the smooth horizontal slot. If the block is drawn back so that s = 0. Each of the two springs has a stiffness of k = 150 lb/ft and an unstretched length of 0.5 ft.
65641. The coefficient of friction between the 2-lb block and the surface is = 0.2. The block is acted upon by a horizontal force of P. Determine the maximum deformation of the outer spring B at the instant the block comes to rest. Spring B has a stiffness of KB = 20 lb/ft and the "nested" spring C has a stiffness of kc = 40 lb/ft.
65642. The car C and its contents have a weight of 600 lb, whereas block B has a weight of 200 lb. If the car is released from rest, determine its speed when it travels 30 ft down the 20° incline.
65643. The "flying car" is a ride at an amusement park, which consists of a car having wheels that roll along a track mounted on a drum. Motion of the car is created by applying the car's brake, thereby gripping the car to the track and allowing it to move with a speed of vt = 3m/s. If the rider applies the brake when going from B to A and then releases it at the top of the drum, A, so that the car coasts freely down along the track to B ( = rad), determine the speed of the car at B and the normal reaction which the drum exerts on the car at B. The rider and car have a total mass of m = 250 kg and the center of mass of the car and rider moves along a circular path of radius r = 8 m.
65644. An electric train car, having a mass of 25 Mg, travels up a 10° incline with a constant speed of 80 km/h. Determine the power required to overcome the force of gravity.
65645. A car, assumed to be rigid and having a mass of 800 kg, strikes a barrel-barrier installation without the driver applying the brakes. From experiments, the magnitude of the force of resistance Fr, created by deforming the barrels successively, is shown as a function of vehicle penetration. If the car strikes the barrier traveling at Vc = 70 km/h, determine approximately the distance s to which the car penetrates the barrier.
65646. A car is equipped with a bumper B designed to absorb collisions. The bumper is mounted to the car using pieces of flexible tubing T. Upon collision with a rigid barrier A, a constant horizontal force F is developed which causes a car deceleration of 3g = 29.43 m/s2 (the highest safe deceleration for a passenger without a seatbelt). If the car and passenger have a total mass of 1.5 Mg and the car is initially coasting with a speed of 1.5 m/s, compute the magnitude of F needed to stop the car and the deformation x of the bumper tubing.
65647. The elevator E and its freight have a total mass of 400 kg. Hoisting is provided by the motor M and the 60-kg block C. If the motor has an efficiency of e = 0.6, determine the power that must be supplied to the motor when the elevator is hoisted upward at a constant speed of vE = m/s.
65648. A car having a mass of 2 Mg strikes a smooth, rigid sign post with an initial speed of 30 km/h. To stop the car, the front end horizontally deforms 0.2 m. If the car is free to roll during the collision, determine the average horizontal collision force causing the deformation.
65649. When at A the bicyclist has a speed of vA = ft/s. If he coasts without pedaling from the top of the hill at A to the shore of B and then leaps off the shore, determine his speed at B and the distance x where he strikes the water at C. The rider and his bicycle have a total weight of 150 lb. Neglect the size of the bicycle and wind resistance.
65650. The firing mechanism of a pinball machine consists of a plunger P having a mass of 0.25 kg and a spring of stiffness k = 300 N/m. When s = 0, the spring is compressed 50 mm. If the arm is pulled back such that s = 100 mm and released, determine the speed of the 0.3 kg pinball B just before the plunger strikes the stop, i.e., s = 0. Assume all sufaces of contact to be smooth. The ball moves in the horizontal plane. Note that the ball slides without rolling.