Problem 1 A rocket burns fuel at a rate of 191 kg/s and exhausts the gas at a relative speed of 8 km/s. Find the thrust of the rocket. Problem 2 A stream of elastic glass beads, each with a mass of 0.5 g, comes out of a horizontal tube at a rate of 96 per second. The beads fall a distance of 0.54 m to a balance pan and bounce back to their original height. How much mass must be placed in the other pan of the balance to keep the pointer at zero? Problem 3 Just before striking the wall, a racquet ball with mass m = 0.232 kg is moving toward the wall at v = 18 m/s and at an angle of θ = 25° with respect to the horizontal. The ball makes a perfectly elastic collision with the solid, frictionless wall and rebounds at the same angle with respect to the horizontal. The ball is in contact with the wall for t = 0.069 s (assume the ball grips the wall during the collision so gravity does not act on it). a) What is the magnitude of the initial momentum of the racquet ball? b) What is the magnitude of the change in momentum of the racquet ball? c) What is the magnitude of the average force the wall exerts on the racquet ball? Now the racquet ball is moving straight toward the wall at a velocity of vi = 18 m/s. The ball makes an inelastic collision with the solid wall and leaves the wall in the opposite direction at vf = -11.9 m/s. The ball exerts the same average force on the ball as before. d) What is the magnitude of the change in momentum of the racquet ball? e) What is the time the ball is in contact with the wall? f) What is the change in kinetic energy of the racquet ball? Problem 4 A 2.9-kg block is traveling to the right (the +x direction) at 5 m/s, and a second 5.4-kg block is traveling to the right at 1.8 m/s. a) Find the total kinetic energy of the two blocks. b) Find the velocity of the center of mass of the two block system. c) Find the velocity of each block relative to the center of mass. d) Find the kinetic energy of the blocks relative to the center of mass. e) Show that your answer for Part (a) is greater than your answer for Part (d) by an amount equal to the kinetic energy associated with the motion of the center of mass. Problem 5 A 2.9-kg block is traveling in the −x direction at 5.4 m/s, and a 1 kg block is traveling in the +x direction at 2.7 m/s. a) Find the velocity vcm of the center of mass. b) Subtract vcm from the velocity of each block to find the velocity of each block in the center-of-mass reference frame. c) After they make a head-on elastic collision, the velocity of each block is reversed (in the center-of-mass frame). Find the velocity of each block in the center-of-mass frame after the collision. d) Transform back into the original frame by adding vcm to the velocity of each block. e) Check your result by finding the initial and final kinetic energies of the blocks in the original frame and comparing them. Problem 6 An object with total mass mtotal = 15.2 kg is sitting at rest when it explodes into three pieces. One piece with mass m1 = 4.9 kg moves up and to the left at an angle of θ1 = 19° above the –x axis with a speed of v1 = 25.1 m/s. A second piece with mass m2 = 5.2 kg moves down and to the right an angle of θ2 = 24° to the right of the -y axis at a speed of v2 = 22.4 m/s. a) What is the magnitude of the final momentum of the system (all three pieces)? b) What is the mass of the third piece? c) What is the x-component of the velocity of the third piece? d) What is the y-component of the velocity of the third piece? e) What is the magnitude of the velocity of the center of mass of the pieces after the explosion? f) Calculate the increase in kinetic energy of the pieces during the explosion. .