Vi m2 a b Figure P9.36 Problems 36 and 43. (a) A metal ball moves toward the pendulum. (b) The ball is captured by the pendulum. (c) The ball-pendulum combination swings up through a height h before coming to rest.
(a) As shown three points in the operation of the ballistic pendulum (and shown in 9.10b). The projectile approaches the pendulum in 9.36a. 9.36b shows the situation just after the projectile is captured in the pendulum. In 9.36c, the pendulum arm has swung upward and come to rest momentarily at a height h above its initial position. Prove that the ratio of the kinetic energy of the projectile–pendulum system immediately after the collision to the kinetic energy immediately before is m1/(m1 + m2). (b) What is the ratio of the momentum of the system immediately after the collision to the momentum immediately before? (c) A student believes that such a large decrease in mechanical energy must be accompanied by at least a small decrease in momentum. How would you convince this student of the truth?
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