68. (a) Figure P9.68 shows three points in the operation of the bal- listic pendulum dis- cussed in Example Figure P9.67 9.6 (and shown in Fig. 9.9b). The projectile approaches the pendulum in Figure P9.68a. Figure P9.68b shows the situation just after the projectile is captured in the pendulum. In Figure P9.68c, the pendulum arm has swung upward and come to rest at a height h above its initial posi- tion. Prove that the ratio of the kinetic energy of the projectile-pendulum system immediately after the collision to the kinetic energy immediately before is m,/(m, + m,). (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 momen- tum. How would you convince this student of the truth? Figure P9.68 Problens 68 and 86. (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.

68. (a) Figure P9.68 shows three points in the operation of the bal- listic pendulum dis- cussed in Example Figure P9.67 9.6 (and shown in Fig. 9.9b). The projectile approaches the pendulum in Figure P9.68a. Figure P9.68b shows the situation just after the projectile is captured in the pendulum. In Figure P9.68c, the pendulum arm has swung upward and come to rest at a height h above its initial posi- tion. Prove that the ratio of the kinetic energy of the projectile-pendulum system immediately after the collision to the kinetic energy immediately before is m,/(m, + m,). (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 momen- tum. How would you convince this student of the truth? Figure P9.68 Problens 68 and 86. (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.

Physics for Scientists and Engineers

10th Edition

ISBN:9781337553278

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter9: Linear Momentum And Collisions

Section: Chapter Questions

Problem 36AP: (a) Figure P9.36 shows three points in the operation of the ballistic pendulum discussed in Example...

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