2. In this problem we are going to analyze the ballistic pendulum. The process is as follows: a bullet of mass m (m in the diagram) is fired with speed v at a wooden block of mass mB (M in the diagram) hanging from the ceiling. The block swings upward and reaches a maximum height of h. By measuring h, we can find the initial speed of the bullet v. The problem is made tricky by the fact that neither momentum nor energy is conserved for the entire process. However, one is conserved for one part of the process and the other is conserved for another part. m (c) M (a) Let's say that at time t = to, the bullet has not yet hit the block. At time t = t₁, the bullet is lodged in the block and the bullet/block system is now moving with a new velocity v', but has not yet changed height appreciably. Is momentum conserved between to and ti? Is energy? Explain why or why not. M+m (b) Use the correct conservation law to find the speed of the bullet/block system at time t₁. Your final answer should be in terms of u, my, and mp. (e) Let's say that at time t = t₂ the bullet/block system has reached its maximum height h. Is momentum conserved between t₁ and t2? Is energy? Explain why or why not. (d) Use the correct conservation law to find the final height of the bullet /block system and solve this for the initial velocity v. Your final answer should be in terms of h, my, and mg. How much mechanical energy was lost in the entire process? Where did this energy go?
2. In this problem we are going to analyze the ballistic pendulum. The process is as follows: a bullet of mass m (m in the diagram) is fired with speed v at a wooden block of mass mB (M in the diagram) hanging from the ceiling. The block swings upward and reaches a maximum height of h. By measuring h, we can find the initial speed of the bullet v. The problem is made tricky by the fact that neither momentum nor energy is conserved for the entire process. However, one is conserved for one part of the process and the other is conserved for another part. m (c) M (a) Let's say that at time t = to, the bullet has not yet hit the block. At time t = t₁, the bullet is lodged in the block and the bullet/block system is now moving with a new velocity v', but has not yet changed height appreciably. Is momentum conserved between to and ti? Is energy? Explain why or why not. M+m (b) Use the correct conservation law to find the speed of the bullet/block system at time t₁. Your final answer should be in terms of u, my, and mp. (e) Let's say that at time t = t₂ the bullet/block system has reached its maximum height h. Is momentum conserved between t₁ and t2? Is energy? Explain why or why not. (d) Use the correct conservation law to find the final height of the bullet /block system and solve this for the initial velocity v. Your final answer should be in terms of h, my, and mg. How much mechanical energy was lost in the entire process? Where did this energy go?
Glencoe Physics: Principles and Problems, Student Edition
1st Edition
ISBN:9780078807213
Author:Paul W. Zitzewitz
Publisher:Paul W. Zitzewitz
Chapter11: Energy And Its Conservation
Section: Chapter Questions
Problem 44A
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