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2. In this problem we are going to analyze the ballistic pendulum. The process is as follows: a bullet of mass mu (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 t₁? 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 v, m,, 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, mb, and mp. 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 mu (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 t₁? 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 v, m,, 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, mb, and mp. How much mechanical energy was lost in the entire process? Where did this energy go?

Principles of Physics: A Calculus-Based Text
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter8: Momentum And Collisions
Section: Chapter Questions
Problem 64P: Sand from a stationary hopper falls onto a moving conveyor belt at the rate of 5.00 kg/s as shown in...
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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 m3 (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. >↑DE (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 t₁? 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 v, 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, mu, and mp. How much mechanical energy was lost in the entire process? Where did this energy go?
Transcribed Image Text: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 m3 (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. >↑DE (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 t₁? 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 v, 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, mu, and mp. How much mechanical energy was lost in the entire process? Where did this energy go?
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