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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 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?

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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**Ballistic Pendulum Analysis** In this problem, we are going to analyze the ballistic pendulum. The process is as follows: a bullet of mass \( m_b \) (\( m \) in the diagram) is fired with speed \( v \) at a wooden block of mass \( m_B \) (\( M \) 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. **Diagram Explanation:** The diagram shows a bullet approaching a block: - The bullet has a mass \( m \) and is moving with velocity \( v \). - The block has a mass \( M \). - After the bullet embeds into the block, the combined system rises to a height \( h \) with a new mass of \( M + m \). **Questions to Consider:** **(a)** Let’s say that at time \( t = t_0 \), the bullet has not yet hit the block. At time \( t = t_1 \), 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 \( t_0 \) and \( t_1 \)? Is energy? Explain why or why not. **(b)** Use the correct conservation law to find the speed of the bullet/block system at time \( t_1 \). Your final answer should be in terms of \( v \), \( m_b \), and \( m_B \). **(c)** Let’s say that at time \( t = t_2 \) the bullet/block system has reached its maximum height \( h \). Is momentum conserved between \( t_1 \) and \( t_2 \)? 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 \( h \), \( m_b \), and \( m_B \). **(e)** How much mechanical energy was lost in the
Transcribed Image Text:**Ballistic Pendulum Analysis** In this problem, we are going to analyze the ballistic pendulum. The process is as follows: a bullet of mass \( m_b \) (\( m \) in the diagram) is fired with speed \( v \) at a wooden block of mass \( m_B \) (\( M \) 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. **Diagram Explanation:** The diagram shows a bullet approaching a block: - The bullet has a mass \( m \) and is moving with velocity \( v \). - The block has a mass \( M \). - After the bullet embeds into the block, the combined system rises to a height \( h \) with a new mass of \( M + m \). **Questions to Consider:** **(a)** Let’s say that at time \( t = t_0 \), the bullet has not yet hit the block. At time \( t = t_1 \), 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 \( t_0 \) and \( t_1 \)? Is energy? Explain why or why not. **(b)** Use the correct conservation law to find the speed of the bullet/block system at time \( t_1 \). Your final answer should be in terms of \( v \), \( m_b \), and \( m_B \). **(c)** Let’s say that at time \( t = t_2 \) the bullet/block system has reached its maximum height \( h \). Is momentum conserved between \( t_1 \) and \( t_2 \)? 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 \( h \), \( m_b \), and \( m_B \). **(e)** How much mechanical energy was lost in the
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