### Physics Problem: Pendulum and Bullet Interaction#### Problem Statement:A bullet of mass \( m \) and speed \( v \) is fired at, hits, and passes completely through a pendulum bob of mass \( M = 2m \) on the end of a stiff rod of negligible mass and length \( L \). The bullet emerges with a speed of \( v/2 \) and the pendulum bob just makes it over the top of the trajectory without falling backward in its circular path. Determine an expression (in terms of \( g \) and \( L \) only) for the minimum initial speed the bullet must have in order for the pendulum bob to just barely swing through a complete vertical circle.\[ v = \text{______} \]#### Diagram Explanation:The accompanying diagram illustrates the scenario described:- A pendulum bob with mass \( M = 2m \) is attached to the end of a rigid rod of length \( L \).- A bullet of mass \( m \) is shown approaching the pendulum bob with speed \( v \).- After passing through the pendulum bob, the bullet exits with a reduced speed of \( v/2 \).- The pendulum swings upwards, showing a dotted arc representing the pendulum bob’s trajectory as it completes a full vertical circle.**Key elements in the diagram:**1. **Pendulum bob (M):** Represented by a gray sphere.2. **Bullet (m):** Represented by an arrow approaching the pendulum bob.3. **Initial and Final Speed of Bullet:** Indicated by \( \vec{v} \) and \( \vec{v}/2 \).4. **Length of Rod (L):** The length of the rigid rod connecting the pendulum bob to its pivot point.5. **Trajectory of Pendulum Bob:** Shown as a dotted circular path.#### Required Calculation:Determine the minimum initial speed \( v \) for the bullet necessary to ensure that the pendulum bob completes a vertical circle.### Solution:The full solution involves principles from conservation of momentum and energy, and it requires a detailed analysis that would include formulating equations and solving them step-by-step. For the web page layout, we might include step-by-step mathematical derivations and explanations to make the understanding clear for the students. However, those details extend beyond this transcription and would generally be added in sections following this initial setup.

Name: ### Physics Problem: Pendulum and Bullet Interaction#### Problem Stat
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Description: ### Physics Problem: Pendulum and Bullet Interaction#### Problem Statement:A bullet of mass \( m \) and speed \( v \) is fired at, hits, and passes completely through a pendulum bob of mass \( M = 2m \) on the end of a stiff rod of negligible mass a

Given : M = 2m To determine: initial speed of bullet

Science

Physics

A bullet of mass m and speed v is fired at, hits, and passes completely through a pendulum bob of mass M = 2m on the end of a stiff rod of negligible mass and length L. The bullet emerges with a speed of v/2 and the pendulum bob just makes it over the top of the trajectory without falling backward in its circular path. Determine an expression (in terms of g and L only) for the minimum initial speed the bullet must have in order for the pendulum bob to just barely swing through a complete vertical circle.

A bullet of mass m and speed v is fired at, hits, and passes completely through a pendulum bob of mass M = 2m on the end of a stiff rod of negligible mass and length L. The bullet emerges with a speed of v/2 and the pendulum bob just makes it over the top of the trajectory without falling backward in its circular path. Determine an expression (in terms of g and L only) for the minimum initial speed the bullet must have in order for the pendulum bob to just barely swing through a complete vertical circle.

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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