**Pendulum and Bullet Dynamics Analysis****Problem Statement:**A bullet of mass \( m \) and speed \( v \) is fired at an initially stationary pendulum bob. The bullet passes through the bob and exits with a speed of \( \frac{v}{7} \). The pendulum bob is attached to a rigid pole of length \( L \) and has negligible mass. Determine the minimum speed \( v \) required for the pendulum bob to barely swing through a complete vertical circle.**Key Variables:**- \( m \): Mass of the bullet- \( v \): Initial speed of the bullet- \( \frac{v}{7} \): Speed of the bullet as it exits the bob- \( L \): Length of the rigid pole- \( M \): Mass of the pendulum bob**Diagram Explanation:**- **Bullet Path**: Initially directed towards the pendulum bob with velocity \( v \).- **Pendulum Bob**: Represented as a circle with mass \( M \).- **Pendulum Arc**: Dashed line showing the bob's path for a complete vertical circle.- **Velocity Change**: Bullet's velocity decreases from \( v \) to \( \frac{v}{7} \).**Question:**What is the minimum value of \( v \) needed for the pendulum bob to complete the vertical circle?**Interactive Component:**- **Input Box**: Allows you to calculate and enter the minimum speed \( v \).Understanding the interplay of momentum and energy conservation principles will aid in solving this problem.

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As shown below, a bullet of mass m and speed v is fired at an initially stationary pendulum bob. The bullet goes through the bob, and exits with a speed of The pendulum bob is attached to a rigid pole of length L and negligible mass. What is the minimum value of v such that the pendulum bob will barely swing through a complete vertical circle? (Use the following as necessary: m, L, g, and M for the mass of the bob.) m v/7

As shown below, a bullet of mass m and speed v is fired at an initially stationary pendulum bob. The bullet goes through the bob, and exits with a speed of The pendulum bob is attached to a rigid pole of length L and negligible mass. What is the minimum value of v such that the pendulum bob will barely swing through a complete vertical circle? (Use the following as necessary: m, L, g, and M for the mass of the bob.) m v/7

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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Concept explainers

Rigid Body

A rigid body is an object which does not change its shape or undergo any significant deformation due to an external force or movement. Mathematically speaking, the distance between any two points inside the body doesn't change in any situation.

Rigid Body Dynamics

Rigid bodies are defined as inelastic shapes with negligible deformation, giving them an unchanging center of mass. It is also generally assumed that the mass of a rigid body is uniformly distributed. This property of rigid bodies comes in handy when we deal with concepts like momentum, angular momentum, force and torque. The study of these properties – viz., force, torque, momentum, and angular momentum – of a rigid body, is collectively known as rigid body dynamics (RBD).

Question

**Pendulum and Bullet Dynamics Analysis**

**Problem Statement:**

A bullet of mass \( m \) and speed \( v \) is fired at an initially stationary pendulum bob. The bullet passes through the bob and exits with a speed of \( \frac{v}{7} \). The pendulum bob is attached to a rigid pole of length \( L \) and has negligible mass. Determine the minimum speed \( v \) required for the pendulum bob to barely swing through a complete vertical circle.

**Key Variables:**

- \( m \): Mass of the bullet
- \( v \): Initial speed of the bullet
- \( \frac{v}{7} \): Speed of the bullet as it exits the bob
- \( L \): Length of the rigid pole
- \( M \): Mass of the pendulum bob

**Diagram Explanation:**

- **Bullet Path**: Initially directed towards the pendulum bob with velocity \( v \).
- **Pendulum Bob**: Represented as a circle with mass \( M \).
- **Pendulum Arc**: Dashed line showing the bob's path for a complete vertical circle.
- **Velocity Change**: Bullet's velocity decreases from \( v \) to \( \frac{v}{7} \).

**Question:**

What is the minimum value of \( v \) needed for the pendulum bob to complete the vertical circle?

**Interactive Component:**

- **Input Box**: Allows you to calculate and enter the minimum speed \( v \).

Understanding the interplay of momentum and energy conservation principles will aid in solving this problem.

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