A bullet of mass m is fired into a block of mass M that is at rest. The block, with the bullet embedded, across a horizontal surface. The slides distance Part A coefficient of kinetic friction is u. . Find an expression for the bullet's speed Vbullet- Express your answer in terms of the variables m, M, µk , d, and appropriate constants. • View Available Hint(s) M+m Ubullet = /2µxgd

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**Physics Problem: Bullet and Block System**

A bullet of mass \( m \) is fired into a block of mass \( M \) that is at rest. The block, with the bullet embedded, slides a distance \( d \) across a horizontal surface. The coefficient of kinetic friction is \( \mu_k \).

**Part A**

Find an expression for the bullet's speed \( v_{\text{bullet}} \).

Express your answer in terms of the variables \( m \), \( M \), \( \mu_k \), \( d \), and appropriate constants.

Solution:

\[ v_{\text{bullet}} = \frac{M + m}{m} \sqrt{2\mu_k gd} \]

Where:
- \( m \) is the mass of the bullet.
- \( M \) is the mass of the block.
- \( d \) is the distance the block slides.
- \( \mu_k \) is the coefficient of kinetic friction.
- \( g \) is the acceleration due to gravity.
Transcribed Image Text:**Physics Problem: Bullet and Block System** A bullet of mass \( m \) is fired into a block of mass \( M \) that is at rest. The block, with the bullet embedded, slides a distance \( d \) across a horizontal surface. The coefficient of kinetic friction is \( \mu_k \). **Part A** Find an expression for the bullet's speed \( v_{\text{bullet}} \). Express your answer in terms of the variables \( m \), \( M \), \( \mu_k \), \( d \), and appropriate constants. Solution: \[ v_{\text{bullet}} = \frac{M + m}{m} \sqrt{2\mu_k gd} \] Where: - \( m \) is the mass of the bullet. - \( M \) is the mass of the block. - \( d \) is the distance the block slides. - \( \mu_k \) is the coefficient of kinetic friction. - \( g \) is the acceleration due to gravity.
**Physics Problem: Calculating Bullet Speed**

**Part B**

*Problem Statement:*

What is the speed of an 11 g bullet that, when fired into an 8.0 kg stationary wood block, causes the block to slide 4.8 cm across a wood table? Assume that the coefficient of kinetic friction (μₖ) is 0.20.

*Instructions:*

Express your answer to two significant figures and include the appropriate units.

*Input Fields:*

- There is a space to enter the value of the bullet's speed labeled as \( v_{\text{bullet}} = \). This space is designed for entering the numerical value and its corresponding units.

*Additional Resources:*

- A hint section is available, titled "View Available Hint(s)," which can provide further guidance on solving the problem.

---

In this setup, you are tasked with determining the initial speed of the bullet using concepts such as conservation of momentum and friction.
Transcribed Image Text:**Physics Problem: Calculating Bullet Speed** **Part B** *Problem Statement:* What is the speed of an 11 g bullet that, when fired into an 8.0 kg stationary wood block, causes the block to slide 4.8 cm across a wood table? Assume that the coefficient of kinetic friction (μₖ) is 0.20. *Instructions:* Express your answer to two significant figures and include the appropriate units. *Input Fields:* - There is a space to enter the value of the bullet's speed labeled as \( v_{\text{bullet}} = \). This space is designed for entering the numerical value and its corresponding units. *Additional Resources:* - A hint section is available, titled "View Available Hint(s)," which can provide further guidance on solving the problem. --- In this setup, you are tasked with determining the initial speed of the bullet using concepts such as conservation of momentum and friction.
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