### Understanding Energy and Motion in a Spring-Loaded BB GunA Red Rider BB gun uses the energy in a compressed spring to provide the kinetic energy needed to propel a small pellet with a mass of **0.22 grams**. By cocking the lever attached to the stock of the rifle, the spring (with a spring constant \( k = 1800 \, \text{N/m} \)) is compressed by **9 cm** from its equilibrium point.#### Questions and Calculations:1. **What is the potential energy stored in the compressed spring?** - Potential Energy Formula: \( PE = \frac{1}{2}kx^2 \).2. **What is the kinetic energy of the pellet when the spring is released?** - Kinetic Energy Formula: \( KE = \frac{1}{2}mv^2 \).3. **What is the muzzle velocity of the BB?** - Use \( KE = \frac{1}{2}mv^2 \) to find \( v \).4. **If the rifle was modified so that the spring could be compressed twice as far, 18 cm, what would be the resultant muzzle velocity of the BB?** - Recalculate potential energy with the new compression distance and solve for the new velocity.#### Instructions:- Enter your calculations and submit each answer. You have 2 attempts for each question.These questions guide you through understanding the conversion of potential energy to kinetic energy and the effect on velocity when a spring's compression is increased.

Answered: Image /qna-images/answer/8797229b-b5eb-4fc3-b0da-e4f85cb37981.jpg

A Red Rider bb gun uses the energy in a compressed spring to provide the kinetic energy for propelling a small pellet of mass 0.22 grams. By cocking the lever attached to the stock of the rifle, the spring (k = 1800 N/m) is compressed 9 cm from its equilibrium point. What is the potential energy energy stored in the compressed spring? Submit Answer Tries 0/2 What is the kinetic energy of the pellet when the spring is released? Submit Answer Tries 0/2 What is the muzzle velocity of the bb? m/s

A Red Rider bb gun uses the energy in a compressed spring to provide the kinetic energy for propelling a small pellet of mass 0.22 grams. By cocking the lever attached to the stock of the rifle, the spring (k = 1800 N/m) is compressed 9 cm from its equilibrium point. What is the potential energy energy stored in the compressed spring? Submit Answer Tries 0/2 What is the kinetic energy of the pellet when the spring is released? Submit Answer Tries 0/2 What is the muzzle velocity of the bb? m/s

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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Question

### Understanding Energy and Motion in a Spring-Loaded BB Gun

A Red Rider BB gun uses the energy in a compressed spring to provide the kinetic energy needed to propel a small pellet with a mass of **0.22 grams**. By cocking the lever attached to the stock of the rifle, the spring (with a spring constant \( k = 1800 \, \text{N/m} \)) is compressed by **9 cm** from its equilibrium point.

#### Questions and Calculations:

1. **What is the potential energy stored in the compressed spring?**
- Potential Energy Formula: \( PE = \frac{1}{2}kx^2 \).

2. **What is the kinetic energy of the pellet when the spring is released?**
- Kinetic Energy Formula: \( KE = \frac{1}{2}mv^2 \).

3. **What is the muzzle velocity of the BB?**
- Use \( KE = \frac{1}{2}mv^2 \) to find \( v \).

4. **If the rifle was modified so that the spring could be compressed twice as far, 18 cm, what would be the resultant muzzle velocity of the BB?**
- Recalculate potential energy with the new compression distance and solve for the new velocity.

#### Instructions:

- Enter your calculations and submit each answer. You have 2 attempts for each question.

These questions guide you through understanding the conversion of potential energy to kinetic energy and the effect on velocity when a spring's compression is increased.

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