A ball of mass m and speed v travels horizontally, hits a wall, and rebounds. Another ball of the same mass and traveling at the same speed hits the wall and sticks to it. Which ball has a greater change in momentum as a result of the collision? Create a momentum bar chart to explain your answer.

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Chapter1: Units, Trigonometry. And Vectors
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### Problem Statement

A ball of mass \( m \) and speed \( v \) travels horizontally, hits a wall, and rebounds. Another ball of the same mass and traveling at the same speed hits the wall and sticks to it. Which ball has a greater change in momentum as a result of the collision? Create a momentum bar chart to explain your answer.

### Explanation

To determine which ball experiences a greater change in momentum, we analyze the situations:

1. **Ball Rebounding:**
   - Initial momentum, \( p_i = mv \)
   - Final momentum after rebounding, \( p_f = -mv \)
   - Change in momentum, \( \Delta p = p_f - p_i = -mv - mv = -2mv \)

2. **Ball Sticking:**
   - Initial momentum, \( p_i = mv \)
   - Final momentum after sticking, \( p_f = 0 \)
   - Change in momentum, \( \Delta p = p_f - p_i = 0 - mv = -mv \)

### Momentum Bar Chart Explanation

- **Rebounding Ball:**
  - Initial momentum bar: Height = \( mv \)
  - Final momentum bar: Height = \(-mv\)
  - Change: The total height of the bars = \( 2mv \)

- **Sticking Ball:**
  - Initial momentum bar: Height = \( mv \)
  - Final momentum bar: Height = \( 0 \)
  - Change: The total reduction in height = \( mv \)

### Conclusion

The ball that rebounds experiences a greater change in momentum (\( 2mv \)) compared to the ball that sticks (\( mv \)).
Transcribed Image Text:### Problem Statement A ball of mass \( m \) and speed \( v \) travels horizontally, hits a wall, and rebounds. Another ball of the same mass and traveling at the same speed hits the wall and sticks to it. Which ball has a greater change in momentum as a result of the collision? Create a momentum bar chart to explain your answer. ### Explanation To determine which ball experiences a greater change in momentum, we analyze the situations: 1. **Ball Rebounding:** - Initial momentum, \( p_i = mv \) - Final momentum after rebounding, \( p_f = -mv \) - Change in momentum, \( \Delta p = p_f - p_i = -mv - mv = -2mv \) 2. **Ball Sticking:** - Initial momentum, \( p_i = mv \) - Final momentum after sticking, \( p_f = 0 \) - Change in momentum, \( \Delta p = p_f - p_i = 0 - mv = -mv \) ### Momentum Bar Chart Explanation - **Rebounding Ball:** - Initial momentum bar: Height = \( mv \) - Final momentum bar: Height = \(-mv\) - Change: The total height of the bars = \( 2mv \) - **Sticking Ball:** - Initial momentum bar: Height = \( mv \) - Final momentum bar: Height = \( 0 \) - Change: The total reduction in height = \( mv \) ### Conclusion The ball that rebounds experiences a greater change in momentum (\( 2mv \)) compared to the ball that sticks (\( mv \)).
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