College Physics
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ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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![**Example Problem: Billiard Ball Collision**
Consider a 0.230 kg billiard ball that is moving at 3.70 m/s when it strikes the bumper of a pool table and bounces straight back at 2.96 m/s (80% of its original speed). The collision lasts 0.0200 s. (Assume that the ball moves in the positive direction initially.)
### (a) Calculate the average force (in N) exerted on the ball by the bumper. (Indicate the direction with the sign of your answer.)
Given values:
- Mass of the ball, \( m = 0.230 \, \text{kg} \)
- Initial velocity of the ball, \( v_i = 3.70 \, \text{m/s} \)
- Final velocity of the ball, \( v_f = -2.96 \, \text{m/s} \) (the direction is negative since it bounces back)
- Time duration, \( t = 0.0200 \, \text{s} \)
Using the impulse-momentum theorem:
\[ F_{\text{avg}} = \frac{m(v_f - v_i)}{t} \]
Calculation:
\[ F_{\text{avg}} = \frac{0.230 \, \text{kg} \times (-2.96 \, \text{m/s} - 3.70 \, \text{m/s})}{0.0200 \, \text{s}} \]
\[ F_{\text{avg}} = \frac{0.230 \times (-6.66)}{0.0200} \]
\[ F_{\text{avg}} = \frac{-1.5318}{0.0200} \]
\[ F_{\text{avg}} = -76.59 \, \text{N} \]
Thus, the average force exerted on the ball by the bumper is:
\[ -76.59 \, \text{N} \]
### (b) How much kinetic energy in joules is lost during the collision? (Enter the magnitude.)
Using the kinetic energy formula:
\[ KE = \frac{1}{2}mv^2 \]
Initial kinetic energy:
\[ KE_i = \frac{1}{2} \times 0.230 \, \text{kg} \times (3.70 \, \text{m/s](https://content.bartleby.com/qna-images/question/c60fc3dd-1ac3-4d9e-b80d-dba4849839ee/8f932a60-9691-4c63-ba06-c7aaff6b2e8c/hz5zxot_processed.png)
Transcribed Image Text:**Example Problem: Billiard Ball Collision**
Consider a 0.230 kg billiard ball that is moving at 3.70 m/s when it strikes the bumper of a pool table and bounces straight back at 2.96 m/s (80% of its original speed). The collision lasts 0.0200 s. (Assume that the ball moves in the positive direction initially.)
### (a) Calculate the average force (in N) exerted on the ball by the bumper. (Indicate the direction with the sign of your answer.)
Given values:
- Mass of the ball, \( m = 0.230 \, \text{kg} \)
- Initial velocity of the ball, \( v_i = 3.70 \, \text{m/s} \)
- Final velocity of the ball, \( v_f = -2.96 \, \text{m/s} \) (the direction is negative since it bounces back)
- Time duration, \( t = 0.0200 \, \text{s} \)
Using the impulse-momentum theorem:
\[ F_{\text{avg}} = \frac{m(v_f - v_i)}{t} \]
Calculation:
\[ F_{\text{avg}} = \frac{0.230 \, \text{kg} \times (-2.96 \, \text{m/s} - 3.70 \, \text{m/s})}{0.0200 \, \text{s}} \]
\[ F_{\text{avg}} = \frac{0.230 \times (-6.66)}{0.0200} \]
\[ F_{\text{avg}} = \frac{-1.5318}{0.0200} \]
\[ F_{\text{avg}} = -76.59 \, \text{N} \]
Thus, the average force exerted on the ball by the bumper is:
\[ -76.59 \, \text{N} \]
### (b) How much kinetic energy in joules is lost during the collision? (Enter the magnitude.)
Using the kinetic energy formula:
\[ KE = \frac{1}{2}mv^2 \]
Initial kinetic energy:
\[ KE_i = \frac{1}{2} \times 0.230 \, \text{kg} \times (3.70 \, \text{m/s
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