# A 0.23 kg billiard ball that is moving at 2.6 m/s strikes the bumper of a pool table and bounces...

## Question:

A **0.23 kg** billiard ball that is moving at **2.6 m/s **strikes the bumper of a pool table and bounces straight back at **2.3 m/s. **The collision lasts **0.01 s.**

- a)What percent of the original energy is left after the collision?

## Kinetic Energy

A particle of mass {eq}m {/eq} moving at velocity {eq}v {/eq} has a kinetic energy of

$$K = \dfrac{1}{2} m v^{2} $$

## Answer and Explanation:

The kinetic energy before the colllision is

$$K_{i} = \dfrac{1}{2} m v_{i}^{2} $$

and after colision is

$$K_{f} = \dfrac{1}{2} m v_{f}^{2} $$

Since the kinetic energy after collision can not be greater the kinetic energy before the collision, we define the percentual of the original energy lost after the collision

$$\dfrac{K_{f} }{ K_{i} } = \dfrac{v_{f}^{2} }{ v_{i}^{2} } = \dfrac{ ( 2.3 \text{m} / \text{s} )^{2} }{ ( 2.6 \text{m} / \text{s} )^{2} } \approx 0.78 = 78 \% \, . $$

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from General Studies Science: Help & Review

Chapter 4 / Lesson 14