# A 0.24 kg billiard ball that is moving at 2.8 m/s strikes the bumper of a pool table and bounces...

## Question:

A 0.24 kg billiard ball that is moving at 2.8 m/s strikes the bumper of a pool table and bounces straight back at 2.4 m/s. The collision lasts 0.014 s. Calculate the amount of kinetic energy lost during the collision. Be sure to give your value as a negative since energy is leaving the system.

## Kinetic energy loss:

The energy of a moving object is kinetic energy. It is conserved in cases where no external force is acting on the object. The elastic collision has both momenta and the kinetic energy conserved but in the cases of inelastic collisions kinetic energy is not conserved. Thus the system will have some kinetic energy loss because of the thermal energy release or any other energy release.

Thus the kinetic energy loss is formulated as:

$$\color{red}{\text{Kinetic energy Loss}=\frac{1}{2}mv^2-\frac{1}{2}mu^2}$$

Here:

• {eq}m {/eq} is the mass of the object.
• {eq}v {/eq} is the final velocity of the object.
• {eq}u {/eq} is the initial velocity of the object.

Given:

• The mass of the billiard ball {eq}m_1=0.024 \ \text{kg} {/eq}
• The initial velocity of the ball {eq}u=2.8 \ \text{m/s} {/eq}
• The final velocity of the ball {eq}v=-2.4 \ \text{m/s} {/eq}

Thus the kinetic energy loss is:

{eq}\begin{align} \text{Kinetic energy Loss}&=\frac{1}{2}mv^2-\frac{1}{2}mu^2\\ &=\frac{1}{2}(0.024 \ \text{kg})(-2.4 \ \text{m/s})^2-\frac{1}{2}(0.024 \ \text{kg})(2.8 \ \text{m/s})^2\\ &=\color{blue}{-0.02496 \ \text{J}} \\ \end{align} {/eq}