A ball falls freely from a height 1m on the ground and rebounds to a height of o.8m. Find the coefficient of restitution.

To determine the coefficient of restitution for a ball that falls from a height of 1 meter and rebounds to a height of 0.8 meters, we can use a straightforward formula. The coefficient of restitution (e) is defined as the ratio of the relative velocity of separation to the relative velocity of approach. However, in this case, we can simplify it using the heights from which the ball falls and rebounds.

Understanding the Coefficient of Restitution

The coefficient of restitution is a measure of how elastic a collision is between two objects. It ranges from 0 to 1, where:

• e = 1: Perfectly elastic collision (no kinetic energy lost).
• e = 0: Perfectly inelastic collision (maximum kinetic energy lost).

Calculating the Coefficient

In our scenario, we can use the heights to find the coefficient of restitution. The formula relating the heights before and after the bounce is:

e = √(h_rebound / h_drop)

Here, h_drop is the height from which the ball falls (1 meter), and h_rebound is the height to which it rebounds (0.8 meters).

Plugging in the Values

Now, substituting the values into the formula:

e = √(0.8 / 1)

This simplifies to:

e = √(0.8)

Calculating the square root gives:

e ≈ 0.894

Interpreting the Result

The coefficient of restitution of approximately 0.894 indicates that the collision is relatively elastic, meaning the ball retains a significant portion of its kinetic energy after bouncing. This value suggests that while some energy is lost during the impact with the ground, a good amount is still conserved, allowing the ball to rebound to a height that is 80% of its original drop height.

In summary, the coefficient of restitution for the ball in this scenario is about 0.894, reflecting a moderately elastic collision. This concept is crucial in physics, especially in understanding energy conservation and the behavior of objects during collisions.