Coefficient of Elasticity: Exploring Kinetic Energy Conservation in Collisions

What is the coefficient of elasticity for a collision if a ball strikes a surface with a speed of 10 m/s and rebounds just after the collision with a speed of 2 m/s?

A. 0.2

B. 0.5

C. 0.8

Answer:

The coefficient of elasticity for the collision between the ball and the surface is 0.2.

When analyzing collisions, the coefficient of elasticity plays a crucial role in understanding how kinetic energy is conserved in the system. The coefficient of elasticity, also known as the restitution coefficient, is a measure of how much kinetic energy is conserved during a collision. It is defined as the ratio of the final velocity of separation to the initial velocity of approach.

In this scenario, the ball strikes the surface with a speed of 10 m/s and rebounds with a speed of 2 m/s. By using the formula for the coefficient of elasticity: e = (Final velocity of separation) / (Initial velocity of approach), we can calculate the coefficient of elasticity.

Substitute the given values into the formula:

e = 2 m/s / 10 m/s = 0.2

Therefore, the coefficient of elasticity for this collision is 0.2. This means that only 20% of the kinetic energy is conserved during the collision, while the remaining 80% is lost in other forms such as heat or sound.

Understanding and calculating the coefficient of elasticity is essential in various fields such as physics, engineering, and sports, where the conservation of energy in collisions is a significant factor. By knowing this coefficient, we can better predict the outcome of collisions and analyze the efficiency of various systems.