Question

What is the coefficient of restitution of a perfectly elastic impact?

• A. 1.0
• B. 0.5
• C. infinity
• D. 0

Hint:

For perfectly elastic collisions, the coefficient of restitution is always \( e = 1 \). If energy is lost during the collision, \( e \) will be less than 1, and in perfectly inelastic collisions, \( e = 0 \).

Answer 1

The Correct Option is A

Step 1: Understanding Coefficient of Restitution
The coefficient of restitution (e) is a measure of how elastic a collision is. It is defined as the ratio of the relative speed of separation to the relative speed of approach between two objects involved in the collision. Mathematically, \[ e = \frac{\text{relative velocity after collision}}{\text{relative velocity before collision}}. \]
Step 2: For a Perfectly Elastic Collision
In a perfectly elastic collision, there is no loss of kinetic energy. All the kinetic energy is conserved, and the objects rebound without any deformation or heat generation. In such a case, the relative velocity after the collision is equal to the relative velocity before the collision. This means that the coefficient of restitution is equal to 1.
Step 3: Interpreting the Answer Choices
From the given options, the only correct choice is (1) \( e = 1.0 \), which corresponds to a perfectly elastic impact.
Step 4: Conclusion
Therefore, the coefficient of restitution for a perfectly elastic impact is 1.0.