1. What is Coefficient of Restitution?

The coefficient of restitution (COR) is a measure of how much kinetic energy remains after a collision between two objects. It is defined as the ratio of the relative velocity of separation to the relative velocity of approach between two objects after they collide.

2. Dimensional Analysis

The dimensional formula for coefficient of restitution is:

Explanation:

• Since coefficient of restitution is a ratio of two velocities, it has no dimensions
• Velocity has dimensions of [L T⁻¹]
• Ratio of two velocities: [L T⁻¹] / [L T⁻¹] = [M⁰ L⁰ T⁰]
• Therefore, COR is a dimensionless quantity

3. Physical Significance

Details: The coefficient of restitution ranges from 0 to 1, where:

• e = 1: Perfectly elastic collision (no energy loss)
• e = 0: Perfectly inelastic collision (maximum energy loss)
• 0 < e < 1: Partially elastic collision

4. Applications

Applications: Used in sports equipment design, automotive safety, particle physics, and engineering to analyze collision behavior and energy dissipation.

5. Frequently Asked Questions (FAQ)

Q1: Why is coefficient of restitution dimensionless?
A: Because it is defined as the ratio of two velocities, and ratios of similar quantities are always dimensionless.

Q2: What factors affect the coefficient of restitution?
A: Material properties, temperature, impact velocity, and surface characteristics can all influence the COR value.

Q3: Can COR be greater than 1?
A: In classical physics, COR cannot exceed 1 as it would violate energy conservation. Values greater than 1 would imply energy gain during collision.

Q4: How is COR measured experimentally?
A: Typically measured by dropping a ball from a known height and measuring the rebound height, then using the formula e = √(h₂/h₁).

Q5: Is COR the same for all collision types?
A: No, COR depends on the materials involved and the specific conditions of the collision.