How Do You Calculate the Coefficient of Restitution

Coefficient of Restitution Formula:

\[ e = \frac{v_{2f} - v_{1f}}{v_{1i} - v_{2i}} \]

Final Velocity 2 (v₂f):

m/s

Final Velocity 1 (v₁f):

m/s

Initial Velocity 1 (v₁i):

m/s

Initial Velocity 2 (v₂i):

m/s

Coefficient of Restitution (e):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Coefficient of Restitution?

The coefficient of restitution (COR) is a measure of the elasticity of collisions between two objects. It represents the ratio of relative velocities after and before an impact, describing how much kinetic energy is conserved during a collision.

2. How Does the Calculator Work?

The calculator uses the coefficient of restitution formula:

\[ e = \frac{v_{2f} - v_{1f}}{v_{1i} - v_{2i}} \]

Where:

\( e \) — Coefficient of restitution (dimensionless)
\( v_{2f} \) — Final velocity of object 2 (m/s)
\( v_{1f} \) — Final velocity of object 1 (m/s)
\( v_{1i} \) — Initial velocity of object 1 (m/s)
\( v_{2i} \) — Initial velocity of object 2 (m/s)

Explanation: The formula calculates the ratio of relative separation velocity to relative approach velocity during a collision.

3. Importance of Coefficient of Restitution

Details: The coefficient of restitution is crucial in physics and engineering for analyzing collisions, designing sports equipment, automotive safety systems, and understanding energy conservation in mechanical systems.

4. Using the Calculator

Tips: Enter all velocity values in meters per second (m/s). Ensure that the denominator (v₁i - v₂i) is not zero, as this would represent no relative motion before collision.

5. Frequently Asked Questions (FAQ)

Q1: What values can the coefficient of restitution take?
A: COR ranges from 0 to 1, where 0 represents a perfectly inelastic collision (objects stick together) and 1 represents a perfectly elastic collision (kinetic energy conserved).

Q2: How is COR used in sports?
A: In sports like golf, tennis, and baseball, COR determines how much energy is transferred between the ball and club/racket, affecting performance and distance.

Q3: Does temperature affect the coefficient of restitution?
A: Yes, temperature can affect material properties and thus the COR. Colder temperatures generally make materials less elastic.

Q4: Can COR be greater than 1?
A: In classical mechanics, COR cannot exceed 1 as this would violate energy conservation. Values greater than 1 would imply energy creation.

Q5: How is COR measured experimentally?
A: COR is typically measured by dropping an object from a known height and measuring the rebound height, or by directly measuring velocities before and after collision.