How To Calculate The Coefficient Of Restitution

Coefficient of Restitution Equation:

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

Initial Velocity of Object 1 (v₁ᵢ):

m/s

Initial Velocity of Object 2 (v₂ᵢ):

m/s

Final Velocity of Object 1 (v₁f):

m/s

Final Velocity of Object 2 (v₂f):

m/s

Coefficient of Restitution (e):

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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 separation velocity to relative approach velocity and ranges from 0 (perfectly inelastic) to 1 (perfectly elastic).

2. How Does the Calculator Work?

The calculator uses the coefficient of restitution equation:

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

Where:

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

Explanation: The coefficient measures how much kinetic energy is conserved during a collision, with higher values indicating more elastic collisions.

3. Importance of Coefficient of Restitution

Details: COR is crucial in sports engineering, automotive safety, material science, and physics education. It helps predict collision outcomes and design safer products.

4. Using the Calculator

Tips: Enter all velocity values in meters per second (m/s). Ensure the denominator (v₁ᵢ - v₂ᵢ) is not zero. Positive velocities typically indicate direction away from the collision point.

5. Frequently Asked Questions (FAQ)

Q1: What does a coefficient of 1 mean?
A: A COR of 1 indicates a perfectly elastic collision where kinetic energy is completely conserved.

Q2: What does a coefficient of 0 mean?
A: A COR of 0 indicates a perfectly inelastic collision where objects stick together and move with the same velocity after impact.

Q3: What are typical COR values for common materials?
A: Steel balls: ~0.95, Glass: ~0.94, Wood: ~0.5, Clay: ~0.1. Values vary with impact velocity and material properties.

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

Q5: How does temperature affect COR?
A: Temperature can significantly affect material properties, generally decreasing COR as temperature increases due to increased material deformation.