Coefficient Of Restitution Formula Physics

Coefficient of Restitution Formula:

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

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 velocities after and before impact, indicating 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)
\( v_{1i} \) — 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 formula calculates the ratio of the relative separation velocity to the 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, vehicle 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 v1i and v2i are not equal to avoid division by zero. The result is a dimensionless quantity between 0 (perfectly inelastic) and 1 (perfectly elastic).

5. Frequently Asked Questions (FAQ)

Q1: What does the coefficient of restitution value mean?
A: e = 1 indicates a perfectly elastic collision (kinetic energy conserved), e = 0 indicates a perfectly inelastic collision (maximum energy loss), and values between 0-1 represent partially elastic collisions.

Q2: What are typical coefficient of restitution values?
A: Glass balls: ~0.95, Tennis balls: ~0.75-0.85, Baseballs: ~0.55, Clay: ~0.1-0.2. Values depend on materials and impact conditions.

Q3: Does temperature affect the coefficient of restitution?
A: Yes, temperature can significantly affect COR, especially for materials like rubber where stiffness changes with temperature.

Q4: Can the coefficient of restitution be greater than 1?
A: In classical mechanics, COR cannot exceed 1 as this would violate energy conservation. Values >1 would imply energy gain during collision.

Q5: How is COR used in sports?
A: COR determines the "bounciness" of balls in sports like tennis, golf, and basketball, affecting game performance and equipment regulations.