Coefficient Of Restitution Calculator

Coefficient of Restitution Equations:

\[ e = \sqrt{\frac{KE_{\text{final}}}{KE_{\text{initial}}}} \]
\[ e = \frac{\text{relative velocity after}}{\text{relative velocity before}} \ (\text{for 1D}) \]

Calculation Method:

Initial Kinetic Energy (KE_initial):

Final Kinetic Energy (KE_final):

Coefficient of Restitution (e):

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1. What is the Coefficient of Restitution?

The coefficient of restitution (COR or e) is a measure of how much kinetic energy remains after a collision between two objects. It quantifies the "bounciness" of a collision, ranging from 0 (perfectly inelastic) to 1 (perfectly elastic).

2. How Does the Calculator Work?

The calculator uses two main equations for coefficient of restitution:

\[ e = \sqrt{\frac{KE_{\text{final}}}{KE_{\text{initial}}}} \]
\[ e = \frac{\text{relative velocity after}}{\text{relative velocity before}} \ (\text{for 1D collisions}) \]

Where:

\( e \) — Coefficient of restitution (dimensionless)
\( KE_{\text{initial}} \) — Initial kinetic energy (J)
\( KE_{\text{final}} \) — Final kinetic energy (J)
relative velocity — Speed difference between objects before/after collision (m/s)

Explanation: The coefficient represents the ratio of final to initial relative speeds or the square root of the ratio of kinetic energies after and before collision.

3. Importance of Coefficient of Restitution

Details: COR is crucial in physics, engineering, and sports for analyzing collisions, designing safety equipment, optimizing sports equipment performance, and understanding energy conservation in impacts.

4. Using the Calculator

Tips: Choose calculation method (energy or velocity), enter the required values. For energy method, both energies must be positive with initial energy > 0. For velocity method, velocity before cannot be zero.

5. Frequently Asked Questions (FAQ)

Q1: What does e = 0 mean?
A: e = 0 indicates a perfectly inelastic collision where objects stick together and maximum kinetic energy is lost.

Q2: What does e = 1 mean?
A: e = 1 indicates a perfectly elastic collision where kinetic energy is conserved (no energy loss).

Q3: What are typical COR values for common materials?
A: Glass balls: ~0.95, Tennis balls: ~0.75-0.85, Baseballs: ~0.55, Clay: ~0.1-0.3, depending on conditions.

Q4: Does COR depend on impact velocity?
A: Yes, COR often decreases with increasing impact velocity due to material deformation and energy dissipation.

Q5: When is the velocity method applicable?
A: The velocity ratio method works best for one-dimensional collisions where velocities are measured along the line of impact.