Coefficient of Restitution Calculator

Historical Background

The coefficient of restitution (COR) is a fundamental concept in the study of collisions in classical mechanics. The idea originated from the study of elastic and inelastic collisions, first explored by physicists like Sir Isaac Newton. COR provides a quantitative measure of the elasticity of collisions, showing how much kinetic energy remains for motion after an impact. It has since become an essential parameter in fields such as sports, engineering, and material science.

Calculation Formula

The formula to calculate the Coefficient of Restitution is:

\[ e = \frac{V{2rel}}{V{1rel}} \]

Where:

• \( e \) is the Coefficient of Restitution (dimensionless).
• \( V_{2rel} \) is the relative velocity after collision (m/s).
• \( V_{1rel} \) is the relative velocity before collision (m/s).

Example Calculation

Suppose the relative velocity before collision is 10 m/s, and the relative velocity after collision is 4 m/s. Using the formula:

\[ e = \frac{4}{10} = 0.4 \]

The Coefficient of Restitution in this case is 0.4, indicating a partially inelastic collision.

Importance and Usage Scenarios

• Physics and Engineering: Understanding collision dynamics in automotive safety design, ballistics, and mechanical systems.
• Sports Science: Used in sports like tennis, basketball, and soccer to determine how balls bounce on different surfaces.
• Material Testing: Helps in assessing the elasticity of various materials and their ability to recover after impact.

Common FAQs

1. What does a Coefficient of Restitution of 1 indicate?

   • A COR of 1 signifies a perfectly elastic collision where no kinetic energy is lost.

2. What does a Coefficient of Restitution of 0 mean?

   • A COR of 0 indicates a perfectly inelastic collision, where the objects stick together and all kinetic energy is lost in the form of deformation or heat.

3. Can the Coefficient of Restitution be negative?

   • No, COR is a positive value ranging from 0 to 1, representing the ratio of relative velocities.

This calculator simplifies the process of determining the Coefficient of Restitution, allowing users to quickly assess the nature of a collision.