Coefficient of Restitution Experiment – For Schools, Teachers, and Students
Definition
The coefficient of restitution (e) is a dimensionless quantity that measures the elasticity of a collision between two bodies. It is defined as the ratio of the relative velocity of separation to the relative velocity of approach along the line of collision.
This concept is demonstrated in Dencity – Online Science Lab and Simulations to enhance interactive learning.
Theory
The coefficient of restitution is mathematically expressed as:
e = (Relative velocity of separation) / (Relative velocity of approach)
For a collision between two bodies A and B, where:
- u_A and u_B are initial velocities before collision,
- v_A and v_B are velocities after collision,
The coefficient of restitution is given by:
e = (v_B – v_A) / (u_A – u_B)
where all velocities are considered along the line of impact.
Key Properties of the Coefficient of Restitution:
- e = 1 → Perfectly elastic collision (no kinetic energy lost).
- e = 0 → Perfectly inelastic collision (bodies stick together after impact).
- 0 < e < 1 → Partially elastic collision (some kinetic energy is lost).
In vertical motion scenarios, such as a ball dropped from a certain height, the coefficient of restitution can be calculated as:
e = sqrt(h_2 / h_1)
where:
- h_1 is the initial height from which the ball is dropped,
- h_2 is the height to which it rebounds.
Several factors affect the value of e, including material properties, surface texture, and temperature.
Real-World Applications
The coefficient of restitution has numerous practical applications, such as:
- Sports Science: Used in designing cricket balls, tennis balls, and golf clubs to optimize performance.
- Automotive Safety: Helps engineers predict collision behavior in car crash testing.
- Video Games & Animations: Used for realistic physics simulations of bounces and impacts.
- Astronomy: Helps analyze planetary collisions and asteroid impacts.
- Physics Experiments: Determines energy dissipation during impact in laboratory experiments.
- Online Science Lab: Helps students visualize and simulate collision mechanics interactively.
Observations and Key Learnings
- Increasing the elasticity of materials increases the coefficient of restitution (e).
- Reducing surface roughness increases e, making collisions more elastic.
- The relative velocity of approach does not affect e, as it depends on the material properties.
- Higher values of e result in more elastic collisions, retaining more kinetic energy after impact.
- In height-based experiments, decreasing the rebound height (h_2) reduces e, indicating more energy loss during impact.
