What is the Coefficient of Restitution?
The Coefficient of Restitution (e) measures how "elastic" a collision is between two objects. It ranges from 0 (perfectly inelastic collision) to 1 (perfectly elastic collision).
Formula
$$e = \frac{v_{\text{sep}}}{v_{\text{app}}}$$
Where:
- e is the coefficient of restitution (dimensionless)
- v_sep is the relative velocity after collision (separation speed)
- v_app is the relative velocity before collision (approach speed)
Calculation Example
Consider two cars colliding:
- Car A velocity before: 50 m/s, Car B velocity before: 10 m/s
- Car A velocity after: 20 m/s, Car B velocity after: 30 m/s
Step 1: Calculate the approach speed (relative velocity before collision)
$$v_{\text{app}} = 50 - 10 = 40 \text{ m/s}$$
Step 2: Calculate the separation speed (relative velocity after collision)
$$v_{\text{sep}} = |20 - 30| = 10 \text{ m/s}$$
Step 3: Calculate the coefficient of restitution
$$e = \frac{10}{40} = 0.25$$
A coefficient of 0.25 indicates a mostly inelastic collision where significant kinetic energy was lost.