Momentum (Further Mechanics)
Momentum and restitution
- In a collision, total momentum is conserved.
- The bounciness is the coefficient of restitution $e$:
$$e = \frac{\text{speed of separation}}{\text{speed of approach}}, \qquad 0 \leq e \leq 1$$
- $e = 1$ is perfectly elastic (no energy lost); $e = 0$ is inelastic (bodies stick).
Practice
The coefficient of restitution e is:
e = (speed of separation)/(speed of approach), between 0 and 1.
Practice
A perfectly elastic collision (no kinetic energy lost) has:
e = 1 is perfectly elastic; e = 0 is inelastic (bodies stay together).
Practice
Total momentum is conserved in a collision regardless of the value of e.
Momentum is always conserved; e only describes how much kinetic energy is kept.
You've got it
Key idea
- total momentum is conserved in a collision
- $e = \dfrac{\text{separation speed}}{\text{approach speed}}$, with $0 \leq e \leq 1$
- $e = 1$ elastic (no energy lost); $e = 0$ inelastic (stick together)