Classification
| Property | Elastic (e = 1) | Perfectly Inelastic (e = 0) | Partially Inelastic (0 < e < 1) |
|---|
| Momentum | Conserved | Conserved | Conserved |
| KE | Conserved | NOT (max loss) | NOT (partial loss) |
| Bodies after | Separate | Stick together | Separate |
| Example | Atomic collisions | Bullet in block | Real macroscopic |
Elastic Collision (1D) — Formulae
v1=m1+m2(m1−m2)u1+2m2u2
v2=m1+m2(m2−m1)u2+2m1u1
Special cases:
| Case | v_{1} after | v_{2} after |
|---|
| m_{1} = m_{2} (u_{2} = 0) | 0 | u_{1} |
| m_{1} >> m_{2} (u_{2} = 0) | ≈ u_{1} | ≈ 2u_{1} |
| m_{1} << m_{2} (u_{2} = 0) | ≈ −u_{1} | ≈ 0 |
Perfectly Inelastic Collision
vf=m1+m2m1u1+m2u2
ΔKEloss=2(m1+m2)m1m2(u1−u2)2
For m_{1} = m_{2}, u_{2} = 0: vf=2u1; KE loss = 50%.
Coefficient of Restitution
e=relative velocity of approachrelative velocity of separation=u1−u2v2−v1
For bouncing ball (dropped from H, bounces to h):
e=Hh