Calculator · Engineering Mechanics
Collision Calculator
Direct central impact of two particles along one line: momentum is conserved, and the coefficient of restitution links the separation speed to the approach speed.
Particles before impact
Signed along the line of impact, positive to the right.
0 ≤ e ≤ 1. e = 1 is perfectly elastic; e = 0 is perfectly plastic.
Results
| Final velocity v₁ | 0.2 m/s |
|---|---|
| Final velocity v₂ | 3.2 m/s |
| Approach speed u₁ − u₂ | 5 m/s |
| Separation speed v₂ − v₁ | 3 m/s |
| Total momentum before | 10 kg·m/s |
| Total momentum after | 10 kg·m/s |
| Momentum residual | 1.7764e-15 kg·m/s |
| Kinetic energy before | 25 J |
| Kinetic energy after | 15.4 J |
| Kinetic energy lost | 9.6 J |
| Fraction of energy lost | 38.4 % |
| Reading | Partially elastic (e = 0.6): part of the kinetic energy is lost, but the particles still separate. |
Technical reference
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
v₂ − v₁ = e·(u₁ − u₂)
- u₁, u₂
- velocities before impact, signed along the line of impact[m/s]
- v₁, v₂
- velocities after impact, same sign convention[m/s]
- e
- coefficient of restitution, 0 ≤ e ≤ 1[–]
The calculator assumes linear momentum is conserved through the impact — no external impulse is modelled — and solves the two equations above together for v₁ and v₂. e = 1 makes the separation speed equal the approach speed (elastic, kinetic energy conserved); e = 0 makes the separation speed zero, so the particles move off together (perfectly plastic). An intermediate e is partially elastic, with the momentum residual shown as a numerical check only.
Assumptions
- · Two point particles in direct central impact: all velocities lie on one line, positive to the right.
- · Linear momentum is conserved through the impact.
- · The separation speed equals e times the approach speed; 0 ≤ e ≤ 1.
- · Only e = 0 is perfectly plastic; an intermediate e is partially elastic, not 'perfectly inelastic'.
- · Oblique two-dimensional impact is not modelled in this version.
Related tools
- Constant Acceleration
- Projectile Motion
- Circular Motion
- Curvilinear Motion
- Newton's Second Law
- Work–Energy
- Impulse–Momentum
A collision is an instantaneous two-particle event, so it does not continue into the single-particle Particle Motion Lab.