Collision calculator
Momentum is conserved in every collision. Kinetic energy is conserved only in an elastic one, and the difference is what gets absorbed.
Combined velocity if they stick together
8m/s
- First body after an elastic collision
- -4
- Second body after an elastic collision
- 16
- Total momentum
- 20 000 kg m/s
- Energy absorbed in the inelastic case
- 120 000
- Share of energy absorbed
- 60.000 %
Show the working
- Mass of the first body = 1000
- Velocity of the first body = 20
- Mass of the second body = 1500
- Velocity of the second body = 0
- Total momentum = 1000*20 + 1500*0 = 20 000
- Combined velocity if they stick together = (1000 + 1500) > 0 ? 20 000 / (1000 + 1500) : 0 = 8
- First body after an elastic collision = ((1000 - 1500)*20 + 2*1500*0) / (1000 + 1500) = -4
- Second body after an elastic collision = ((1500 - 1000)*0 + 2*1000*20) / (1000 + 1500) = 16
- ke_before = 1000*20^2/2 + 1500*0^2/2 = 200 000
- ke_after_inelastic = (1000 + 1500) * 8^2 / 2 = 80 000
- Energy absorbed in the inelastic case = 200 000 - 80 000 = 120 000
- Share of energy absorbed = 200 000 > 0 ? 120 000/200 000*100 : 0 = 60
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
Scenarios & local history
Compare a saved scenario
Recent calculations
The formula
- momentum is conserved: m1 u1 + m2 u2 = m1 v1 + m2 v2
- elastic: v1 = ((m1-m2)u1 + 2 m2 u2)/(m1+m2)
- perfectly inelastic: v = total momentum / total mass
A crumple zone is a deliberate attempt to make a collision as inelastic as possible over as long a time as possible.