Conservation of Momentum Calculator
Find the final velocity in a perfectly inelastic collision where two masses stick together, using conservation of momentum.
How it works
m₁·u₁ + m₂·u₂ = (m₁+m₂)·v · v = (m₁·u₁ + m₂·u₂)/(m₁+m₂)
In a perfectly inelastic collision the two objects stick together and move as one afterwards. Momentum — mass times velocity, a signed quantity — is always conserved in a collision with no outside forces, so the combined mass moves at the momentum-weighted average of the two initial velocities. Kinetic energy, by contrast, is not conserved: some is lost to heat, sound and deformation, which is exactly what makes the collision inelastic. Use signs to set direction: positive one way, negative the other.
Worked example
A 2 kg cart at +5 m/s hits a 3 kg cart at −1 m/s and they couple: total momentum = 2×5 + 3×(−1) = 7 kg·m/s, over 5 kg total, so v = 1.4 m/s. Kinetic energy falls from 26.5 J to 4.9 J — about 21.6 J lost.
Sources: Momentum — Wikipedia
Frequently asked questions
What is the difference between elastic and inelastic collisions?
Both conserve momentum. An elastic collision also conserves kinetic energy and the objects bounce apart; a perfectly inelastic one — modelled here — has the objects stick together and loses the most kinetic energy possible.
Why do velocities have signs?
Momentum is a vector, so direction matters. Choose one direction as positive and the opposite as negative; a head-on approach means one velocity is positive and the other negative, and the sign of the answer tells you which way the combined mass moves.
Where does the lost kinetic energy go?
Into heat, sound and permanent deformation of the colliding bodies. Momentum has nowhere to go and is conserved, but kinetic energy can convert into these other forms, which is why the after-collision energy is lower.
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Educational estimate. Check the formula and units for your exact case.