Momentum and why cars crumple
Physics · GCSE · The School
Momentum is mass times velocity
p = mv, in kilogram metres per second. A 1,000 kg car at 20 m/s has 20,000 kg m/s. It is a vector, so direction counts: two objects of equal mass moving towards each other at the same speed have momenta that cancel, and a sign convention has to be chosen before any calculation.
In a collision, total momentum is conserved
The total before equals the total after, provided no external force acts. A 1,000 kg car at 20 m/s hitting a stationary 1,000 kg car and locking together gives 20,000 kg m/s shared by 2,000 kg, so they move off at 10 m/s. This holds whether the objects bounce apart or stick together — kinetic energy does not.
Force is how fast momentum changes
F = Δp ÷ Δt. The change in momentum in a crash is fixed: the car is going at 20 m/s and it is going to stop. What can be changed is the time taken. Double the stopping time and you halve the force, and the force is what injures people.
Which is what every safety feature does
A crumple zone collapses over perhaps half a second instead of stopping dead in a hundredth. An airbag does the same for the head; a seatbelt stretches slightly rather than holding rigid. None of them reduces the change in momentum — that is set by the speed and the mass. They all extend the time it takes, and so lower the force. A rigid car would be worse, not better.
A second example: pushing apart, not colliding
Two skaters, both at rest, push off each other. Total momentum before is zero, so it must still be zero after — the two momenta afterwards are equal and opposite. A 50 kg skater moving off at 2 m/s (100 kg m/s) means the other, at 40 kg, moves off the other way at 2.5 m/s, because 40 × 2.5 = 100 too. Momentum conservation applies just as much to things flying apart as to things colliding.
Elastic and inelastic collisions
Momentum is conserved in every collision, but kinetic energy is not. An ELASTIC collision keeps kinetic energy the same before and after — two snooker balls bouncing apart is close to this. An INELASTIC collision, like the crash above, loses kinetic energy to sound, heat and deformation even though momentum still balances. Naming which kind a collision is explains why the wreck is warm and dented but the sums still add up.