Momentum and Collisions Model

Change the values

mass A

velocity A

mass B

velocity B

contact Δt

stop time Δt

Arrows: violet = momentum of A, teal = momentum of B, white = total momentum, pink = force. To the right is the positive direction. Friction is ignored.

Not to scale in time. At Normal speed the motion is shown about 4 to 16 times slower than real life, depending on the speeds you choose. The contact in stage 4 is slowed down about 8 to 80 times, and distances during the contact are rescaled so that the squashing of the buffers can be seen. Stage 5 is about 10 times slower throughout. Force arrows are scaled to fit, so compare them only with each other.

Worked example

A: 200 kg at +5.0 m/s. B: 300 kg at rest. They stick.
before: 200 × 5.0 + 300 × 0 = 1000 kg m/s
after: (200 + 300) × v = 1000
v = 1000 ÷ 500 = +2.0 m/s

How to write it in the exam

Momentum is mass multiplied by velocity: p = mv. Its unit is kg m/s.
Momentum has a direction. Choose one direction as positive; a velocity or momentum the other way is negative.
When no resultant external force acts, the total momentum before a collision or explosion equals the total momentum after it.
If the objects stick together, the momentum after is the combined mass multiplied by their common velocity.
Impulse is the force multiplied by the time for which the force acts. It equals the change in momentum: FΔt = Δ(mv). Its unit is N s.
The resultant force is the change in momentum per unit time: F = Δp / Δt.
A crumple zone does not change the change in momentum. It makes the time of the impact longer, so the force (Δp / Δt) is smaller.