04 · 16 min
Momentum
Momentum, conservation in collisions, and impulse.
p = mv
The idea
Momentum is mass times velocity, p = mv. It is a vector. In a straight-line problem, pick a positive direction and give a velocity backward a negative sign.
When no resultant external force acts, total momentum stays the same. That is why recoil happens: the forward momentum of a bullet is balanced by the backward momentum of the rifle. In a sticking collision the masses move off together and you can solve one equation for the shared velocity.
Impulse is the change in momentum. A force acting for a time gives impulse = Ft = Δp. The same change in momentum hurts less if the time is longer, because the force is smaller. That is the idea of a crumple zone.
Formulas
Momentum
p = mv
State the direction. The unit kg m/s is the same as the newton second.
- p
- momentum
- kg m/s
- m
- mass
- kg
- v
- velocity
- m/s
Impulse
impulse = Ft = Δp
Use a constant force, or the average force, over the contact time.
- Ft
- impulse
- N s
- F
- force
- N
- t
- time
- s
Worked examples
Force from a change in momentum
A 1 500 kg car travels at 12 m/s and stops in 6.0 s. Find the size of the average braking force.
- Mass
- 1 500 kg
- Initial velocity
- 12 m/s
- Time
- 6.0 s
Try it on paper first. Then open the working one step at a time.
Two trolleys that stick
A 2.0 kg trolley at 3.0 m/s hits a 1.0 kg trolley at rest. They stick together. Find their shared speed.
- m1 and u1
- 2.0 kg at 3.0 m/s
- m2 and u2
- 1.0 kg at 0 m/s
Try it on paper first. Then open the working one step at a time.
Checks
A bullet of mass 0.050 kg travels at 400 m/s. What is its momentum, in kg m/s?
A 4.0 kg trolley at 5.0 m/s collides with a 6.0 kg trolley at rest and they stick. What is their shared speed, in m/s?
A force of 25 N acts for 0.20 s. What impulse does it give, in N s?
Which is a unit of momentum?
Easy places to lose a mark
- Conserving kinetic energy in a collision that sticks. Momentum is conserved; kinetic energy is not.
- Adding speeds instead of momenta when the masses differ.
- Dropping the sign of a rebound. If right is positive, a leftward velocity is negative.
Practical
Collision carts
Compare momentum and kinetic energy before and after a collision.