Skip to the calculator
Rule Calculator

Momentum Calculator

With mass 1500 kg, velocity 20 m/s, time taken to stop it 0.15 s, momentum comes to 30,000.00 kg·m/s — momentum. It is reached in 5 steps, the last of which is 1500 * 20, and each one is printed on the page with its numbers filled in. The formula is the one published by NIST Special Publication 811, not an approximation fitted to it.

Momentum from a mass and a velocity, with the kinetic energy that goes with it and the impulse needed to stop the object in a given time.

Formula and sources checked · How we check

Mass 1500 kg, Velocity 20 m/s, Time taken to stop it 0.15 s

30,000.00 kg·m/s

Momentum for the example below. Editing a field recomputes the calculator below; this figure holds the answer the page was loaded with.

It is written into the HTML rather than drawn by a script, so a search engine reading this page without running JavaScript still finds an answer.

Momentum
30,000.00 kg·m/s
Momentum p = mv
1500 * 2030,000 kg·m/s
Kinetic energy ½mv²
0.5 * 1500 * 20 ^ 2300,000 J
Impulse needed to stop it
abs(30000)30,000 N·s
Average force over that time
abs(30000) / 0.15200,000 N
That force in US tons-force (2,000 lb)
200000 / (2000 * 0.4535924 * 9.80665)22.481 tf

Ask about this in the chat

Worked example

A 1,500 kg car at 20 m/s carries 30,000 kg·m/s of momentum and 300,000 joules of kinetic energy. Stopping it in 0.15 seconds — about what a crumple zone buys — needs an average force of 200,000 newtons, roughly 22.5 US tons-force. Doubling the stopping time halves that force, which is the entire purpose of the crumple zone.

How to work it out yourself

  1. 1.Momentum is linear in velocity and kinetic energy is quadratic. Double the speed and the momentum doubles while the energy quadruples, which is why a small speed increase costs so much more in braking distance.
  2. 2.Momentum is conserved in a collision; kinetic energy generally is not. Use momentum to work out what happens after an impact, and energy to work out how much damage it did.
  3. 3.The force line is an average over the stopping time. A real impact peaks well above it, which is why safety design targets the peak rather than the mean.

The formula

  1. Momentum p = mv1500 * 20
  2. Kinetic energy ½mv²0.5 * 1500 * 20 ^ 2
  3. Impulse needed to stop itabs(30000)
  4. Average force over that timeabs(30000) / 0.15
  5. That force in US tons-force (2,000 lb)200000 / (2000 * 0.4535924 * 9.80665)

Source: NIST Special Publication 811 — guide for the use of the SI, BIPM — the SI Brochure, base and derived units

Questions people actually ask

Why does a longer stopping time reduce the force?
The impulse — force times time — has to equal the momentum you are removing, and that total is fixed by the mass and speed. Spread it over twice the time and the force halves. Crumple zones, airbags and safety nets all work by buying time.
Can momentum be negative?
Yes, and the sign matters. Two objects moving toward each other have momenta of opposite sign, and a head-on collision between equal and opposite momenta leaves zero — both stop dead, and all the kinetic energy goes into deformation.
What is the difference between momentum and impulse?
Momentum is what an object has; impulse is what you apply to change it. They share a unit, because an impulse of one newton-second changes momentum by exactly one kilogram-metre per second.

Related

Put this calculator on your site

Free, no attribution required beyond the link.

<iframe src="https://rulecalculators.com/embed/momentum" width="100%" height="420" style="border:1px solid #e7e4de;border-radius:12px" title="Momentum Calculator"></iframe>
Did this answer your question?