Momentum and Impulse Calculator
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Momentum is mass times velocity, p = mv. Impulse is the change in momentum: J = FΔt = Δp. A 0.15 kg baseball going from −40 m/s to +30 m/s gets an impulse of 0.15 × 70 = 10.5 N·s; over 2 ms of contact that is an average force of 5,250 N.
| Initial momentum | −6 kg·m/s |
| Final momentum | 4.5 kg·m/s |
| Average force over 0.002 s | 5,250 N |
Show steps
- \(J = \Delta p = m(v – v_{0}) = 0.15(30 – (-40)) = 10.5\ \text{N·s}\)
- Average force: \(F = \frac{\Delta p}{\Delta t} = 5{,}250\ \text{N}\)
How to use the momentum and impulse calculator
- Choose momentum, impulse from force and time, or the change in momentum.
- Enter the values; use negative velocities for motion in the opposite direction.
- Add a contact time to get the average force of an impact.
Formulas
- Momentum: \(p = mv\) (kg·m/s)
- Impulse: \(J = F\,\Delta t\) (N·s)
- Impulse–momentum theorem: \(J = \Delta p = m(v – v_{0})\)
- Average force: \(F = \frac{\Delta p}{\Delta t}\)
Why longer contact times are safer
For the same change in momentum, a longer stopping time means a smaller force. Airbags, crumple zones and bending your knees when landing all increase Δt to reduce F.
Conservation of momentum
In a collision with no outside forces, the total momentum before equals the total momentum after: \(m_{1}v_{1} + m_{2}v_{2} = m_{1}v_{1}^{\prime} + m_{2}v_{2}^{\prime}\).
Momentum and impulse practice quiz: 10 questions
Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.
Quiz complete
Frequently asked questions
What is momentum?
Momentum p = mv is mass times velocity. It is a vector that points in the direction of motion.
What is impulse?
Impulse J = FΔt is force multiplied by the time it acts. It equals the change in momentum.
How do I find the force of an impact?
Divide the change in momentum by the contact time: F = Δp/Δt.
Why use negative velocities?
Velocity has direction. If an object reverses, one velocity is positive and the other negative, which correctly makes the change larger.
Is momentum always conserved?
Total momentum is conserved when no external net force acts on the system, such as in most short collisions.
Sources
- OpenStax University Physics Volume 1
- OpenStax College Physics 2e
- NIST Special Publication 811: Guide for the Use of the SI
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