All Labs

Momentum & Impulse Lab

Explore how force and time combine to change momentum. Compare different force profiles, discover why crumple zones save lives, and verify the impulse-momentum theorem with real data collection.

Guided Experiment: Impulse-Momentum Theorem

If you increase the contact time during a collision while keeping the impulse constant, what happens to the average force?

Write your hypothesis in the Lab Report panel, then click Next.

Controls

Mass2.0 kg
Initial Velocity5.0 m/s
Final Velocity-3.0 m/s
Peak Force800 N
Duration (Δt)0.020 s

Results

J=Δp=m(vf−vi)=−16.0000 N\cdotpsJ = \Delta p = m(v_f - v_i) = -16.0000 \text{ N·s}
Favg=JΔt=−800.0000 NF_{avg} = \frac{J}{\Delta t} = -800.0000 \text{ N}
Initial Momentum
10.0000 kg·m/s
Final Momentum
-6.0000 kg·m/s
Impulse (from Δp)
-16.0000 N·s
Impulse (from profile)
16.0000 N·s
Average Force
-800.0000 N
Velocity Change
-8.0000 m/s
Adjust peak force or duration so profile impulse matches momentum change

Force vs Time — Constant Force

Shaded area = impulse (J). Same momentum change can be produced with different force shapes.

Data Table

(0 rows)
#TrialProfileMass(kg)v_i(m/s)v_f(m/s)Impulse J(N·s)F_avg(N)Δt(s)
0 / 500
0 / 500
0 / 500

Reference Guide

Momentum

Momentum is the product of mass and velocity. It is a vector quantity with the same direction as velocity.

p=mvp = mv

Units are kg·m/s. A 2 kg cart at 5 m/s has the same momentum as a 10 kg cart at 1 m/s.

Impulse

Impulse is the product of average force and time. It equals the area under a force-time curve.

J=Favg⋅Δt=∫0ΔtF(t) dtJ = F_{avg} \cdot \Delta t = \int_0^{\Delta t} F(t)\, dt

Units are N·s, which are equivalent to kg·m/s. Impulse has direction — it matches the direction of the net force.

Impulse-Momentum Theorem

The impulse delivered to an object equals its change in momentum. This follows directly from Newton's second law.

J=Δp=m(vf−vi)J = \Delta p = m(v_f - v_i)

If the impulse is known, the velocity change is found from Δv=J/m\Delta v = J / m. This connects force, time, mass, and velocity in one relationship.

Crumple Zones

Crumple zones extend collision time. For the same impulse (same momentum change), a longer duration means lower average force:

Favg=JΔt=ΔpΔtF_{avg} = \frac{J}{\Delta t} = \frac{\Delta p}{\Delta t}

Doubling the collision time halves the average force on the passenger. Airbags, foam padding, and crumple zones all use this principle to reduce injury during sudden stops.