Supplement (Extended) content
IGCSE 0625 · Section 1.6 · Extended

Spread the change over more time.

A resultant force is really the rate at which momentum changes. That single idea explains crumple zones, airbags and crash mats: the change in momentum is fixed, so making it happen over a longer time makes the force gentler.

The Key Idea

The resultant force equals the rate of change of momentum: F = Δp ÷ Δt = (mv − mu) ÷ t. For a given change in momentum, a longer time produces a smaller force, and a shorter time a larger one.

SECTION 01

Bounce back, double the force.

A 0.50 kg object travels at 20 m/s toward a wall. Decide what happens on impact, then press Launch. Stopping dead gives a change in momentum of 10 kg m/s. Rebounding at the same speed reverses the velocity, so the change in momentum doubles to 20 kg m/s, and the force doubles with it. The contact time slider then shows how a longer impact softens that force.

SECTION 02

Where this shows up.

It is the time that changes the force

Safety features do not change the momentum that must be lost; that is fixed by the mass and speed. They work by increasing the time over which the momentum changes, which reduces the force, since F = Δp ÷ t. Also remember that when an object rebounds, the change in momentum uses the signed velocities, so Δp is larger than for an object that simply stops.

Worked Example

A 0.16 kg ball hits a wall at 12 m/s and rebounds at 8.0 m/s. The contact lasts 0.050 s. Taking the direction toward the wall as positive, find the average force on the ball.

Step 1 · Change in momentum (mind the sign) Δp = m(v − u) = 0.16 × (−8.0 − 12) = −3.2 kg m/s
Step 2 · Force F = Δp ÷ t = −3.2 ÷ 0.050 = −64 N
Step 3 · Interpret The magnitude of the force is 64 N, and the negative sign shows it acts away from the wall, back on the ball.
Practice this topic →
Six original Cambridge-style questions.
Force as the rate of change of momentum, calculating force from a momentum change, rebounds, and explaining cushioning safety features. Attempt each, then reveal the worked solution.