Force and Rate of Change of Momentum — Momentum | IGCSE Physics

Exam Frequency Analysis

Past paper frequency (2018 to 2024)

This topic accounts for approximately 10% of your exam marks.

stable

Medium

Stable10%

Conservation of momentum and impulse calculations appear consistently across both papers.

Force as the rate of change of momentum

Combining F = ma and the definition p = mv gives a more general form of Newton's second law:

F = Δp / t = (mv − mu) / t

where:
- F = resultant force (N)
- mv − mu = change in momentum, Δp (kg m/s), i.e. final momentum minus initial momentum
- t = time over which the change happens (s)
In words: the resultant force on an object equals its

Contact time and impact force

For a given change in momentum, the force and the are inversely proportional to one another:
- Halve the contact time and the impact force doubles
- Triple the contact time and the impact force falls to a third
Real safety design therefore aims to extend the contact time during a collision to make the impact force as small as possible (see section 5)

Example A — during the same return shot, a 0.40 kg football undergoes the same change in momentum of 8.0 kg m/s in two different scenarios: scenario 1 has a foot-on-ball contact time of 0.050 s, scenario 2 has a contact time of 0.50 s. Compare the average force on the ball.

Scenario 1: F = Δp / t = 8.0 / 0.050 = 160 N
Scenario 2: F = Δp / t = 8.0 / 0.50 = 16 N
The same change in momentum, delivered over ten times longer, gives a force that is ten times smaller

Example B — a 1200 kg car drives at 18 m/s into a wall and rebounds at 4.0 m/s in the opposite direction. The collision lasts 0.20 s. Calculate the average force on the car and state its direction.

Take the car's forward (towards-wall) direction as positive: u = +18 m/s, v = −4.0 m/s
Δp = m(v − u) = 1200 × (−4.0 − 18) = 1200 × (−22) = −26 400 kg m/s
F = Δp / t = −26 400 / 0.20 = −132 000 N
The minus sign tells you the force on the car points in the opposite direction to its original motion, that is, backwards from the wall, as you would expect

Exam tip

Using F = Δp / t: direction is a mark

What comes up: calculate the average force during a collision, given mass, initial and final velocities, and the contact time.

Write (two marks): (1) Substitute the change in momentum (final − initial) and the time into the formula: F = (mv − mu) / t. (2) Evaluate to give the force with the correct unit (N). The mark scheme accepts the alternative route via F = ma and a = (v − u) / t.

Watch out: if the object changes direction, the final velocity carries the opposite sign to the initial velocity. Failing to use the negative sign means the change in momentum is wrong and at most one mark is scored. Always state which direction you have taken as positive before you substitute.