When a force acts on an object that is moving, or able to move, a change…

The idea

A force acting on an object that can move changes its momentum. The size of the force is the rate of change of momentum: F = change in momentum ÷ time taken, which on Higher Tier is written F = m Δv ÷ Δt. Two things follow. For a given change of momentum, a longer contact time means a smaller force; for a short contact time, the force is large. Work out the change of momentum as m v − m u, remembering that a rebound reverses the sign, so a ball hitting a wall at 5 m/s and bouncing back at 4 m/s has a change of velocity of 9 m/s, not 1 m/s. Because the change of momentum is fixed by the masses and velocities involved, the only way to cut the force is to make the collision last longer.

What earns the marks

• Stating that force equals the rate of change of momentum.
• Writing F = m Δv ÷ Δt, or change in momentum ÷ time taken.
• Calculating the change in momentum as final momentum minus initial momentum.
• Dividing by the contact time to give the force, with the unit N.

Common mistakes and how to put them right

• Using the final velocity rather than the change in velocity.

• Forgetting that a rebound reverses the sign, so the change of velocity is larger than the rebound speed.

• Using the time for the whole journey rather than the time of the collision.

• Quoting the unit of a change in momentum as N rather than kg m/s.

Exam tips

• Write down u and v with signs before you subtract; sign errors cost more marks here than anywhere else in the topic.
• Convert a contact time given in milliseconds to seconds before dividing.
• State clearly whether the force you have found acts on the object or on what it hit.