Impulse
Impulse is the change of momentum of an object. It equals the product of force and the time for which it acts. Its unit is N s, which is the same as kg m s⁻¹.
Key formula
Impulse = Ft = mv − mu
Impulsive force F = (mv − mu) ÷ t
where m = mass, u = initial velocity, v = final velocity, t = time of contact.
Impulsive force
An impulsive force is a large force that acts over a very short time during a collision or explosion, for example a bat hitting a ball. For a given change in momentum, a longer contact time gives a smaller force, while a shorter contact time gives a larger force.
Worked example
A 0.5 kg ball hits a wall at 8 m s⁻¹ and bounces back at 6 m s⁻¹ in 0.02 s. Taking the initial direction as positive:
Change in momentum = m(v − u) = 0.5 × (−6 − 8) = −7 kg m s⁻¹ (magnitude 7 N s).
Impulsive force = 7 ÷ 0.02 = 350 N (directed away from the wall).
Applications
Crumple zones, padded gloves and thick gym mats lengthen the contact time to reduce the impulsive force and prevent injury. Nails and hammers use a very short time to give a large force.
Remember
- Impulse = Ft = change in momentum.
- Longer time → smaller impulsive force (for the same impulse).
- Include direction: a bounce reverses velocity sign.