Impulse
A short, hard hit and a long, gentle push can change momentum by the same amount.
Lesson at a glanceShow the key points
- Impulse J = ∫F dt over the contact time equals the change in momentum Δp.
- On an F–t graph, impulse is the area under the curve.
- Very large forces acting for very short times are called impulsive forces.
- For a given change in momentum, stretching the contact time lowers the peak force (airbags, bending knees, catching with give).
A cricketer catching a fast ball pulls the hands back. A high jumper lands on a thick mat. A car crumples at the front. All three are stretching out time to shrink a force.
Force over time
During a collision the force rises sharply, peaks, and drops back to zero, all within milliseconds. We rarely know its shape. But Newton’s second law in the form tells us what its total effect must be. Integrate over the collision:
On a force–time graph the impulse is the area under the curve. A large force for a short time and a small force for a long time can have exactly the same area, and so produce exactly the same change in momentum.
A 160 g ball reaches a fielder at 30 m/s. (a) What impulse must the hands deliver to stop it? (b) Compare the average force if the catch takes 0.05 s with one that takes 0.2 s.
Impulsive forces
A force that is very large but acts for a very short time, such as a bat on a ball or a hammer on a nail, is called an impulsive force. During that brief moment, ordinary forces like gravity or friction deliver negligible impulse (a modest force × a tiny time). That is why we can apply momentum conservation across a collision even when gravity or friction acts on the bodies.
- 1Impulse ; it’s the area under the F–t curve.
- 2Same Δp over a longer time means a smaller average force.
- 3During brief collisions, ordinary external forces contribute negligible impulse.
Check yourself
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