Momentum and impulse
Objective. Apply impulse-momentum principles with direction.
- 1. Learn
- 2. Worked example
- 3. Practice
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Learn: the key idea
Momentum is the product of mass and velocity, p = mv, and impulse is the change in momentum caused by a force acting over time, I = Ft = mv − mu, where u and v are initial and final velocities. In any collision or interaction with no external forces, total momentum is conserved, meaning the combined momentum before equals the combined momentum after. For example, if a 2kg ball moving at 3m/s is brought to rest by a force over 0.5 seconds, the impulse delivered is 2×0−2×3 = −6 Ns, so the average force is −6/0.5 = −12N.
Worked example
A 0.5kg ball moving at 4 m/s is struck by a bat and rebounds at 6 m/s in the opposite direction. Find the impulse exerted by the bat on the ball.
- 1Take the initial direction as positive, so initial velocity u=4, final velocity v=−6
- 2Impulse = change in momentum = mv − mu
- 3Substitute: 0.5(−6) − 0.5(4) = −3 − 2
- 4Impulse = −5 Ns, meaning 5 Ns in the direction opposite to the ball's initial motion
Answer: Impulse = −5 Ns (5 Ns opposing initial motion)
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Practice
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Start practisingCommon mistake. Students forget to assign consistent positive and negative directions, adding momenta of objects moving in opposite directions as if both were positive. Always define a positive direction first and use signed velocities throughout.
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