2.7 - Impulse and Impulsive Force

Impulse and Impact Time

• Impulse, $J$, is a change in momentum:

• Impulsive force is the rate of change of momentum during a collision or impact over a short time:

• $t$ is the impact time. Impulse is measured in $\mathrm{N}\mathrm{s}$ and force in N.
• For a fixed change in momentum, $F\propto 1/t$: extending impact time reduces the force; shortening it increases the force.
• A long-jump athlete bends the legs on landing to reduce the impulsive force on the body.

Newton’s Third Law and Applications

• Newton’s Third Law of Motion: every action force has a reaction force of equal magnitude in the opposite direction.
• Follow through in football: following a strong kick produces a larger impulse, a larger change in the ball’s momentum and a higher ball velocity. The foot acts on the ball; the ball reacts on the foot.
• Car crumple zone: deformation extends collision time, reducing impulsive force for the change in momentum. The car acts on the obstruction; the obstruction reacts on the car.
• Mortar and pestle: the hard mortar stops the fast-moving pestle in a short time, producing a large impulsive force. The pestle acts on the mortar; the mortar reacts on the pestle.

Worked Examples

Plasticine sticking to a wall: $m=0.058\mathrm{kg}$, $u=10\mathrm{m}{\mathrm{s}}^{-1}$, $v=0$.

Impulse acts opposite to the plasticine’s initial velocity.

Golf ball: $m=45.93\mathrm{g}=0.04593\mathrm{kg}$, $u=0$, $v=50\mathrm{m}{\mathrm{s}}^{-1}$, $t=0.005\mathrm{s}$.

The force acts in the direction of the ball’s final velocity.