Impulse on a tennis ball

Problem

A tennis ball of mass $m = 60\;\mathrm{g}$ arrives at a racket at $v_i = 25\;\mathrm{m/s}$ and bounces back at $v_f = 30\;\mathrm{m/s}$ in the opposite direction. Calculate the magnitude of the impulse transferred to the ball.

Solution

The impulse equals the change in momentum (impulse–momentum theorem): $J = \Delta p = m\,(v_f - v_i)$ Since the ball bounces back, the two velocities have opposite directions. Take the incoming direction as positive: then $v_i = +25\;\mathrm{m/s}$ and $v_f = -30\;\mathrm{m/s}$. Convert the mass: $m = 60\;\mathrm{g} = 0{,}060\;\mathrm{kg}$. $J = 0{,}060\;\mathrm{kg}\cdot\big(-30 - (+25)\big)\;\mathrm{m/s} = 0{,}060\cdot(-55)\;\mathrm{kg\,m/s}$ $J = -3{,}3\;\mathrm{kg\,m/s}$ The negative sign indicates that the impulse is directed towards the racket (opposite to the incoming direction). The required magnitude is: $\ev{\abs{J} \approx 3{,}3\;\mathrm{kg\,m/s}}$

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Topics: Quantità di moto e urti Concepts: Impulso · Quantità di moto