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Question

A force applied by the cue (stick) caused a 200g cue ball to speed up from rest to 7.8m/s in 3 seconds. What is the change in momentum of the cue ball? What is the impulse on the cue ball? How much force was exerted on the cue ball?

Answer 1

The Impulse-Momentum Theorem says the change in momentum of some object is equal to the impulse applied to it. The change in momentum is the final momentum (P₂) minus the initial momentum (P₁). Since momentum is mass times velocity, P₂ = mv₂ = (200/1000)(7.8) = 1.56 kgm/s and P₁ = mv₁ = (200/1000)(0) = 0 kgm/s. That means that change in momentum is 1.56 - 0 = 1.56 kgm/s. That means the impulse is the same as that (except we usually use units of Ns for Impulse) so the Impulse is 1.56 Ns. (Note that kgm/s is the same as Ns)

Since Impulse is average force multiplied by the time it is exerted, then Impulse = F•t so 1.56 = F(3) or F = 1.52/3 = 0.52 N.

You can check your answer by considering Newton's 2nd Law which says F = ma. The average acceleration is (v_f - v_i)/Δt = (7.8 - 0)/3 = 2.6 m/s² so the average force is (200/1000)(2.6) = 0.52 N