During the 2007 French Open, Venus Williams (Figure 8.3) hit the fastest recorded serve in a premier women’s match, reaching a speed of 58 m/s (209 km/h). What was the average force exerted on the 0.057 kg tennis ball by Williams’ racquet? Assume that the ball’s speed just after impact was 58 m/s, the horizontal velocity before impact is negligible, and that the ball remained in contact with the racquet for 5 ms (milliseconds).
Figure 8.3 Venus Williams playing in the 2013 US Open (Edwin Martinez, Flickr)
STRATEGY
Recall that Newton’s second law stated in terms of momentum is
𝐅net=Δ𝐩Δ𝑡.�net=Δ�Δ�.
As noted above, when mass is constant, the change in momentum is given by
Δ𝐩=𝑚Δ𝐯=𝑚(𝐯f−𝐯i),Δp=�Δv=�(vf−vi),
where vf is the final velocity and vi is the initial velocity. In this example, the velocity just after impact and the change in time are given, so after we solve for Δ𝐩Δp, we can use 𝐅net=Δ𝐩Δ𝑡�net=Δ�Δ� to find the force.
Discussion
This quantity was the average force exerted by Venus Williams’ racquet on the tennis ball during its brief impact. This problem could also be solved by first finding the acceleration and then using Fnet = ma, but we would have had to do one more step. In this case, using momentum was a shortcut.
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