During the 2007 French Open, Venus Williams hit the fastest recorded serve in a premier women’s match, reaching a speed of 58 m/s (209 km/ h). What is the average force exerted on the 0.057-kg tennis ball by Venus Williams’ racquet, assuming that the ball’s speed just after impact is 58 m/s, that

Question

During the 2007 French Open, Venus Williams hit the fastest recorded serve in a premier women’s match, reaching a speed of 58 m/s (209 km/ h). What is the average force exerted on the 0.057-kg tennis ball by Venus Williams’ racquet, assuming that the ball’s speed just after impact is 58 m/s, that the initial horizontal component of the velocity before impact is negligible, and that the ball remained in contact with the racquet for 5.0 ms (milliseconds)?

Strategy
This problem involves only one dimension because the ball starts from having no horizontal velocity component before impact. Newton’s second law stated in terms of momentum is then written as

F[latex]_{net} = \frac{Δp}{Δt} .[/latex] (8.13)

As noted above, when mass is constant, the change in momentum is given by

[latex] Δp = mΔv = m(v_f − v_i). [/latex] (8.14)

In this example, the velocity just after impact and the change in time are given; thus, once Δp is calculated,F[latex]_{net} = \frac{Δp}{Δt} .[/latex] can be used to find the force.

Accepted Answer

To determine the change in momentum, substitute the values for the initial and final velocities into the equation above.

[latex] \begin{matrix} Δp = m(v_f – v_i) \ = (0.057 kg)(58 m/s – 0 m/s) \ = 3.306 kg · m/s ≈ 3.3 kg · m/s \end{matrix} [/latex] (8.15)

Now the magnitude of the net external force can determined by using F[latex]_{net} = \frac{Δp}{Δt} .[/latex] :

[latex] \begin{matrix} F_{net} = \frac{Δp}{Δt} = \frac{3.306 kg ⋅ m/s}{ 5.0×10^{−3} s} \ = 661 N ≈ 660 N, \end{matrix} [/latex] (8.16)

where we have retained only two significant figures in the final step.
Discussion
This quantity was the average force exerted by Venus Williams’ racquet on the tennis ball during its brief impact (note that the ball also experienced the 0.56-N force of gravity, but that force was not due to the racquet). This problem could also be solved by first finding the acceleration and then using [latex] F_{net} = ma [/latex], but one additional step would be required compared with the strategy used in this example.

Question 8.2: During the 2007 French Open, Venus Williams hit the fastest ...

Related Answered Questions