Calculating Force: Venus Williams’ Racquet

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).

Serena Williams is a famous tennis player. In this image she is hitting a tennis ball with a tennis racket.

Figure 8.3 Venus Williams playing in the 2013 US Open (Edwin Martinez, Flickr)

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
Recall that Newton’s second law stated in terms of momentum is

$F_{net} = \frac{Δ p}{Δ t} .$
As noted above, when mass is constant, the change in momentum is given by

$Δ p = m Δ v = m (v_{f} - v_{i}),$

where v_f is the final velocity and v_i is the initial velocity. In this example, the velocity just after impact and the change in time are given, so after we solve for $Δ p$ , we can use $F_{net} = \frac{Δ p}{Δ t}$ to find the force.
Solution
To determine the change in momentum, substitute the values for mass and the initial and final velocities into the equation above.

$\begin{matrix} Δ p & = & m (v_{f} - v_{i}) \\ = & (0 .057 kg) (58 m/s – 0 m/s) \\ = & 3 .306 kg·m/s \approx 3 .3 kg·m/s \end{matrix}$
8.1

Now we can find the magnitude of the net external force using $F_{net} = \frac{Δ p}{Δ t}$

$\begin{matrix} F_{net} & = & \frac{Δ p}{Δ t} = \frac{3.306}{5 \times 10^{- 3}} \\ = & 661 N \\ \approx & 660 N. \end{matrix}$
8.2

0 of 2 steps open

How did it go?

Strategy

Solution