Calculating Force: Venus Williams’ Racquet

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

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

In this example, the velocity just after impact and the change in time are given; thus, once $\mathrm{\Delta }p$ is calculated, $F_{\text{net}}=\frac{\mathrm{\Delta }p}{\mathrm{\Delta }t}$ can be used to find the force.

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

Now the magnitude of the net external force can determined by using $F_{\text{net}}=\frac{\mathrm{\Delta }p}{\mathrm{\Delta }t}$:

where we have retained only two significant figures in the final step.

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 $F_{\text{net}}\text{=}\text{ma}$, but one additional step would be required compared with the strategy used in this example.