Activities in High-Speed Photography

Average Force of Impact in a Tennis Ball Collision

Introduction

The video clip below shows the collision of a tennis
ball with a vertical wall. (The clip was rotated 90°
for display purposes.) Play the clip and then step through
the frames one-by-one. You'll see that there are 10
images: 2 before the collision, 5 during the collision,
and 3 after the collision. Even though the clip runs
at 30 frames per second, the actual time interval between
frames is 9.02 x 10^{-4} s.

The video clip was produced by extracting each image from the original multiple-image photograph that contained all ten images. That photograph is shown below. Although it appears that the ball makes an oblique incidence with the wall, the ball actually strikes and rebounds from the wall at right angles. Successive images of the ball were swept horizontally by a rotating mirror that reflected the images to the camera. Therefore, the horizontal dimension is a time scale rather than a distance scale. This technique was used so that the images would not overlap and obscure useful information about the collision.

The Problem

In a collision, the change in momentum of an object is equal the impulse on that object:

The impulse is given by:

^{,
}

where is the average force acting on the object during the collision. For the tennis ball collision, the change in momentum can be determined from successive images of the ball before and after the collision. The duration of the collision can be estimated from the number of images that show the ball in contact with the wall. Therefore, the average force of impact can be determined.

Download a larger version of the video clip for analysis. Save it to your working directory.

Analysis

Click on the links to access help files.

- Use the video analysis tools at your disposal to obtain measurements of the vertical position of the ball. Since the ball changes shape both during and after the collision, you'll need to estimate where the center of the mass of the ball is in each image. You can use the diameter of an actual tennis ball for establishing a scale factor. The time intervals may be recorded as 1/30 s by your video analysis program. You'll need to correct the time scale.

Carry out a graphical analysis in which you do the following.

- Determine the velocities of the ball before and after the collision. We suggest using the first two and the last two images.
- Determine as nearly as possible the total time that the ball is in contact with the wall.
- Find the mass of a tennis ball. Then calculate the average force of impact.
- Does your result make sense?

Discussion

Make quantitative estimates of the uncertainties in each measurement. Calculate the overall uncertainty in the average force.