Average Force of Impact of a Racquetball Collision

Goal

Determine the the average force of impact of a racquetball colliding with the floor.

Introduction

A racquetball was thrown downward onto the floor. A high-speed camera recorded the collision at a rate of 1200 frames per second (1/1200 s per frame). Download and play one of the two clips below. You'll decide what data to collect from the video clip in Logger Pro and how to analyze it in order to determine the average force of impact of the ball with the floor. The clips are provided in both MP4 and MOV format. Use either format. Note that the camera was rotated 90°; that's why the ball appears to be moving sideways.

 MP4 1960.mp4 1963.mp4 MOV 1960.mov 1963.mov

Prelab: Theory, Design, and Prediction

 Important! In order to avoid confusion, the words vertical and horizontal as used in the instructions refer to the apparent dimensions in the video clip. In your theory, ignore the vertical motion of the ball. At the end of the experiment, you'll discuss whether that was a good assumption.

Answer the following before proceeding with the method.

1. How will you scale the video clip to real world distances?

2. In order to measure the change of horizontal momentum of the ball in the collision, what three things must you know? State each in a phrase and assign them a symbol.

3. Which of the three things above cannot be determined from the video clip? How will you determine this piece of data?

4. In order to use the change of horizontal momentum to determine the average force of impact in the collision, what else must you measure? How can you measure this from the video clip? Assign a symbol to this measurement and define it clearly.

5. Starting with a fundamental physics principle, determine the formula that you will use to calculate the average force of impact in the collision. Write your formula in terms of the four symbols defined above.

6. Sketch a quarter-page graph of your prediction of the horizontal velocity of the ball as a function of time, including times before, during, and after the collision. Assume that +x is to the right.

7. What part of the ball will you click on to mark positions in Logger Pro? Keep in mind the fact that the ball changes shape during and after the collision.

Notes about the Video and Graphical Analysis

1. When you import the video clip into Logger Pro, a frame rate of 29.97 fps is assumed by LP, because that's the standard frame rate for the NTSC video format that video cameras use. However, the real world frame rate is 1200 fps (assume 4 significant figures). There are two methods to deal with this: i) The simplest method, if available in the version of LP that you're using, is to use the Options -> Movie Options command to set the actual frame rate. ii) Otherwise, create a calculated column in LP to convert the NTSC time to the real time.

2. Scale the video using a known distance. You'll need to look up this distance or measure it yourself.

3. Plotting the horizontal position as a function of time will give you two distinct linear regions separated by the collision. You can apply a linear fit to each region independently by dragging the cursor across only the points that you want to fit. Avoid using points in the collision region where the velocity is changing.

4. By default, Logger Pro creates columns for vertical and horizontal velocities. Delete these columns. Applying a linear fit to the data is a much better way to determine velocity.

Data and Calculations

Record the following in a textbox.

1. the filename of your video clip

2. any additional data that you use that is not obtained from the video clip. State how you obtained this data, and label it descriptively.

3. the information that you obtain from your Logger Pro analysis to use in the calculation of the average force of impact

4. Starting with your formula for the average force of impact, substitute your data and relevant coefficients from your fits to show your calculation of the average force

Discussion

Answer the following on a second page of your Logger Pro file.

1. What is the uncertainty in your calculation of the average force of impact? Consider this: The limiting factor is your estimate of the number of frames that the collision lasts. Use that estimate to determine the relative uncertainty in the collision duration. Assuming this is the only important error, this will also be the relative uncertainty in the force of impact. Use that relative uncertainty to calculate the absolute uncertainty in the average force. Knowing that, round your value of force to the appropriate number of significant figures and express your final result for the average force of impact like this: Fave = Rounded value ± Absolute uncertainty.

2. Does ignoring the vertical motion of the ball introduce significant error into the determination of the force of impact? In order to answer, investigate your graph of the vertical position as a function of time. What are the vertical velocities before and after the collision? If you used these velocities to calculate the force of impact, what would the result be? Show your work. Is the result significant when compared to the force calculated using the horizontal velocities? (Use your answer to question 1 to help in determining significance.)

3. Does your result for the average force of impact make sense? How much force would it take to squash a racquetball about the same amount as that shown in the video? (If you think in pounds rather than newtons, check your textbook or other source for a conversion factor.)