This lab provides the opportunity to investigate a realworld collision. 
Determine the value in newtons of the average force of impact of a
ball rebounding in a collision.
The textbook theory that serves as a foundation for this
lab is in sections 9.13.
Two collisions are available for study in this lab. One collision is that of a tennis ball with a wall, and that is that of a racquetball with the floor. For the former collision, a tennis ball was shot horizontally from a slingshot
toward a wall. In the photo to the right, former NCSSM students Eric Deren and
Sean McGrew load the slingshot. Here's a video clip of the slingshot in action. This was a segment in an
ESPN documentary about NCSSM.
In the other collision, a racquetball was thrown downward onto the floor. Download and play one of the 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. Some clips
are provided in both MP4 and MOV format. Use either format. For the racquetball collisions, note that the camera was rotated 90°; that's why the ball appears to be moving sideways.
For the collisions, a highspeed camera recorded the collision at a rate of 2.000E3 frames per second (1/2000 s per
frame).

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.

Submit your answers to the following before proceeding with the method. Upload your scanned file, named L133PLlastnamefirstinitial.pdf to Brainhoney.

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

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.

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

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.

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.

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

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 and the ball as a whole moves throughout the collision. (Do you see why this would exclude the point of the ball that contacts the wall first?)
We're providing notes to guide you rather than giving you a stepbystep list of instructions.

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 2000. fps (assume 4 significant figures).
There are two methods to deal with this: i) The simplest method 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.

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

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.

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.
:
Throughout your work, use the same symbols that you defined in the prelab unless the instructor recommended that you use different symbols. 
Record the following in a textbox on the same page as the graphs.

the filename of your video clip

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

matching tables and equations of fit

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

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
Answer the following on a second page of your Logger
Pro file. Provide complete explanatory answers.

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: F_{ave} = Rounded value ± Absolute uncertainty.

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.)

Does your result for the average force of
impact make sense? How much force would it take to squash a racquetball or tennis ball 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.)
Write your conclusion on the same page as the discussion. Review the lab guide as needed to see what to include.
Submit your Logger Pro file to WebAssign.
