Video Lab 9

Trapped! Analysis of a Real Collision

Introduction

In one type of physics problem involving a collision, one is given initial and final velocities of an object, the mass of the object, and the duration of the collision. One can then calculate the average net force of impact using the relationship:

F_ave = Dp/Dt.

This method provides no information about how the force changes with time during the collision. Such information may be difficult to obtain; nevertheless, it can provide some interesting insights into the collision process.

The purpose of this lab to investigate a real collision that takes place over a time span of only about 5 milliseconds. Even with such a short duration, details of how the force changes as a function of time can be obtained from multiple-image high-speed photographs. Such a photograph is shown below.

The photo shows 8 successive images of an elastic strip being struck by a BB. The images were produced by 8 flash bursts approximately half a millisecond apart in time. Different colored filters were placed over each flash unit, thus making it possible to distinguish overlapping images in the photo.

The strip was initially hanging vertically from a clothespin and the BB approached at high speed from the left, striking the strip in the center. The strip hung freely, with nothing being attached to the lower end. The BB was able to stretch the strip, because the BB was moving much faster than the speed at which disturbances could travel along the length of the strip.

Interestingly, the BB did not penetrate the strip but was trapped instead. The BB is within the vertex of each wishbone-shaped image. (In the first, red image, the BB has barely begun to stretch the strip. The slight curvature of the strip on either side of the BB is due to the puff of air from the air gun.) Obviously, the strip is decelerating the BB at the same time that the BB is accelerating the strip. The purpose of the lab will be to determine how the force on the BB changes with time during the collision. This information can be obtained from position vs. time data.

Prelab

The following exercise provides practice in using the video analysis feature of Logger Pro 3.2.  The instructor will do the analysis as a demonstration.  Then you'll do your own analysis for the collision of the BB with the strip.

The photograph below shows 8 flash images of the BB before striking the strip. This is not the same BB that struck the strip in the photograph above. However, it was fired from the same gun under the same conditions. Previous tests with the gun show that the muzzle speed doesn't vary more than 5% for the same number of pumps. The time interval between images in the photo below is 0.000298 s. A distance scale has been superimposed. This scale was photographed in the same plane as that of the BB's path.

In order to be able use the video analysis tools in Logger Pro, you'll need a video clip created from eight identical frames of the image below. This will allow you to click on successive images of the BB and have the software record the screen coordinates of the image.

Right click here and save the video file to your computer.

Analysis of the Collision

Collecting data

1. Download the clip assigned you by the instructor. The time interval between images is given beside the filename in the table below.  Proceed with the analysis of the collision in a similar way to what what was demonstrated in the Prelab. That is, save the video clip to your working directory, open Logger Pro, and insert the clip.

2. Set the origin at the first image of the BB.  Then mark each image successively. Locating the position of the BB may be a difficult where images overlap. Since you know the BB is at the vertex of each image, you can center the cursor on this vertex. However, locating the vertex is more difficult where two images overlap. The color that is produced by such an overlap can help you find the vertex. For example, where the 3rd image overlaps the 4th in the image at the top of the page, the vertex appears white. Where the 5th, red image overlaps the green, you get yellow. Where green overlaps blue, you get cyan (Carolina blue).  If you have trouble locating the BB positions, click on the name of the Image File above in order to see a larger version.

3. After you've marked the eight images of the BB, set your scale factor. Then select Page, Auto Arrange to arrange your windows. You may need to use the command twice.

4. Insert a text box with the Insert, Text command.  Then Auto Arrange once more. Use this box as a lab journal to record your answers to any questions or problems as they are given. Be sure to number each of your responses with the corresponding number of the list item.  Items that require a recorded answer are given in bold font. Begin by recording your name and your partner's name.

5. Based on your reading of the introduction of this experiment, write the goal.

6. Record the time interval for your video clip and the mass and diameter of a BB.

7. Save your file with the name vlab9-xyz.xmbl before going on.

Fitting the data

8. The Time column assumes an interval of 1/30 s between frames. Change the numbers now to the actual ones for your clip.

9. Double click on the Time column heading. Select the Options tab. Set the Displayed Precision to 6 decimal places, since time was measured to the nearest microsecond.  Repeat for the X column, but set the Displayed Precision to the number of decimal places that corresponds to the precision of the measurement. Make that judgment based on the diameter of a BB and your ability to position the cursor.

10. Examine the data table. Note that velocities are already calculated.  Find out what method Logger Pro uses to calculate the velocities. First double click on one of the Velocity column headings.  In the equation window, you'll see the name of the function used to calculate the velocity. Now go to Help, Logger Pro Help. Select the Index tab and type in the keyword functions. Hit the Return key.  Scroll down the page to the table of functions, and find the function used to calculate velocity.  Select the name of the function and its description, and then copy and paste the information into your text box.

11. Now select File, Settings for <filename>.  Record the relevant value(s).  Due to the way in which the velocities are calculated, the values obtained near the beginning and end of the time range are questionable. Explain why.

12. You could use the velocity calculations to get acceleration in the same way that position was used to get velocity.  However, the results for acceleration would be even more questionable than those for velocity.  Instead, you'll use a curve-fitting method to get the acceleration.  By default, the graph plots both X and Y vs. Time. Click on the vertical axis and select only X.  Using the Analyze, Curve Fit command, try a quadratic fit to the X vs. Time data. What do you learn from this?

13. The plan is to get a good fit to the X vs. Time data and then find the second derivative of the fit in order to obtain the acceleration.  Fit the X vs. Time data with a polynomial fit. Try orders 3, 4, and 5 and decide which one is the best choice.  Explain your choice. Selecting the fit with the smallest RMSE value may not be the only consideration.

14. List the fit coefficients exactly as they are given. Don't overlook powers of ten.

15. If you haven't saved your file for a while, do it now.

16. Calculate the second derivative of your equation of fit.  List the coefficients without rounding them.

17. Create a new, calculated column using the Data, New Calculated Column command.  Name this column Acceleration, give it a short name, and enter the units. For the Equation, enter the second derivative of your equation of fit. Click on the Options tab and select a Displayed Precision of 2 significant figures. After you select Done, the values of acceleration, which should be quite large, will be displayed in scientific notation.

18. Since the force exerted on the BB by the band is the only important force in this situation, it is essentially the net force. Create one more new, calculated column to calculate this force. Label it and select the Displayed Precision appropriately.

19. Change the vertical axis of your graph to the force. Describe in words how the magnitude of the force changes with time.

20. This completes the analysis of the data. Save your file before moving on to the Discussion.

Discussion

The Webster's Revised Unabridged Dictionary gives the following as a definition of paradox: "an assertion or sentiment seemingly contradictory, or opposed to common sense; that which in appearance or terms is absurd, but yet may be true in fact." The BB-elastic strip collision presents an opportunity to pose a paradox and then attempt to resolve it. Note that while a paradox may seem contradictory, it "yet may be true in fact." Therefore, your job will be to explain how the following paradox can be true.

22. An examination of your Force vs. Time graph should reveal that the magnitude of the force on the BB is greatest at the beginning of the collision and then decreases. This force can only be due to the action of the elastic strip. Yet, you know from experience that the more you stretch an elastic band, the more it pulls back on you. The elastic strip in the photograph seems to be stretched more at the end of the collision than at the beginning. How is it possible for the force on the BB to be greatest at the beginning of the collision? Give the photograph a close examination. Then write a paragraph in which you resolve the paradox.

Submit your file to the BlackBoard course site.