How Can Physics Students Measure a Runner's Acceleration Using Simple Equipment?

[aeroengphys]

Homework Statement

A world-class runner can complete a 100 m dash in about 10s. Past studies have shown that runners in such a race accelerate uniformly for a time tu and then run at constant speed for the remainder of the race. A world-class runner is visiting your physics class. You are to develop a procedure that will allow you to determine the uniform acceleration au and an approximate value of tu for the runner in a 100m dash. By necessity your experiment will be done on a straight track and include your whole class of eleven students.

(a) By checking the line next to each appropriate item in the list below, select the equipment, other than the runner and the track, that your class will need to do the experiment.
- stopwatches - Tape measures - Rulers - Masking Tape - Metersticks - Starters Pistol - String - CHalk

(b) Outline the procedure that you would use to determine au and tu, including a labeled diagram of the experimental setup. Use symbols to identify carefully what measurements you would make and include in your procedure how you would use each piece of the equipment you checked in part (a).

(c) Outline the process of data analysis, including how you will identify the portion of the race that has uniform acceleration, and how you would calculate the uniform acceleration.

*note, the u in 'tu' and 'au' is meant to be a subscript*

The Attempt at a Solution

(a) For a i checked: stopwatches, metersticks, starter's pistol, and chalk.

(b+c) So based on my knowledge of physics, I know that a = v - v0 / t. So here's what I'm thinking. Measure out 2m intervals using the meter sticks (for the 1st 10 meters) draw chalk lines, and have students stand by those lines with a stop watch. Then have 3 students standing at 10 meter intervals (20m, 30m, 40m from the starting position). THen have 1 student standing at 60m, and another at 100m. Have the 11th student fire the pistol. When the pistol is fired, the students start their stop watches. As the runner reaches their line, they will stop their watches and record the time. This will be repeated several times to filter out any sources of error from the stop watches. Based on this, i can use the times and distances to determine the velocity within each distance. Once the velocity is calculated I can determine the acceleration of the runner over a distance of 2m, 4m, 6m, 8m, 10m etc. So that was pretty much my original idea. To be perfectly honest I have my doubts about it. I'm probably either overthinking this or not thinking hard enough. If anyone could help steer me towars an approproiate experiment, or help revise mine, i'd greatly appreciate it.

Larry

 

[weatherhead]

something to think about: you don't know (and aren't told) how long the initial burst of acceleration is. It might be that after your 10m measuring section the acceleration is still happening, but after 10m your resolution for measuring this suddenly drops.

Also, you haven't said much about the data analysis part. Again, there are a couple of ways to go at this depending how much you know about graphs, calculus etc, whether you have a computer available, whether you're planning to factor in any kind of resistance into your experiment.

 

[m2003]

Hi Larry,

Thank you for sharing your proposed experiment. Your idea of using stopwatches, metersticks, starter's pistol, and chalk seems appropriate for this experiment. However, I would suggest also using a video camera to record the race, as it can provide accurate and precise measurements of the runner's position and time.

In terms of your procedure, I would suggest using a longer distance, such as 20m or 30m, for the uniform acceleration portion of the race. This will allow for more accurate measurements and calculations. Also, instead of having the students at 10m intervals, I would suggest having them at 5m intervals to increase the number of data points and improve the accuracy of the results.

As for data analysis, you can use the recorded video to analyze the runner's position and time data. The portion of the race with uniform acceleration will appear as a straight line on a position vs. time graph. You can then use the slope of this line to calculate the uniform acceleration.

I hope this helps. Let me know if you have any further questions.

Best,