A Question of Timing…

The city of Geneva has been consumed by a fitness craze lately and it seems like everyone has taken up walking. To maximize the health benefits people are walking at both a brisk and constant rate.

A local physics teacher capitalizes on the trend and has assigned extra credit work to his top two students, Jane and Fred. Their task is to determine the average speed of a particularly enthusiastic walker, Mr. D. To determine Mr. D’s speed the students are given the following materials:

1. Stopwatches (2)

2. Metric measuring tape (1)

In the space provided explain a procedure the students could use to determine Mr. D’s average speed.

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Pretty trivial you may think, but not so fast…

To make the task worthy of extra credit the teacher has programmed a constant error into each stopwatch so that each reads a little longer or shorter than it should!

As an example, consider a stopwatch that measures the time it takes a runner moving at 5 m/s to travel 10 meters.

If the stopwatch works correctly it should read:	_______ seconds.
If the stopwatch always adds 2.4 seconds to each measurement, then instead of reading the time above it will actually read:	_______ seconds.

THE GOALS:

Fred and Jane want to:

1. Determine Mr. D’s average speed.

2.

Uncover the error programmed into the stopwatches.

You will earn your team 20 points for each goal you help Fred and Jane reach.

Procedure:

Fred and Jane have marked off a starting line as well as a line at 12 meters and another at 24 meters. Each stands at the line as indicated and starts timing when Mr. D crosses the starting line and stops their clock as Mr. D passes their respective line.

Start		Fred		Jane

12 m

24 m

Mr. D. is very accommodating and gladly allows the team to time him for the following 10 trials.

Trial	Fred (12 m)	Jane (24 m)	Difference in Times
1	6.22	8.02
2	6.22	8.01	How far did Mr. D travel in this time?
3	6.19	8.05
4	6.20	8.02
5	6.19	7.98
6	6.20	8.01
7	6.20	8.01
8	6.19	8.01
9	6.19	8.02
10	6.18	8.01
Averages

Jane suggests that she and Fred switch positions and repeat the experiment. Maybe she’s on to something… The new data is listed below.

Trial	Jane (12 m)	Fred (24 m)	Difference in Times
1	3.03	11.20
2	2.98	11.18	Again, how far did Mr. D travel in this time? ANS: _____m
3	3.04	11.19
4	3.03	11.20
5	3.01	11.17
6	2.99	11.20
7	2.99	11.23
8	2.99	11.19
9	3.03	11.19
10	3.01	11.19
Averages

Analysis:

As was the case with the example stopwatch, the ones used above can either add or subtract time from the true times. Determine what should be done to the data to answer the question and explain exactly what you did in the space below. Use the back of this paper if necessary. BE METHODICAL!!

Explain why Jane’s idea to switch and retake data is so important. Can the problem be solved without doing this?

FINAL ANSWERS:

Mr. D’s SPEED = _______ m/s ERRORS: JANE’S = ______ s

FRED’S = ______ s

Conclusion/Extensions:

The actual average speed of Mr. D is _______ m/s.

The error programmed into each stopwatch is for Jane, _______ seconds and for Fred, _______ seconds.

We will be determining the average speed of a muon in lab soon. The experiment setup is very similar to the one used here to determine the average speed of the walker Mr. D. Like the stopwatches used in the experiment above, the timers inside the photo multiplier tube are subject to making errors as well. It’s up to us to determine what these errors are and calibrate our data accordingly. To determine the correct time of flight for the muon (and thus the correct speed), we will use a technique very similar to the one used above.