A Question of Timing…
The city of
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.
_________________________________________________________________________________________________________________________________________________________________________________________________________________________________
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.

_______ seconds. 

_______ 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.