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Stopwatch Uncertainty Activity

This activity was inspired by an activity in Lillian McDermott's Physics By Inquiry book.

In the Logger Pro Sample Movies folder, there is a file called "Basketball Shot.mov" that I like to use for this.  It shows a typically nerdy physics teacher halfheartedly lofting a basketball near the goal for a complete airball, since all he wants is to collect a parabolic graph.  

1.  Ask the students, "How accurate are you with a stopwatch?"  You may choose to give them a moment or two to play with the stopwatches to decide.  Discuss the responses briefly.  There is always agreement that stopwatches aren't the best way of measuring things, since there is always reaction time.  I discuss with them the difficulty of measuring various types of events with stopwatches, a footrace, a rocket launch, etc.

2. Next I tell the class we are going to try and determine a reasonable estimate of the variation in stopwatch measurements in this class.  I pass out a bunch of stopwatches, And show the video on the projector.  We repeat the video several times, each time I ask for their time from the moment the ball is released until it hits the ground.  I record all of the values on the chalkboard.  Occasionally, if a value is much different from the others, we discuss if we have confidence in it, and decide whether or not to discard it.

3. After a large number of values is obtained, I ask "How should we deal with these numbers?"  Typically, the class suggests averaging them (this often comes before graphical analysis, so students don't usually suggest that approach).  We produce an average of the numbers.  Then I ask, "Which measurements are the best?"  Clearly, the ones closest to the average are the best. Next, I ask, "What's the worst-case accuracy I can expect for a typical stopwatch measurement in this class?"  The answer is the value farthest from the average.  I suggest that we should decide on a range of values for stopwatch accuracy from our data, and use that throughout the year.  Any measurement reported from using a stopwatch should be reported as ___ plus/minus 0.2 s.  Typically this is what we come up with.
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