Measurement Uncertainty Activities

I was inspired after a recent [Global Physics Department Meeting](!/), where we discussed uncertainty, to update the measurement uncertainty activities we do at the start of the year.

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I just finished these activities with my Honors Physics classes.

I have a different purpose in mind for each station beside practicing measuring and the crank-three-times method (I found [this document]( extremely helpful in refining my understanding of uncertainty and introducing me to the crank-three-times method):

1. **area of the desk**: I want students to appreciate that using a reasonable measuring device can result in results with relatively small uncertainties. I also wanted students to appreciate how the uncertainty of individual measurements are compounded during calculations. I was pleased that students mentioned how the curved edge of the desk made this measurement more uncertain and how ensuring that the meter stick was parallel to the side being measured was challenging.

2. **classroom volume**: I want student to appreciate that the uncertainty of a measurement is not solely due to the measurement device (e.g., the meter stick) but also to how you use it (e.g., having to lay meter sticks end-to-end or marking and moving a meter stick). This is also a good opportunity for students to learn to express results using unit prefixes that are easier to comprehend. Cubic meters work better than cubic centimeters.

3. **dime volume**: I want students to appreciate that what is a reasonable measuring device for one measurement is not for another. You shouldn’t use a ruler to measure the thickness of a dime; if you do, your uncertainty as a percentage of your measurement is huge. Students suggested using both alternative measuring devices (e.g., calipers) as well as entirely different techniques (e.g., water displacement of multiple dimes).

4. **time light**: I wrote a LabVIEW VI that lights a bulb on the computer screen for a specific amount of time. This activity reinforces the lesson from #2 (i.e., the uncertainty of measuring a time interval with a stopwatch is overwhelmingly due to human reaction time and not the precision of the stopwatch display). I also wanted to gather this data to calculate the uncertainty of this type of measurement which we can use in future labs. Below are the results.

5. **cart on a ramp**: This also reinforces the lesson from #2 but involves additional uncertainty due to the interaction of multiple people (i.e., one person calling out second intervals and others marking position). Students realized that they couldn’t define a single measurement uncertainty for all position measurements since it appeared that the uncertainty was greater the faster the cart was moving. I also wanted to gather this data to calculate the uncertainty of this type of measurement which we can use in a lab next week.

6. **pendulum period**: I want students to realize that the experimental procedure can have a dramatic affect on uncertainty (i.e., timing 10 cycles results in much less uncertainty than timing just one).

Throughout the day, we captured 275 time measurements for the blinking light. I created a histogram in LoggerPro and calculated the standard deviation:

histogram of time light

The distribution appears to be gaussian in nature and the standard deviation is 0.1 seconds. So, this year, when using a stopwatch to measure a time interval, we will use ± 0.1 seconds as our measurement uncertainty. The actual value programmed was 4.321 s.

Here are the histograms for the position measurements:

histogram of position at 1 s

histogram of position at 2 s

histogram of position at 3 s

The distributions for the position measurements had much greater uncertainty than I hoped. Also, they were more complicated to make; so, I don’t have as much data as I do for the timed light. I’ll have more classes do this activity next week which will provide more data. Regardless, we may need to reconsider next week’s accelerated motion lab since measuring position visually based on a stopwatch time has a very high uncertainty. In past years, we used spark timers and tapes for accelerating objects, but our spark timers no longer make clear dots on the tape. Any suggestions?

6 thoughts on “Measurement Uncertainty Activities

  1. Andy Rundquist

    I wonder if you would get “better” data for the cart if you marked out positions and had different kids stop their stopwatches when the cart hit those positions. That’s sort of the opposite of what you did (call out times and measure positions). I think the act of stopping the watch when you see the car cross a line might be more accurate than looking at a point when you hear someone say “1 second!”.

    I really like all of these activities, by the way. Getting the students to really think about uncertainties and how they affect measurements is very cool. Thanks for the great post! -Andy

    1. geoff Post author

      That’s a good idea. I think it would reduce the uncertainty. We could have a good discussion about experimental design. It would also provide an opportunity to discuss independent and dependent variables and how they should be represented on a graph.


  2. gasstationwithoutpumps

    Measuring time is generally the easiest thing to do precisely. It might be worthwhile to have students research the precision and accuracy of various standard measuring tools (clocks, precision timers, lab scales, bathroom scales, meter sticks, calipers, interferometers, … ) and notice that time is one of the most accurately measurable things—largely because we can make extremely stable oscillators and count pulses.

    For measuring position at high speed, a common solution these days is to use a high-speed camera of the object in front of a scale (as seen on Mythbusters in a large fraction of the episodes). A high-speed camera is expensive for class (entry-level systems are advertised for $20,000), but even an ordinary 29.97 frame/sec video camera can give you much better precision than eyeballing things while someone calls out stopwatch numbers.

    1. geoff Post author

      Great point about measuring time. I think I’ll leave it open to groups to decide how the want to gather their data for this lab and encourage them to use the results from this activity to influence their decision.

      We’ll use the video camera for our free-fall lab and they do work great. We use a Casio Exilim EX-FH20 when we need the high frame rate. For this early lab, I want to keep it low-tech and have them make measurements and create graphs by hand before we break out the sensors, cameras, and LoggerPro. Maybe I’m too old fashion 🙂


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