Measurement Uncertainty Activities

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

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](http://www.av8n.com/physics/uncertainty.htm) 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:

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 Â± 0.1 seconds as our measurement uncertainty. The actual value programmed was 4.321 s.

Here are the histograms for the position measurements:

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?

Measurement Uncertainty Activity

In previous years, my students have always struggled to really understand measurement uncertainty. Due to my background in the computer-based measurement and automation industry, I was always troubled that I didn’t do I better job helping them understand. So, this year, I developed a set of six activities to provide a hands-on way to practice applying the definitions as well as provide a context to discuss the complexities of measurement uncertainty. Each group investigated one of the activities and then whiteboarded and presented their results with the rest of the class. Each activity had the group determine the measurement uncertainty of a measuring device and calculate the maximum percent uncertainty of their measurements. However, each activity also had a deeper purpose that led to good class discussions during whiteboarding.

1. Measure the dimensions of a block with a ruler. Deeper purpose: calculate the percent uncertainty of the volume of the block.

2. Measure the width and length of the lab table with a modified meter stick (cm precision). Deeper purpose: how does having to make multiple measurements to measure the length affect the measurement uncertainty?

3. Measure the period of a pendulum with the wall clock. Deeper purpose: how does the percent uncertainty change if 2, 5, 10, or 20 oscillations of the pendulum are measured instead?

4. Measure the temperature of ice water and hot water with a digital temperature probe. Deeper purpose: is the percent uncertainty of the cold-water measurement actually greater than that of the hot-water measurement? How does measuring the temperature differ than all the other measurements (difference vs. absolute)?

5. Measure the time for a ball to drop from the table to floor and the ceiling to floor with a digital stopwatch. Deeper purpose: Are the measurement as precise as the measurement uncertainty of the digital stopwatch (1/100 of a second)?

6. Measure the speed of the cart on the track using a photogate connected to the computer. Deeper purpose: What does the computer actually measure? What determines the measurement uncertainty? Determining the actual uncertainty of a photogate connected to a laptop running Logger Pro via a LabPro is well beyond the scope of this course (although, in my Advanced Physics course, we figure it out). Still, students realizing that computer-based measurements don’t have infinite precision is an important lesson.

The class discussions that occurred while whiteboarding were fantastic and this year’s students have a much greater appreciation of measurement uncertainty than those of previous years.