# 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.

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:

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:

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?

# Nuclear Physics Project Reflections

I have a few notes to share about the outcome of the Nuclear Physics Project.

If you are interested in seeing the final projects, the entire nnhsphysics wiki is available. If you don’t want to read every page, I created an index that highlights several project pages that cover a variety of topics in a variety of ways.

In terms of the quality of the projects, many students were very creative with their presentation methods. I strongly encouraged and pushed students to find creative ways to present their projects. I should have spent more effort encouraging students to have strong science, technology, and society-related content. In general, the content wasn’t as thorough, complete, and as accurate as I had hoped.

Overall, I think students learned a great deal about the history of nuclear weapons and nuclear power. I forget that events that I lived through (Three Mile Island, Chernobyl) are consigned to the last pages in my students’ U.S. History text that they never get to read.

In terms of technology, I was very impressed with Wikispaces. Wikispaces is ideal for classroom projects. I was able to easily create accounts for nearly 150 students very easily even though students don’t have school e-mail addresses. It is trivial to search by student name to see their recent edits to their pages and comments that they have made. The permissions model is sufficiently flexible to allow everyone to view content, yet only members to edit and comment on it.

I was also impressed with Scribd. It was very reliable and makes it easy to embed documents in Wikispaces. I found the ability to embed the document, either as individual pages to scroll through or as a slideshow, particularly useful.

A couple technologies were disappointing. TeacherTube was unreliable in terms of being accessible and successfully uploading videos. The 24-or-more-hour delay for approval, while understandable, was frustrating at times. The only reason I used it at all was that it wasn’t blocked by my school’s web filters.

Speaking of web filters, it goes without saying that they made these projects more cumbersome and frustrating than I would have liked. That said, the technology staff at my school was great about unblocking sites that were obstacles to students working on their projects.

Also disappointing was the wireless performance in my classroom. All students were able to connect via wireless but would frequently have difficulties logging into Wikispaces or posting comments on Wikispaces. They were particularly frustrated when they would compose a thoughtful comment only to lose it when the submission timed out. Reflecting back on this experience, I wonder if this was due to some sort of latency issue and Internet Explorer’s relatively short timeouts. I may try using Firefox to see if that mitigates the issue.

Overall, I would definitely try something similar to this again. Next time, I would like to plan a bit more ahead and have more time for the project so I could involve educators and students from other schools. If you have any tips for me for next time, please share!

# Holography

There is a long tradition at my school of students creating holograms as a final activity in physics. Everyone gets to make their own and keep it. I have heard several alumni mention that they still have their hologram. Just this week, an alumni who is also a dean remarked that he still has his hologram from 20 years ago. Sometimes the purpose of an activity is learning; sometimes, just to inspire. This is the later.

I’m not sure how we first made holograms, but at some point in the distant past, now retired teachers must have attended a holography workshop led by Dr. Jeong from Lake Forest College. A couple of summers ago, I attended a Chicago Section AAPT meeting and was surprised to learn that Dr. Jeong was leading the workshop!

For years we have been making reflection holograms. These usually turn out well. The disadvantage is that there isn’t much depth and, therefore, the 3-D effect isn’t as dramatic. The advantage is that reflection holograms are easily visible in white light (sun light is especially effective).

Last year, after attending Dr. Jeong’s workshop, we decided to try and also make transmission holograms. Dr. Jeong actually demonstrated how to make an “omnigram” which is a combination of a reflection hologram and a transmission hologram on a single slide. We tried this, but only the transmission holograms were visible. The transmission holograms were amazing. They have an incredible depth which allows larger objects (or a collection of small objects) to be captured. The disadvantage is that a laser is required to view the hologram (a green laser pointer works better than a red one).

This year, we provided students an option to make either type of hologram. They split about 50-50. As the price of laser pointers continue to fall, we may soon only make transmission holograms.

We order all of our supplies from Integraf. We use the PFG-03M holography slides, the JD-4 processing kit, and the DL-4B laser diode. The setup for transmission holograms is relatively simple. I have detailed photos of the slide holder (on the left) and laser (on the right). The objects are positioned between the slide holder and laser. In the back, is the shutter which blocks the laser light and consists of foam board covered with black felt with a base of two large binder clips.

I built the slide holder from a 2.5″ picture frame. The picture frame is painted a flat black. Black backing material is glued to the top of the picture frame to ensure that laser light does not enter the sides of the slide. The picture frame is secured to a base which is a tea tin filled with sand and covered with black felt. The picture frame backing is slid behind the slide in the frame to secure the slide (emulsion side faces the scene).

The diode laser is secured by a clothespin in a tea cup filled with sand. It is is positioned on a base which consists of three physics texts covered with black fabric. I added a switch and a two-pin connector to the battery box which results in a more reliable connection and easier operation.

If you are interested in making your own holograms, feel free to contact me and I’ll try to answer any questions that you may have. Dr. Jeong is very approachable and provided several tips based on questions that I posed.

Update

I realized that it would be helpful to show some examples of these holograms. It was challenging to photograph them, but here is my best attempt for a transmission hologram:

And here is a reflection hologram:

# Nuclear Physics Project

This year, after completing our four major units of second semester in regular physics, we planned on a project that would address Illinois Science Goal 13: “Understand the relationships among science, technology and society in historical and contemporary contexts.” This project has the potential to move beyond content and integrate perspectives from many other disciplines. I had some ideas in mind, but after the Fukushima disaster, my colleague and I decided that our final project would focus on nuclear physics. Here is the description of the project that we will distribute to students:

One aspect of this project that I’m really excited about is that we will be publishing all of the projects on Wikispaces so that they can be viewed by other students and professional both within and outside of our school.

I’m also very excited about the manner in which students will present their projects online. In order to highlight how technology influences the communication of scientific ideas and events throughout our society and how that has changed throughout history, we’ve encouraged students to create a juxtaposition between the time period of the topic and the presentation method that they select. For example, if their topic is historical, choose a presentation method that is modern (e.g., Marie Curie and her Facebook status updates). Or, if their topic is modern, choose a presentation method that is historical (e.g., black-and-white news documentary of fusion reactor).

I’m very interested in your feedback or involvement. Do you know of other topics related to nuclear physics that we should add to our potential topics list? Do you have ideas for other engaging presentation methods? Are you or your students interested in viewing and commenting on these projects in late May? If so, please contact me either via Twitter (@gcschmit) or via e-mail (geoff at this domain). Regardless, when the projects are published, I’ll post the link here.

Update: 20/6/11 11:09 PM

All of the student projects are on nnhsphysics wiki hosted by Wikispaces. I created an index of sample projects which contains projects on a variety of topics created in a variety of mediums.

# Circuits Lab Practicum

This year, we created a new lab practicum for the circuits unit. In addition to the traditional activities of having students draw a circuit diagram from a written description, build the circuit, and measure the voltage across and current through a specified resistor; students had to infer the circuit diagram for a collection of lightbulbs based on their observations.

This activity was inspired by an old Science Olympiad circuits event. As shown in the following photo (which is somewhat hard to discern due to the pattern of the fabric), four labeled light bulbs protrude through holes in the fabric. The fabric hides the wires connecting these light bulbs. Students turn on the power and then make observations by unscrewing and screwing in the light bulbs. Based on their observations, they draw the circuit diagram and justify their conclusion.

Students were most engaged in this activity of the lab practicum compared to the others. I think the fact that it was a unique way for them to apply their knowledge and inference abilities made it so interesting. It also had the unexpected benefit of reinforcing the idea that physical order of the light bulbs has no effect on their brightness. That is, the first light bulb in series from the positive terminal of a battery is not the brightest because it is “first.” Several students commented that there were several circuit diagrams that they could draw that would match their observations. It was reassuring that they came to this conclusion!

# 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.

# Polar Bears around an Ice Hole

I started some of my classes today with the “Polar Bears around an Ice Hole” riddle:

The game is in the name of the game – polar bears around an ice hole – invented in the days of Ghengis Khan.

A clue for you to keep you true – like petals around a rose, you can count each bear’s nose.

How many polar bears do you see?

You then roll a bunch of dice. (I created six 5″ dice from styrofoam and black pom poms.) A physics teacher from another school uses this as his introduction activity on the first day of school and shared the activity a couple of years ago. I had planned on using this activity as an extended analogy to introduce specific aspects of the class culture:

• You may feel frustrated as you try to figure physics out. That’s okay.
• Physics is hard to understand until you know the “rules of the game.”
• But, once you discover the rules, physics often seems easy and you may be surprised that others don’t understand.
• However, remember that you didn’t always understand.
• When you discover the rules and understand without someone just telling you the “answer”, you are excited.
• The journey to understanding is very important. So, no one is going to tell you the answer, but we’re all here to support each other on our journeys.
• Being told the “answer” at most gives you one answer that you didn’t know. Learning to think critically and arrive at the answer with support develops a skill that you will use to find many answers.

As the activity progressed, I realized that this activity also served as an excellent example of scientific inquiry. As we continued to try and solve the riddle, I introduced several important ideas:

• make careful observations
• gather lots of data (many roles of the dice)
• look for patterns, compare and contrast, look for extremes
• simply the problem being investigated (roll fewer dice)
• constrain the variables (set dice to specific values)
• propose a hypothesis, test it, modify it based on results, repeat

After discussing the activity, I grabbed my notebook and nonchalantly asked who solved the riddle within the first five minutes. I then announced that they would receive As for today. I then asked who solved the riddle in ten minutes and announced that they would receive Bs. Next, who solved the riddle in fifteen minutes and announced that they would receive Cs. Everyone else would receive Fs. This provided a great hook to transition to our discussion about standards-based grading.