Serendipity with Center of Mass Demo

Recently I set up a demonstration that I hadn’t done for a while. You balance a dynamic track on a thin board. You then place two carts with different masses on it so the center of mass of the two-cart system is directly over the thin board that acts like a fulcrum. The track stays balanced. I used to tie the carts close together with a thread. Their magnets would repel and send the carts flying apart when I burned the thread with a match. This was a little tricky to set up and difficult to repeat quickly if something went wrong. I decided to try the spring-loaded plungers built into the carts. I avoided this before because it requires touching the carts to release the plunger.

It turns out this wasn’t a problem, the carts still separated cleanly. This made doing the demo a lot easier. I was in my room on the weekend trying this out and decided to make a video of the demo in slow-motion. This would be good for discussion and as a back-up if things went wrong. I marked the initial position of the center of mass of the carts with a white sticker. The blue cart is 0.75 kg and the red cart is 0.25 kg. Here is the result in 300 frames per second:

After viewing the video I was thinking about how it showed that the internal force of the plunger did not affect the velocity of the center of mass. It was zero before the separation and zero up to the point an external force acts on the red cart hitting the end of the track.

I thought if I could get the carts to move back toward each other with the same speed, the track would stay balanced too. This would be difficult to arrange in reality, but with video editing, it was easy. I imported the video into iMovie and used the rewind feature. Now it shows the two carts heading toward each other, compressing the spring, then flying back out. The track stays balanced the whole time, even with the excited physics teacher flapping his arms around and poking the blue cart with a pencil during the collisions, see for yourself:

This is what every one-dimensional elastic collision looks like if the velocity of the center of mass is zero from your frame of reference. There is a well-known technique exploiting this fact that makes solving for the 2 final velocities of an elastic collision much easier algebraically than using conservation of momentum and energy. I have shown this technique to my students before but felt they really didn’t understand why it worked.

This video seemed to be a good tool to try and improve their understanding. They see that if you are in the center of mass' frame, in an elastic collision the carts change direction after the collision, retaining their original speed. All you need to do is first subtract the velocity of the center of mass from their initial velocities to put yourself in the frame of reference where vcm is zero.

After switching the direction of the speeds, you need to go back to the rest frame by adding it back to the final velocities. The video gives the algorithm for doing this more meaning for the students:

1. Find vcm, it equals the total momentum divided by the total mass.
2. Subtract vcm from the initial velocities.
3. Change the sign of the result. You now have the final velocities in the center of mass' frame of reference.
4. Add vcm to the final velocities, you now have the final final velocities in the rest frame of reference.

I suggest having students use video analysis to implement this technique. I still want my students to be able to write out the equations for conservation of momentum and energy. They can do it after using the center of mass technique to check their results.

Loudest Sounds Ever

I was researching some articles about sound safety (great NY Times educators page to start you off here) and I stumbled upon this great interactive infographic about the loudest sounds.  It was created by an air conditioning company of all things, as part of their research into exactly how loud their products were compared to other things. As they say in the explanation, they might have traveled down a bit of a rabbit hole:

So we started to delve into the dark world of decibels to make the blinking things easier to understand. We initially wanted to create an amazingly informative infographic to best explain how loud our air conditioners are. However, we didn’t know where the ‘cut-off’ point should have been and we got somewhat carried away until we found the worlds loudest noise!

Rube Goldberg-esque Magnets & Marbles

Its mesmerizing. This is quite the set-up and while quite complex can be used to discuss a variety of things with students. As the video description mentions its not quite a Rube Goldberg machine because its done in several takes even one "scene" has quite a few energy transfers and they do begin with a single marble starting. I kind of want to just play it over and over again for my students and see what they notice.

 

The Mechanical Universe is going dark soon!

We just learned from the Southern California section of the American Association of Physics Teachers that The Mechanical Universe will soon be disappearing from Learner.org. As of June 30, 2016, the series will no longer be available for purchase and will no longer be streamed (video on demand).

If you don't own your own copy, the series will cease to exist in a little more than a month and well ahead of the beginning of the 2016-17 academic year. The reasons are detailed in the SCAAPT article linked above.

The Mechanical Universe was produced in the 1980s at Caltech by a team led by physics professor, David Goodstein.  Each of the 52 half-hour episodes focused on a specific topic from the introductory college physics curriculum. Episodes featured high production values consistent with Caltech's proximity to The Entertainment Capital of the World.

The series was fairly exhaustive (outside of fluids, perhaps), and featured state-of-the-art computer animations. It followed closely on the heals of Carl Sagan's Cosmos, and it shares some video used in that iconic series.

Some critics would scoff at The Mechanical Universe's increasing age: 1985 was a long time ago. Others would scoff at the mere fact that the series engages in content exposition (unapologetically). I don't mind exposition from time to time (especially as review). And if an equally well-produced, thorough, and encyclopedic series with a fresher production date exists, please let me know about it.

A collection of expurgated versions of this college television course were "edited specifically for use in the high school curriculum." These were known collectively as the High School Adaptation. I do not have specific knowledge of their fate, but I expect it to align with that of the original series.

I have used high school and college versions of many episodes throughout my career, and would hate to be without them. I have developed sets of questions for students to answer while watching those episodes. Without distribution I fear the series will fade into the mists of history, as Goodstein might say.

The full set (52 episodes) is available for purchase for $200 via the Mechanical Universe page at Learner.org. The clock is ticking.

Moon shadow

As noted in a post in 2014, most of the United States will be able to see a total solar eclipse in August 2017. That is all kinds of cool and lots more information will be available as the date gets closer. This is an incredible video of the eclipse shadow, something I had never seen focused on before, for the 2012 Total Solar Eclipse in Australia.

The Sweeping Shadow - Total Solar Eclipse, Nov 14 2012,The Granite, FNQ, Australia. 

from Colin Legg on Vimeo.

Worst (electric) shock of my life

I was recently reminded of a bad shock I took once, in the name of science of course. One of my high school students had really enjoyed our film can Leyden jar. He enjoyed dabbling in science on the side (who doesn't?) and made me a massive Leyden jar out of a pickle jar and a terra cotta pot. It is over a foot tall and while we presumed it was functional I was a new enough teacher that I did not want to try it out. It was covered in orange duct tape with "DANGER" written all over it. In fact, I hid it whenever there were substitutes in my room so no one would even be tempted.

Years later that same student came back to visit me, while studying physics in college, and we reminisced about his project. With another physics teacher in the room we decided to test it. We charged it up with my Van de Graaff generator and I touched it. It hurt. A lot. In fact I felt the shock all the way from my hand to my shoulder on the same arm. It was larger than I had anticipated and it hurt for awhile afterwards.

Now I regularly allow the current from my Van de Graaff generator to flow through a long aluminum rod through me to the ground while demonstrating. I try to avoid the shock from my dissectable Leyden jar demo but I'll take it if necessary. The shock from this massive Leyden jar was worse. By a lot. Now at least I can tell my students how bad the shock was and use it as a starting point to our discussion about shocks and safety.

It was my understanding that if the shock had been large enough to continue across my heart it could have been a lot worse. I would like to measure the size of the "shock" off of it, and the smaller Leyden jars I have students make but never have. I would think the large one would surpass my analog ammeter and RAFT multimeters. 

I recently posed this question to the Exploratorium's Teacher Institute Listserv to see if anyone had any ideas about how to achieve this. They agreed the equipment available to me would almost certainly be fried by my massive Leyden jar. The level of equipment necessary was apparently expensive and usually only available at universities and research facilities. Public high school: poor, fewer cool toys. Got it. 

The other take-away was that measuring the "shock" was difficult because there were many things to measure.  I show my students this table when we begin our electrostatics unit and continue to reference it through our current electricity unit. While the level of shock is often determined by current, as with this table, you can also measure the energy, power, capacitance and even the distance it jumps. The shock is incredibly short lived, however, making measuring it difficult.

I wanted to share my story as a cautionary tale and hoped to add, "If you wanted to test how bad the shock from a demonstration might be you should measure the shock before by [detailed safe procedures]." 

Since there is no easy way to do so I'll just say it's not a good idea because it really hurt.

Don't look at the sun!

Anecdotal but an example of the burden of being a science teacher and knowing better. ;)

A neighbor boy was all excited to show me his magnifying glass, a little plastic thing he probably got in a goody bag. “Look Bree, if I look at the sun it burns a bit!”

You can probably imagine how loudly I shouted “Nooooo!” He was persistent and I had to actively block his eye and the magnifying glass from the sun for a while with my own shadow. I tried to direct him to looking at things on the ground with the magnifying glass. I had him hold the magnifying glass at arm’s length to view another neighbor. “He’s upside down!?”

He continued to play with it for quite a while, and my science-oriented heart swelled a bit, when he conducted some side experiments with a translucent cup on the ground.

“Look, the shadow is green like the cup! If I tilt the cup the shadow changes. If I move the magnifying glass the little sun changes.”

Out of respect for my friendship with his mother I did not teach him about the heat at the focus of the magnifying glass. Although when he briefly aimed it skyward again I was tempted.

The next time we got together I brought home some of my eclipse viewing glasses. I told all the neighbors (there are nine under the age of ten within a few houses) that they were the only safe way to view the sun. Their response was less than impressed, “Oh, it looks like an orange ball.” Then they tried to see if they could ride their bikes or walk or play tag while wearing them. Hey, everyday can’t be a victory.

To CER with Love

We've all asked students to analyze their lab results. Sometimes we have constructed conclusion questions we hope will lead students to the big "aha!" realizations about their data. We may assume more advanced students can recognize connections on their own and just ask them to "write a conclusion." No matter our request, we are often met with students that fall drastically below those expectations, even while others exceed them.

While NGSSifying (sure, it's a word!) your curriculum one relatively easy step is to add Claim-Evidence-Reasoning Conclusions to your existing labs and activities. Often abbreviated as CER (or occasionally as ClEvR) it is a scaffolded method to help students organize the findings of their experiments. It is mentioned specifically in Appendix F Science & Experimentation Practices:

"An explanation includes a claim that relates how a variable or variables relate to another variable or a set of variables. A claim is often made in response to a question and in the process of answering the question, scientists often design investigations to generate data."

You have to start by asking them a question, an open ended one is even better! Perhaps the hardest break from their old habits is to wait until after their experiment to write a claim. It is not a hypothesis to be proved. Their claim is their answer to the question you posed based on their experiment. The next step is to describe their evidence that supports this claim without any explanation. This is difficult for students that are used to runningeverythingtogetherforthesakeoffinishingasfastaspossible. The third and final step is to explain the reasoning behind their evidence.

This is definitely something made more clear with an example. A photocopy of this chart was given to me at a NGSS training years ago and it is still my go-to to explain this method because there is an example for every discipline. When I show this to my students I usually the Earth Science one since they have less experience with that field of science.

Question	Claim	Evidence	Reasoning	Rebuttal
Earth Science How was the Grand Canyon formed?	The Grand Canyon was mainly formed by water cutting into and eroding the soil.	The soil in the Grand Canyon is hard, cannot absorb water and has few plants to hold it in place. When it rains in the Grand Canyon it can rain very hard and cause flash floods. The flash floods come down the side of the Grand Canyon and into the Colorado River.	Water moving can cause erosion. Erosion is the movement of materials on the Earth’s surface. In terms of the Grand Canyon, the water moved the soil and rock from the sides of the Grand Canyon into the Colorado River where it was then washed away.	Some people may think the Grand Canyon was cause by a large earthquake, but the Grand Canyon is not near any tectonic plate boundaries. Furthermore, earthquakes in Colorado are rare and do not tend to be very large - largest earthquake on record had a magnitude of 6.6.

Adapted from “Supporting grade 5-8 Students in Constructing Explanations in Science” (CER) McNeill & Krajcik; Table 2.2 Examples of the Different Components for Scientific Explanations.

I've seen this taught down to the middle school level with graphic organizers representing each step to help guide students into adopting the process. You can find graphics organizers like these (left and right) from a variety of sources, just google "Claim Evidence Reasoning graphic organizers" and you will find lots more. There were even a few that took the shape of a hamburger ...

I've made a poster similar to the example on the right for my room and when a Claim-Evidence-Reasoning format fits our lab experiences I try to use it. So far, it has been about as hit-or-miss as the ol' "Just write a conclusion" format. I think the main reason for that is that I have not embraced it and taught the process repeatedly. Kids know when you half-heartedly attempt something and they reciprocate in kind.

The time I think the format was more successful was during my PVC Dart Gun Lab, a more structured format of the draft I previously posted. I wanted to informally assess the groups and their progress so I printed out quarter sheets with the different questions on them. I wrote the group member's names on them, which also made assigning the groups easier, and asked them to record their Claim-Evidence-Reasoning on it to return to me by the end of the period. It was a quick way to read each and give the groups feedback before they each turned in their own individual labs. I found quite a few that wrote claims as if they were hypothesis, a few more squished their evidence and reasoning together and quite a few more didn't actually offer any evidence despite having collected data. I like to think that this check in helped some students edit their individual labs but having since graded them, I know I didn't get through to them all.

Coulomb's worth of sand?

I teach Coulomb's Law to my regular Physics (mostly juniors and seniors) as well as my freshmen Conceptual Physics students during our Electrostatics unit.  The younger students struggle every year and because of their math level I agonize over including it in Conceptual Physics at all. The sheer size of the numbers involved confuse them and then the use of this "strange unit" called a Coulomb doesn't help. Every year I try to equate the use of the Coulomb as the unit of charge to a dozen eggs which helps some but not all.

 

A few years ago I decided that I wanted to make them a visual, something they could see that would help them understand the size of the Coulomb. I thought of the Mole cubes I had seen in Chemistry, they are about a cubic foot and proudly proclaim "1 Mole of" and list the masses of different gases. I could do the same thing and say I had a box with a Coulomb's worth of air in it but since they couldn't see the air this probably wouldn't help with their understanding. I wanted a Coulomb Cube, I just had to figure out how big to make it and what to put in it.

I tell my students this story as a way of introducing a Coulomb and they follow the same thought process I had when asked: "What is something fairly uniform and small that we could gather a Coulomb worth of?" Students usually volunteer answers: "Marbles! Rice! Sugar! Salt!" and then usually arrive just as I did at grains of sand.

When I first looked into this problem I found quite a few resources on the different sizes of grains of sand on math websites. Apparently it is a common estimation problem to figure out how many grains of sand there are on a beach, in a dessert or on the whole planet. Using the smallest average grain of sand CosmologyScience.com determined a cubic foot of sand would hold one billion grains of sand.

The Math Dude estimates "8,000,000,000 grains of sand per cubic meter." Since his are in metric, I'm going to discuss the calculation with his values. If we take a Coulomb to be 6.25x10¹⁸ charges ("grains of sand"), if we divide a Coulomb by the estimated number of grains of sand in a cubic meter we get:

Since I wanted to build a cube, (although at this point I already realized I was in trouble) I found the cube root of this amount of cubic meters to see how large my cube was going to be on a side.

So, I didn't build a Coulomb Cube, and realized that I had trouble grappling with such a large number as well. When I tell my students this story and tell them I would need a cube that was almost a cubic kilometer their jaws drop. While I don't have a physical manipulative to show them, discussing the thought problem at least illustrates the sheer volume of a Coulomb. Get it? *ba-dum-bum-CHING*

Ice Scream - a new ExploratoRio Science Snack

When broadcast television was something people watched, networks would pitch their "encore presentations with the line, "If you haven't seen it before, it's new to you!"

Somewhere in the running conveyor belt that is my Facebook feed, I recall seeing a video of a Kennedy half dollar coin being set into a cavity in a chunk of dry ice. The coin and ice produced vibrations and sound.

When two students ran me through the paces of their Bubble Suspension build (for our upcoming ExploratoRio2016 on Wednesday, April 13), they left some dry ice behind in my classroom sink.

So it's me, some sublimating dry ice in a sink, and no one else around. Recipe for serendipity if ever there was one.

After dousing the frozen carbon dioxide and blowing the subsequent cloud out of my sink a few times (that never gets old), I found a nearby electrophorus and pressed it into the sublimating mound.

What happened next is best relayed in the form of a video, which drops the action to 1/8th speed at about 20 seconds in.



So unexpected was the sound that I decided a new ExploratoRio Science Snack was in order. The title of "Ice Scream" wrote itself with little help from me.

The details (as much as I know them or foresee them) are in the recipe linked to below.

Ice Scream - ExploratoRio Science Snack.

Note: Adopting the look and feel of the original Exploratorium Science Snackbookq was not an accident.