Modeling Unit 9

Unit IX Momentum

(I can’t believe it’s really over!)
Jon mentioned that he does this unit a little differently, in that he has his students provide the definition of momentum on the Unit VIII test.  At the start of class he shows that list to the students.  What he has found is that most have a very good concept of momentum.  He said the modeling unit focuses more on changes in momentum (which tends to have more errors).  Usually from their definitions, he can lead them to the equation for momentum:

\vec{p} = m\vec{v}
\Delta \vec{p} = m \Delta \vec{v}

He said he also makes sure that they know that the units are \left(kg \cdot m/s\right).  After being part of the Global Physics Department Meetings, Andy Rundquist, aka superfly, mentioned that he calls this “derived” unit a pom (particle of momentum), others at the meeting, name it after one of the students.  Jon mentioned that he names it after the first student that asks what is that unit called.

Next, Jon and Chris showed us the beginnings of collisions.  They attached a force probe to a ring stand at the end of a track.  They replaced the hook with a rubber bumper, and then had the extended spring end of the cart collide with the rubber bumper.  At the other end of the track they had a motion detector hooked up.  After zeroing and making sure that all probes were defined in the right direction, they had them collide.  On the projected screen, they had a plot of F vs t for the force probe data and a plot of v vs t for the motion detector.

They used the stats function on the v vs t plot to find the cart’s velocity before and after the collision (max and min values), and they multiplied these by the mass of the cart. (using the equations from the beginning of the unit \large \vec{p} = m\vec{v}.

Jon then walked/guided us through the derivation of Newton’s second law to show the relationship between Impulse (J) and Momentum

F = ma
\large a = \frac{\Delta v}{\Delta t}
\large F = m \frac{\Delta v}{\Delta t}
F \Delta t = m \Delta v

Jon then asked, “What is p\Delta v, to which we all replied momentum.  He said, well we call F\Delta t Impulse.  He then asked, “What changes a velocity?”  To which we replied, “A force.”  He followed with, “What changes momentum?”  We answered, “Impulse.”  {If only all education was to people who already knew the material!}

Since the impulse changes the momentum, the magnitude of the change in momentum should be equal to the impulse.  Since impulse it force times time, we can find that quantity as the area under the F vs t plot.  Jon used the integration tool in LoggerPro, and amazingly enough, the value “matched” the change in momentum calculated from the v vs t plot.

We then jumped into Unit IX worksheet 1.

We agreed that #7 has some issues in that, for a rocket to go anywhere, it must lose mass.  Since we aren’t given that information, it technically can’t be solved.  However, Jon mentioned that we often start with idealized situations, and then add complexity.  We also agreed that most of our students wouldn’t know this anyway.

As we came back from lunch, we watch the PSSC video on Frames of Reference:

Frames of Reference

After that video, Jon and Chris showed us a cool video for E&M:

They next had a “student” come to the front of the room and sit on a stool, which was on a turntable.  They put a tennis ball in each of the student’s hands, and started gave the student a spin.  While spinning the student was told to release the ball so that it his a certain target.

Jon then thanked the student, removed the stool and got up onto the turntable himself.  He then had Chris throw a bowling ball to him.  After getting help to stop spinning, he threw the ball back to Chris.

From there, we moved into the actual paradigm lab.  We had a track with 2 carts.  Most groups had a small picket fence/flag to insert into the top of the carts.  Other groups just used a bent index card.  They also had two ringstands, each with a photogate attached.

Chris and Jon showed us several ways that the carts could combine, and we as a class agreed on 7 combinations we would study in our 7 groups.

  1. 1 stationary cart, 1 moving with it’s spring plunger extended (between the two carts)
  2. Both carts moving towards each other, one with plunger extended
  3. One car moving towards the other, colliding with velcro between making carts stick
  4. 1 moving cart, with magnetic repulsion causing the “collision”
  5. Varying the mass of one cart, 1 cart moving w/ plunger out
  6. varying mass of cart with both carts moving w/ plunger out
  7. Both carts moving with velcro collision

From there we quickly ran through the pertinent parts of the paradigm lab discussion:
What can we measure?
To determine the graphical and mathematical relationships that exists between the total momentum of the system before and after a collision.

Right at the end of the day, Jon showed us a few more demonstrations.  First he hung a electrical tape “nest” from the ceiling.  Here are pictures:

Inside that cradle he placed a raw egg.  He set the length of the string to stop just before the floor, seen here:

Then, while standing on a stool, said to the students, think of this as you driving the car one day.  You happen to come around a bend in the road, texting away, and a tree decides to move itself into the road.  What happens if you are properly belted?  With that, he dropped the egg.  Since it’s in the nest, it bounces like a bungee jumper.  In his class, he then pulls another raw egg out of his pocket and says, this is what happens if you forget about your seat belt {drops egg -> splat!}.  Any questions?

Hey then gets 2 students to help him with his next demonstration.  He has one student help him hold a cotton table cloth as seen here:

If you look carefully, you’ll notice that they make a slight lip at the bottom of the sheet.  As the egg hits the sheet, they rotate it to horizontal, so that the egg won’t roll off.  Here’s an action shot of the egg hitting the sheet {quite impressive given that I was using an iPhone if I do say so myself}:

Lastly, Jon took out a tennis ball and the bowling ball (David recommended using a basketball to avoid damaging the floor, however, they didn’t have an inflated one handy).  Drop both from the same height, and you see that both return to about the same height.  Then, stack the tennis ball on top of the bowling ball and drop.  One word, Awesome!  Here are some pictures:

After that, FIU PER asked us to go into the hallway for a practice poster presentation of the research before they head off to the AAPT national meeting in a few weeks.  The couple things that jumped out to me {yes I’m probably butchering their edu-jargon terms, but I’ll give you the basic idea}:

  • To great strategies for modeling are seeding and passive direction
    • seeding: give one of the groups (especially struggling groups)  an important insight, so they have a key ingredient to share during the board meeting.
    • passive direction: as the teacher, don’t be inside the circle (sitting w/students) if they don’t need you.  Allow them to take ownership of the meeting.  During the group work, determine where the misconceptions and errors are.  Let the groups work them out, only step in if they are floundering or off task.
    • The guy had a third term he dropped, but I don’t remember it.  Basically he talked about learning what the students were doing, and planning you questions while they are working.  Give the class a chance to ask them, and add them in as necessary.
  • Another poster talked about one powerful benefit of whiteboarding, namely that it allows students to interconnect with their peers, which improves their sense of belonging.  This improved attitude they have shown, had increased retention rates in the subject at the college level.  They speculate it would have an even more profound at the HS level.
  • A third poster described how modeling allows for personal (mastery) interactions and more importantly “vicarious” interactions
    • Their research has shown this is especially important for female students’ success in physics.

We start the last day with Unit IX worksheet 2 & worksheet 3

After finishing my work, I multi-tasked by looking at my twitter feed.  John Burk (@occam98) asked a great question while at a new teacher mentoring workshop:

To which I replied the concerns parents express with not “teaching” their child.  I’ve been using a lab based program (CPO Physics), and I’m guessing modeling teachers have similar issues.  I know I always have to go in to the idea that my job isn’t to tell the answer, but to find the best way to help their child learn the concept.  John replied that there is a lot of talk about this very issue in the modeling listserve.  For those that are thinking of moving into modeling, make sure you give a little thought to the question, “What is your job as a teacher?”  Is it to make sure you tell all the facts you expect the students to know, or is it to create an environment in which they can best learn your subject?  Personally, I hate when teachers talk about “covering” material.  I’ll get off my soapbox now.

We next went about whiteboarding our results to the worksheets.
Notes from board meeting

  • Some of the problems need to be modernized, not sure if students would know what a “Geo” is, Cooper Mini or Smart Car might be better names for the small car.
  • wkst 2 #7 needs to be cleaned up, give students names to avoid “former/latter” terminology

Lab Practicum
(def: looking for 1 final result not collection of data, using skills in the lab to now test the model)
Set up 2 carts 1 with known mass and 1 with unknown mass (tape masses to cart so they can’t be seen and can’t slide around) “stuck” together.

Use conservation of momentum to determine unknown cart’s mass- contest for either grade or some other prize

What worked?

  • Egg seat belt demo
  • All the other demos from Jon
  • Designation of tasks in labs
    • changing collision scenarios for each group
  • PSSC Frame of Reference Video
  • Having a practicum
    • Jon breaks his class into 4 groups – all members must know how to do it
    • Quiz the next day (small part of grade), only selects 1 persons quiz from each group for group grade
    • Quiz is practicum calculations with slightly different numbers
      • Fixes freeloaders
  • The practicum is a means of measuring mass without the needing gravity

What didn’t work?

  • Re-word questions Worksheet 2 #7&8
  • Re-think rocket question Worksheet 1 #7

To finish the day, we took the FCI as a Post-Test, then worked on some surveys for FIU.  With that, warm up the bus, it’s been a pleasure:


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