Wednesday, October 5, 2011

Modeling Unit 7


Unit VII: Energy

Jon and Chris then started the paradigm lab by asking for 3 volunteers
  1. Held a bowling ball and walked at constant speed
  2. Pushed against a wall
  3. Lift a small mass
Group was then asked, "Who is doing the most work?"

Physics defines work in a more specific way
A change in position due to a force that is applied in the direction of the change in position
-Establish direction early on and physics specific definition of work

-Student "1" does no work on the bowling ball

-Pushing a stuck car - you should push parallel to maximize work
-Teach students the concepts before introducing the math

Jon dropped a bowling ball - had cohort brainstorm different types of energy.
Discussed the energy transfer mechanism -> work

"We" then began Unit VII worksheet 1 before doing any labs.  Worked on the assignment individually and then presented a problem on whiteboards.

#3) still has velocity at the top
Discussion of energy as a scalar

Be careful to use "transfer" instead of "lost" when referring to energy

Jon and Chris then used a Piece of equipment with four wooden track, each with a different shape and unique color  (the only similar product I'm finding on the internet is this).

The students are then asked,
  1. "Which ball will reach the end of the track first?"
  2. "Which will hit the ground the farthest from the table?"
Answer to #1 - ball on the "blue" track  & #2 - all are the same except the "yellow" track



Then moved on to "Spring Lab"
Mass hanging on a spring, which is hanging from the Force sensor
Purpose: To determine the mathematical and graphical relationships that exists between force and displacement of a spring

Each group was given 2 different spring (1 short & 1 long)
{Overall there were 2 different lengths and 2 different spring constants for this lab.} 
{Some groups randomly selected 2 lengths with same k, others had 1 of each k}


Group plotted F vs x  results on whiteboard

Chris took us on a tour of the ASU Modeling website.  Most of the important stuff he showed us is password protected.  For those that are reading this that have not attended a workshop, sorry, I can't help you.  Chris showed us some of the math resources he uses to help students with trig/vectors.  Since there are several teachers present that also teach chemistry, Chris showed us some of the chem resources as well.  One thing we discussed was using flame tests or emission tubes to show the quantized model of the atom.  Someone asked about diffraction glasses, so if that person is reading this, go here. Chris also showed us two important inventory tests that we can use as pre- and post-tests to assess our students understanding.  One was the Force Concept Inventory (FCI) (Mechanics) and the other was the TUGK2 test (graphing).

After the tour, Chris also mention a book to us that he has stumbled on due to modeling that he has found to be very informative: Preconceptions in Mechanics.

Jon and Chris also mentioned joining the Modeling Association and the American Association of Physics Teachers, as they both have a tremendous amount of materials for physics teachers.

Before we got into the heavy stuff again, Jon also showed us a great website with lots of demos: U of Minn Demos.

From there we began to discuss the lab from the previous day (Hooke's Law Lab).  A few of the key points that came up we that we felt that this was great opportunity to discuss the limitations of a model, namely the fact that the spring will not always be a linear relationship.  Most groups, due to the strength of the spring also found that the beginning of the plot (near the origin) was also a non-linear relationship.  Other important questions the were raised, such as, "Did the length of the spring effect the spring constant?"

If the groups followed traditional graphing protocol, they would have plotted $\Delta x$ vs F, which leads to a great series of questions.  What does the slope of the graph represent? What does it mean to have a bigger slope on the graph?  How can we manipulate the graph such that an increase in slope means a stronger spring?

You can also possibly delve into significant digits.  What is the variation/uncertainty in the applied Force?  What would that do to you calculation?

Jon also mentioned, that if you have the resources/equipment, set up the experiment with both the force probe and the motion detector, so even if the spring is bouncing, you can get F vs $\Delta x$ data.

From there, we began working on Unit VII worksheet 2
A few things to note:
#5 This problem is a great reminder of the graphical derivations from kinematics.
     Specifically the derivation of the area when you know the slope of the line
     See derivation of $\large \Delta x = v_o t + \frac{1}{2} a \left(\Delta t \right)$

From there Jon tried to create a demonstration, however he was missing some necessary materials.  Here's a list of what you need (not what he had):
  • 1.5" PVC pipe (Jon uses an 8 ft pipe, but shorter is ok) (clear tube if you can afford it)
  • 1/2" drill bit (to make a hole drilled about 2" from one end of the PVC pipe)
  • 3/8" hose barb (something like this, may need different size depending on vacuum tubing)
  • Teflon tape (wrapped around barb before it is screwed into 1/2" opening in pipe)
  • 40 mm Competition Ping Pong Ball (as we saw, the basic/cheap ones won't work)
  • 3" packing tape
  • Jon also mentioned you may need a coupler on each end for added surface area
  • Soda can (with a book on top for added inertia)
So far Jon hasn't gotten the demo to work, once he does, I'll post pictures/videos.
{Update 7/13: Here's some pictures and videos taken during today's successful launches)

While he was tinkering to get that to work, one of the cohort near me was talking about a cool demo she does with her class.  She gives the kids garbage bags (unused) and asks who can inflate them with the fewest number of breaths.  Once the kids are about ready to pass out, she shows them how you can do it with one breath (Here's a great set of resources, if you scroll down until you see pg 13 in bottom right corner, you'll see the explanation.)

Once Jon conceded that he wasn't going to get his demo to work today, we moved on to another lab.  The set up was a modified version of Option 1 of the Energy Transfer Lab in the Teacher Notes (see bottom of page 8 of the notes) in which the track was on an incline.  By adding this twist, you can show the transfer of energy from elastic to kinetic to gravitational energy.

We again worked through, What do you notice? What can you measure?
Chris then briefly showed us this:



Before continuing with then circling/striking out what we can/cannot manipulate.
From there, we stated the purpose:
To determine the graphical and mathematical relationships that exist between the initial starting position, the launch speed, and the maximum height.

We ended the day experimentally determining the spring constant for the metal loop.

We started today by finishing the modified lab.  After finishing, we all made whiteboards of our results and presented them.

During the presentation, a few ideas came up.  One, the groups that used the motion detector had much better results than those that measured the compression with their eyes.  Two, instead of measuring the spring constant with hanging weights separately, we could attach force sensors to the top of the car and measure the force directly during the launch.  Third, we could use a level app from smart phones to measure the angle of inclination of the track.  Four, we could use video analysis to measure the change in height (although I'm not sure if this would be as accurate as the motion sensor).

In the end, adding an inclined ramp to this lab, definitely increase the level of difficulty.  I think this would be good for a second year class, or possibly AP.  However, I think adding studying 3 forms/modes of energy in one experiment is a bit too much for first year students (especially standard level).

One of the groups placed their energy pie charts on a sketch of their velocity vs time graph, which proved to be a great way of showing the energy relationship (most of us just made a pseudo-motion map with a sketch of the track).

One other piece of advice from Jon was to make sure that you stress energy "transfer" not energy "loss" when discussing friction or other losses of energy due to non-conserved forces.

Jon also mentioned that, surprise-surprise, he had a homemade launcher instead of buying the circular metal spring.  He took a piece of 2x4 and attach two 16 penny nails (far enough apart to rest the track in between the nail).  Once the track is place perpendicular to the wood, in between the nails, he stretches a rubber band (new each lab) between the nails (over the track).  Here's a rough sketch of a top view:


Where the yellow oval represents the rubber band, the blue circles are the nails, the grey rectangle is the track and the brown rectangle is the 2x4.  If you need to keep it level, just add a 2x4 to the other end of the track.

From there we moved to a paradigm demonstration for "potential" energy.  (I have it in quotes as we were told this name can carry with it bad misunderstandings, instead you should just call it gravitational energy or elastic energy, etc.)

Jon said that "energy" can cause pain.  So he had Chris come to the middle of the room (simulating a student from the class).  He told Chris to stick one foot out in front of him, and then asked, "Would you rather me drop this bowling ball (from waist high) or this tennis ball (also from waist high)?"  Obviously we were all cheering for the bowling ball.  Chris then asked, "Would you rather me drop the bowling ball from here (waist high) or from here (just above his shoe)?"  Chris then asked us, do you really need to do anything else to teach $\Delta {E_g} = mg\Delta h$?  Then (just to remind us of the spring equation), he suggested having 2 rubber bands, and basically run through the same thing, which rubber band would you like to have snapped on your arm, and from what distance?

After that we started working on Unit VII worksheet 2b.  Like most of these, we worked individually and then each group was assigned one problem to whiteboard.

During the board meeting we had a great discussion as to exactly how energy flow diagrams and energy bar graphs should depict the drawing.  One part of the group felt that if the type of energy is known, it should be identified (even if the interaction is outside the system); others felt that if it wasn't part of the system, it should not be named.  I'm not sure who "won" the debate, and we basically left it up to each person to use as he/she sees fit in their class.  During the discussing, it was pretty obvious that even the experienced teachers in the room had some misconceptions about energy and what it really means to define a system.  We agreed that this is a tricky concept, and talked about to what level of understanding we should try to get our students.  Is it enough for them to merely identify the types of forces present and just that energy is entering/leaving the system, or do they need to describe the the exact means by which the energy is leaving (form of heat or work).  {My guess is that in the end it depends on your students and the standards/goals for your class}

One thing that came to mind for me was my Thermo I&II teacher who stressed that if it's not important enough to be identified as part of your system, the interaction doesn't deserve a name.  I'm also well aware that my students are not sophomore engineers in a Thermo class but 1st or 2nd year high school students.

We then went on to discuss our reading from last night, Making Work Work.  We did a different style of discussion in which each group wrote down 3 things they felt important within the article and then we shared our thoughts.

We finished the day by wrapping up Unit VII
What worked:
After we go the hang of them, we liked the energy bar graphs and flow diagrams
We liked the lively discussion over worksheet 3b
We liked the chaos/challenges of the last lab (cart on the incline w/spring launch)*
We felt that when Chris showed the graph he expected, we better understood what to do**
We liked struggling through the lab, it gives us a better appreciation for what I students will experience

What didn't work:
We realize that we need to be reading the "readings" provided to the students, so we know what "they know" for each lab.
We felt that the prior knowledge requirements/level was too high for the last lab*
We felt that same lab did not have clearly defined objectives**

* and ** comments show just how split we were for the lab

Jon, Chris, and David Jones (the FIU instructor who helps facilitate this workshop) talked a little bit about the fact that the binder and online resources are not a script we have to follow, rather the tools that have emerged from numerous teachers struggling with this style of teaching.  They encouraged us to use what we liked, and modify or omit what we didn't.  In essence they reminded us that we are professional teachers who know our students and school culture.  One of the great characteristics of the modeling method is how easy it is to adapt things to suit a given school.  As we grow in using some or all of this material, we were encouraged to share our take on it with others, so the material continues to evolve.  Their biggest hope was that we didn't just copy the binder as is and pass it out to our students.  I think the biggest advantage to coming to this workshop is beginning to find how I might use all this resources.  For those merely reading this blog, or the others like it, I strongly recommend you set aside the time and come to a workshop.  One of the foundations for this system is that you have to experience something for yourself to truly learn it, watching or reading about it, simply don't work.  (Yes that includes you Kahn Academy) {sorry, just had to get that in somewhere}

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