Thursday, October 13, 2011

Conservation of Energy Lab

I saw a question today in twitter:

Modelers: how do you develop 1/2mv^2 from lab? how do you develop mgh from lab?
At the modeling workshop this summer, we did exactly that,  however, instead of just rehashing that post, (you can read it here), I figure I would tell you how I tweaked the experiment for my AP class. 

Since my AP-B class is a second year class, my students already have a working idea of the relationships (as time goes in and I fully switch to modeling, they should know the models) from the first year.  So instead of using the labs as a discovery of the relationships, I like to have some challenge in the lab in which the students have to predict something using their data. 

Here's the setup:
vernier cart
vernier track
vernier spring launcher
motion detector attached to track opposite the launcher

Set up the track at an angle (ie - place a book under one end of the track)

Using LoggerPro and the motion detector, pull the cart back to compress the spring and let go.  Stop the detector after the cart has reached it's highest point on the track. 

The Analysis:
Have LoggerPro display a position vs time and a velocity vs time graph.  From the velocity vs time graph, highlight the data, and use the "Statistics" function.  The minimum value will be the compression ($\Delta x$), and the max value will be the maximum displacement ($d_{max}$).  Highlight the data from the velocity vs time graph, and the maximum value is the maximum velocity ($v_{max}$). 

(Note- if you want to do so, you can have the kids look at what position the max speed occurs (x=0)

Repeat the procedure several times, recording $\Delta x$, $v_{max}$, and $d_{max}$ into a second data set.  Plot $d_{max}$ vs $\Delta x$.  Have the students linearize this first graph, and they should see that $d_{max}$ is proportional to $\left( \Delta x \right)^2$.  Now plot $v_{max}$ vs $\Delta x$, lead student to plot $\left( \Delta x \right)^2$ on the x axis, since that will allow this graph to relate to $d_{max}$.  They should find that they need to plot $v_{max}^2$ on the y axis.

(If you want to take it a step further and include the masses to fully develop conservation of energy, go for it.  As I said, my kids already knew those relationships from last year)

So here was my twist, how do you relate the maximum displacement to the vertical height?  Since my students knew the energy relationships, I had them use their data and trigonometry to calculate the angle of the track.  Just to give you heads up, here is what they should get...

From trigonometry, you know:
$h_{max}=d_{max}sin \theta$

And since mass is used for both kinetic and gravitation energy, you can rewrite the energy conservation as:

$g*d_{max}sin \theta = \frac{1}{2}v_{max}^2$


$\large \theta=arcsine \left(\frac{g*d_{max}*v_{max}^2}{2}\right)$

I then measured the angle of the track using a level app in my iPhone to compare the actual angle to the one predicted by the groups.  The app I has was able to measure to the tenth of a degree.  Most groups were able to get within $0.5^o$ of the value measured on my iPhone.

Wednesday, October 5, 2011

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:
$\large \vec{p} = m\vec{v}$


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

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:

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:

Modeling Unit 8

Unit VIII: Central Force Particle Model

Jon started today by giving a brief demo.  He had a rubber stopper tied with a string attached to a hanging mass.  In between the two was a plastic tube (think very sturdy straw), which he held in his hand.  He asked us where he would need to release the ball in order to hit a certain object.  He then asked where he would need to release it to hit a different object, in a different part of the room.  He then socratically questioned us to say that the speed of the rotating stopper was constant, but the velocity was continuously changing.

He then asked us, what causes a change in velocity? (answer: unbalanced force)
What direction must the force be? (answer: towards the center*)
What direction is the acceleration? (answer: towards the center)

*Chris showed us a demo we can do if the class doesn't agree that the force/acceleration is towards the center.  He grabbed the bowling ball (yes, the bowling ball, again) and a broom, and asked one of the students to make the ball move in a circle.  She first started out inside the circle of the ball and was constantly pulling the ball towards herself.  Chris then had her stand outside the circle and put a cup as a reference point for the center of the circle.  She again had to constantly push the ball towards the cup.

From there, Jon led us to derive an equation for the average speed of an object in circular motion:

$\large \overline {v} = \frac {\Delta x}{\Delta t} = \frac {2 \pi r}{\Delta t}$

From there, we walked through the tradition questions for paradigm labs:
What do you notice?
What can you measure?
What can you manipulate?

Then Jon helped us to create the purpose:
To determine the graphical and mathematical relationships that exist between the speed of the stopper and the amount of mass hanging on the string.
{We did not study the mass rotating, however you could have part of the class investigating this, and the radius if you want to "kick it up a notch" - Bam!}

We found that this lab was very tricky and had lots of error.  A couple points to minimize the error:
  • Have the lab members keep one job: timer, recorder, twirler
  • Make marks on the string to help see where it needs to be to keep a constant radius
    • This is huge!
  • Possibly use a force sensor held against the table.
  • Possibly use video analysis to determine the actual radius
    • as the ball drops, the length of the string is no longer the true radius
    • cut a slit in a tennis ball and squeeze over stopper to make a more visible point.
We also discussed what to do if a group has "bad" results.  We agreed that early in the year, make sure you are doing a thorough job of checking the groups while they are experimenting to avoid this.  However, as the groups get comfortable with the whiteboarding process, letting mistakes slide into the meeting can make it more interesting.  Think through when you want to call on those groups.  We also agreed that we need to remind students that the data measured isn't wrong, the procedure to keep multiple variables may have been insufficient, but the data is the data.  Encourage the students to discuss the subtleties of their procedures to determine where groups differed.  If the class is getting bogged down, don't be afraid to say, "Let's come back to this after all the groups have presented."  

If the students didn't already, have them create graphs of $F_{hanger}$ vs $v^2$ instead of $m_{hanger}$ vs $v^2$.  When they do so, ask what the slope represents.  If they aren't sure, ask what the units of the slope are (kg/m).  Since the slope is constant, what mass and distance are staying constant?  To which, they should reply the mass of the stopper and the radius of the circle.  From there you should be able to derive the centripetal force equation:

$\large F_c = \frac {m v^2}{r}$

When we came back from lunch, Jon again attempted to shoot his ping pong launcher.  See the results in this blog post.

After that, we began work on Unit VIII worksheet 1 & worksheet 2

A couple great ideas from one of our cohort to help students "see" circular motion:
  • Cut a wedge out of a disposable pie pan, then roll the ball roulette style
    • ball will come out in a straight line
  • Have student's run down multiple flights of stairs as fast as they can
    • may need to make this a "mental" experiment not an actual one.
    • ask students what they must do to turn from one flight to the next while at a landing
Before the workshop started today, I saw a very cool video on youtube that I'll show, just because I thought it needs to be seen:

We started to day whiteboarding our summaries of Arons' Chapter 5.  For those that haven't read it, it's a fantastic book with sharp insight into the shortcomings of teaching physics.  It's written at a very high level, but once you get used to it, it has a lot to tell you about how you should be teaching physics.

From there we finished up Unit VIII
What worked?
  • We liked the demo with making the bowling ball move in a circle
    • Especially the person outside the circle
  • Getting insight into what to do (and what not to do) during a lab
    • once members determine the job they can do, stick with it
    • POGIL
  • Student discussions help them get understanding as to what lab was showing
  • The idea that data isn't wrong, the method of isolating variables may not be sufficient
  • The fact that we (the students) are always finding the graphical and mathematical relationships
    • once you get the hang of it, you know what to do when the models get more difficult
    • new lab, same analysis
What didn't work?
  • Teacher notes require editing/more detail on graphs
    • Centripetal force lab
  • Even though we knew what the outcome should be, struggling through labs is very helpful
  • For labs that fail (class completely lost), come back as a teach demo and explain how you are doing the experiment differently
    • demo vs lab less time if you don't have it (due to lost period of failed lab)
  • If you have problem students or limited supplies, split the class and have half do the lab and the other half work on problems & switch part way through.
  • Use record player and put a thin piece of wood (less than 1x4) across the deck, have students measure coefficient of sliding friction $\mu_{k}$, and predict what is the greatest radius to place the penny such that it won't slip. (Find $\mu_{k}$ from maximum angle with no slip).
    • vernier has a lab for accelerometer and turntable
      • difficult to due with calculators, not too bad with computers
  • Would be nice to see a paradigm lab for universal gravity
  • One member mentioned that this graphical analysis is very important as the next generation standards will implement a lot more graphical analysis.

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}

Modeling Unit 6

Unit VI: 2-D Particle Model

Our introductory/paradigm demo was Jon and Chris tossing a ball back and forth.  Jon then asked questions like: "Once it leaves my hand, where will it go?""Does the ball have a choice as to where it goes after it leaves my hand?"

One thing that come to mind during this demo was the following video from

What do you notice?
What can you measure?
{at this point, Jon showed us the equipment that we would be using}
{Jon build hold that converts dynamic cart w/ spring into ball launcher}
Here's a rough sketch:

Where the blue shape is the dynamics cart with the spring plunger extended, the silver circle is the ball to be launched, and the brown shape is the holder Jon built out of wood.  He also cut/routed a groove for the ball to roll in on the top of the "shelf."
After being shown equipment What can you manipulate?

{If you don't have time to build this and have students tape it, use videos in loggerpro}
Open logger pro
Click Insert - Movie
Click “expand menu” in bottom right corner
Click scale icon (looks like a ruler)
Make sure you have scale (meter stick) in the movie
Click and trace standard length in screen & define length
Click on track (find name) button and click on specific point on object
Continue clicking on the same spot of the object (vernier advances to next frame)

Jon and Chris then tried to show us the classic Monkey-Blow gun demo using the Pasco equipment:

Since this is quite expensive, Jon explained how he made a "homemade version" of this:
Electric conduit (1/2 inch? Metal)
Nail with cone of paper hot glued in
12 V power source (3 or 6 V should also work)
Target - Balloon with brass mass inside, washer stretching the opening
            Stuffed animal with metal screw in its head

He attaches the Electromagnet to the ceiling in the back of his room and runs the ingoing and outgoing wires above is ceiling (drop-down I'm guessing) to the front of his room.  He uses the conduit as the blow gun and makes darts by gluing cones of paper to the head of the nail.  Have the two wires run up the side of the conduit and each extent the bare wires beyond the opening of the conduit.  Bend the wires so they touch in the middle of the opening.  As the dart shoots out, it will separate the wires, breaking the connection. Here's his sketch:
(click to embiggen) 

I missed this day of the workshop, however, a few of my cohort were gracious enough to take notes.  I'm doing my best to take what they gave me.  Any help to clarify things would be greatly appreciated.

The day began with everyone working on Unit VI worksheet.  Everyone worked individually, and then the groups met to create whiteboards.

- Useful to separate horizontal and vertical givens in table:

-Good to explicitly show + state that t is the same for horizontal and vertical motion
-Good to keep algebra in variable until the last step - then plug in number

#4 Would be interesting in adding a horizontal & vertical motion map for car and ball

-stress constant velocity in horizontal direction

- ESL students have difficulty with "how long" thinking it means distance

LoggerPro basket ball shot analysis follow up
- After students have generated data, insert 3 graphs + auto arrange
  • x vs t
  • y vs t
  • $v_x$ vs t
  • $v_y$ vs t
-Highlight first 1.5 second to analyze
  •  compare slope of x vs t and average value of $v_x$ from $v_x$ vs t graph
  • lead students to see that $v_x$ is constant by $v_y$ is changing (slope is 9.8 $m/s^2$)
  • If you want, have students insert a quadratic fit onto y vs t graph and lead them to find what the meaning of the constants are in the regressed equation.
Next on the agenda was to split up an article to have summarized on whiteboards by the groups.

After lunch, Jon and Chris asked for feedback for Unit VI
What worked:
Video analysis lab
Plan for Dart Gun for Classic Monkey Problem
Worksheet #3
Wells Reading
Hammer article about Lisa & Ellen
Group Work
Adaptability of labs to every level of student (*response to comment on what didn't work)

What didn't work:
Transition from 1D to 2D - we would like to see the process
Time constraints
Simplicity of labs*