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:
Equipment
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:

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

Therefore:

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

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

or

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

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?
Purpose:
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
Notes:
  • 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 Veritasium.com:
 


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:
Materials:
Electric conduit (1/2 inch? Metal)
Nail with cone of paper hot glued in
Electromagnet
Wire
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*

Wednesday, September 28, 2011

Modeling Unit 5

Unit V: Constant Force Particle Model

"Atwood Machine" with vernier track
From there, we started the next unit.  Here's what each end of the track looked like (the middle is just a track)



Jon changed the first question slightly:
What factors will effect the motion? (between letting go of the cart and hanging mass hitting ground)
What factor effects the cart’s acceleration?
Hanging mass
Mass of car
Friction: {adjust tilt of track until cart rolls at constant speed}
(pasco hanger approx. applies force to balance friction)
Mass of pulley
Mass of the earth/gravity
Angle of the track - ?
Starting speed -?

{Chris showed us a quicker way of working through the process by guiding us to eliminate the factors mentioned that cannot be adjusted (Mass of Earth) or that could be removed with creative lab design.  The last two options we left open, that depending on your class, you may or may not want to divide and conquer.}

Purpose: What is the graphical & mathematical relationship that exist between the mass of the cart and the force that is accelerating it.

Before getting started, we talked about multiple variations to this experiment
  • Keeping the mass of the hanger while adding mass to the car
  • Using photogate(s) above the track instead of motion detector
    • Variation of this option is to attach picket fence to cart the cart and use vernier program
  • Using kinematic equations and measure total time with stopwatch for total distance measured
  • Having the students predict the mass of the system from data, and then, after showing prediction to the teacher, measuring the mass and comparing results to predictions {I like this!}

Equipment
Attach right angle to cart
Pulley at end of track
Hanger
String
Motion detector
Standard masses

Next up were some demonstrations of  Newton's 3rd Law:

Same track set up, with Force sensors attached to the top of each car.  The twist for this demonstration is to use the magnets to apply to force between the two cars and not the direct contact.  There are a couple of things to note for this demonstration.  Have one car against the stopper and start with the second car "far away" from the first car.  Zero both probes, and make sure you reverse the direction for one of them so they both have positive in the same direction of the track.  Have the magnets inside the car so the same pole faces outward and thus repel the cars.  Push the force probe of the second car (not the car itself)

From there, were picked up on the lab with which we finished yesterday.  Before starting the experiment we briefly discussed the merit of breaking the lab groups into different types of investigations, in which we would have 3 different trials: "A" would look at keeping the mass of the cart constant, but adding mass to the hanger; "B" would keep the hanger constant, and add mass to the car; "C" would move mass from the car to the hanger, keeping the mass of the system constant.  In an effort to save time, we have everyone do option "C" but I may or may not look at all the groups (maybe in my honors class?)

Also showing a way to move through the whiteboard process more quickly (as needed by time constraints or if class is not productive in meetings), Jon walked us through a "Circle the wagons" meeting.  In this format, all the groups show their white boards, and the teacher leads the group to try to draw conclusions in looking at all the results at once.

{As we were getting started, Jon also mentioned that when you are "normal" whiteboard meeting after a lab, in subsequent labs, start with a different group each time and change the order you call the groups forward.}

During the meeting, we had a great discussion on whether you should explain/guide to the students before starting the lab that they will need to plot Force vs acceleration so that the slope is mass, or wait until the end.
{My thought is to wait until the end, have all the groups manipulate their graphs, as teacher does it on projected screen}

At this point, Jon showed us a quick follow up demo/lab (used vernier "Lab 9 – Newton’s 2nd Law")
Jon taped an accelerometer to the force probe (Jon uses Velcro tape at his school).  Then you just click the record data button, and then push the cart back and forth.  Viola, data showing $F \propto a$
           
From there, we started individual work on Unit V worksheet 1 (#'s 1-4) and worksheet 2 (#'s 1-3)

As we got started, we briefly discussed strategies for word problems (w/ forces).  A summary of what we said was:
  • Have students sketch what is happening and identify the system with dotted circle/box
    • Get the words out of the word problem
  • Create a Free Body Diagram
  • Next to FBD, draw an arrow showing the direction of acceleration 
    • That will be "+" direction for the problem
      • This convention will aid circular motion problems later in the year

Notes from whiteboard session:
  •  Wkst 2: #2 is a great problem since a given number isn’t use in the calculation, but rather for analysis at the end.
  • Wkst 2: #3 mass not given, so students need to determine it from the Weight
    • Chris- Make sure units are included in the calculation not just at the end
    • Possibly change wording of problem since the normal force changes not F­­­w
 Jon then went on to describe how he helps his students understand "elevator" problems.  If you are standing on a bathroom scale, and you want to increase your "weight" you can pull on the bottom of the counter and squeeze the scale.  This is the same effect as when the elevator is accelerating upwards.  On the contrary, if you want to lose "weight," you can push on the top of the counter and push you body off the scale.  This same effect occurs when the elevator accelerates downward.


From there, we Jon showed us some fun demos 
  1. Have student kneel w/elbows touching knees & hands “praying”.  Put chapstick at tip if fingers.  Then have student place hands behind his/her back. They then need to try to knock over the chapstick by touching their nose to it.  Due to differences in center of mass, girls should be able to do this, while boys usually can't.
  2. Have student stand facing the wall, with toes touching the base of the wall.  Have student take 3 steps (toe to back of heel) away from the wall.  Bend at the waist $90^o$ with their forehead touching the wall.  Place a small chair (or other "small" mass) in their hands and tell them to stand up.  Again, boys will struggle,  girls will tend to be successful.
  3. Have one student (biggest student) sit all the way back into a chair with his/her feet flat on the floor.  Have a second  student (smallest) stand in front of first student and push into the first student's forehead.  Tell first student, without moving their feet, to stand up.  At the same time, the second student pushes on the forehead of the first, preventing him/her from standing up.
  4. Have student stand with right shoulder and outside of right foot touching the wall.  Then tell the student to lift his/her left foot.
Friction Lab
We then moved on to a lab on Friction. We used a friction block and force probe.  The basic procedure was to the block at constant speed with different masses resting on top of the block.  We used the vernier file "Lab 12a Static Kinetic Fric."  A sketch of the graph produced looked basically like this:


The max force represents the static friction force, and when the force is basically horizontal (red line) then the friction force equals the measured force.



To speed things up, each group given different normal force ("zero mass" was mass of block plus 250 g) and needed to get good data (slope of oscillating data was as close to horizontal as possible).  Find the average value of the force using the statistics button.

Unit V Feedback
The Good:
  • We felt we were becoming comfortable using computer based equipment
  • Continuation of the sequence of showing 3rd law  (adding non-contact interaction)
  • Low tech demo’s/labs

The Bad:
  • Modified atwood machine has a lot of physics baggage we’ll need to use as a paradigm

Suggestions:
  • When it comes to multiple representations of event
    • FBD, motion maps, graphs, equations
    • Only let students say verbal description of the event– Carbon dioxide not "See" "Oh" "Two"

Modeling Unit 4

Unit IV: Free Particle Model

Jon began the unit by asking us to describe the motion of the following event:
{He tweeked the activity as we do not have student desks, what he said to do in the classroom was to have a student sit at a desk that everyone can see.  Push the desk so that it starts moving at near constant speed, and then stop pushing.}

We were to describe the motion using our 4 tools (written description, motion maps, kinematic equations, and kinematic graphs (x vs t, v vs t, and a vs t).  {We were to make those tools describe the motion from before it started moving until after it stopped.}

After we were done with our individual answers, Chris shortened the process by just asking individuals to share their ideas/draw their graphs on the board.  {I'm guessing that he was trying to make up for lost time due to our lengthy discussion earlier, and would do this through whiteboards, but I could be wrong.}

During this process, students often want to jump to why the objects are doing what they are doing.  Which leads to a discussion on forces.

From there, Chris said that he then does a mini-lecture on contact forces (forces caused by to objects being in contact) and fundamental forces (Gravity, Electro-magnetic, Strong, and Weak). {He said that he doesn't get into Normal and Friction forces at this point, but I might.  I'll have to think on this some more.}

From there, he makes use of a hovertoy (examples here and here, or make your own similar by hot-gluing the top to a "sport-top" water bottle to a CD, and slipping an inflated balloon over the cap. If your school has an airtrack, that would obviously work as well. ).  With the air turned off, push the puck across the table.  Then turn on the air, and push the puck.  Ask the students what is different about the two trials.  Guide the discussion until they realize that, for the whole series of demos, no force acting on the object leads to no change in motion; force applied leads to a change in motion. "No Force, No Change."

{Newton's first law, but like much of modeling, focus on the concept not the name.  Chris mentioned that he steers the conversation away from the term inertia, and instead focuses on the terms "balanced" and "unbalanced" forces.}

From there, Chris introduced Free Body Diagrams (FBD), in which you show the forces acting on the object (or system).  He started with a FBD for the puck resting on the table:



The circle/dot in the center represents the object, the arrows represent the forces acting on the object.  Chris said it was up to you if you wanted a convention such as all arrows point away from dot, or arrows point to show how the force is acting (Push-inwards arrow, Pull-outwards arrow).  The convention used in modeling for the name of the force is the numerator is the acting object, the denominator is the object in question.  So the two forces here are the force of the table on the puck $F_{T/P}$ and the force of Earth on the puck $F_{E/P}$ (AKA the force of gravity/ weight of the puck).  If need be, remind students that the earth is the object that creates gravity, not that gravity is an object itself (Thus $F_{G/P}$ would be incorrect).

{By the way, when I was a wise-a$$, acted like a student, and said that the puck is resting on the table, so the table can't be pushing up, Jon went into the closet, found a bowling ball and rolled it to me.  He told me to lift the ball and hold it shoulder-high at arms length.  Then asked if I'm pushing the ball to keep it at that same height. Touche Jon!}
{By the way, a bowling ball is another cheap prop you can use for the earlier part of the lab.}

He then showed a FBD for the puck at the instant he first pushed it:



The added force is the force of "your" hand on the puck $F_{H/P}$

From this discussion, Chris had us work on Worksheet 1, and then had groups whiteboard answers. {My only concern with this is that many of these problems get into 2D FBD's.  I'm not sure if I want to get to that before I've really had the students do any hands-on with forces}

Chris mentioned that this worksheet does a great job of bringing out student misconceptions about forces.  Most students get stuck, so instead of whiteboarding answers, for this problem, he has them whiteboard their questions about the worksheet.


At this point, we moved on to the paradigm demonstration: Dropping a bowling ball from shoulder height.
We again went through the usual questions, however, Chris added one more to the mix:
What do you notice? What can you measure? What forces are present? What can you manipulate?
We then created the purpose: To determine the graphical and mathematical relationship between the force of the earth on the object and mass.

We were then thrown a curveball for the experiment, we were given a Vernier Dual Range Force Sensor (Jon mentioned that spring scales work just fine) and some standard masses, and guided to plot mass vs Force.  As we saw that the data made a straight line, we could find the slope of that line. 

Each group then whiteboarded their results.  About the time the groups were getting lazy with the presentation (since we all had approximately the same numerical results), Chris threw out a question, "What is the connection between the slope of your line and dropped bowling ball from the start of the lab?"

For the groups that plotted Force in units "N" (which are, as of this point in the process, possibly unknown units) vs mass in kg, we found that the slope was eerily similar to the number we measured when finding the acceleration of object dropped (picket fence and rubber ball over motion detector) in the previous units.  That acceleration describes the acceleration of the dropped ball.  If all the groups used grams (which are the units printed on most standard masses), guide them through questioning to the value of slope with mass in units of kilograms.

Chris also noted, that making the connection between $N/kg$ and $m/s^2$ will payoff when Electric fields come up later in the year. {Obviously, this point will need to be reinforced throughout this unit and others for the students to remember it during E&M.}

We began today with a series of demonstrations that together, will help students to conceptualize the "Normal" Force.  First up was a very nifty contraption which shows that even small forces do in fact, move a wall (Jon said that this even works with a brick wall!)

Jon attached a metal rod to the wall with modeling clay.  Between the table an the rod, he placed a T-pin his Biology teachers unknowningly provided to him.  Glued to the T-pin is a small piece of mirror.  A few feet away, they had a laser set up, which was pointed at the mirror.  As you push on the wall, the wall moves, which causes the bar to roll the mirror, which in turn changes the reflection of the laser.  Students can see the effect of you pushing on the wall by watching the laser dot on the opposite wall move up and down. {Hopefully that made sense.}  Here's a picture of the setup:


Next he suggested (they didn't find any springs until later in the day) to take the bowling ball and set it on top of a spring, which is itself on the table (you'll bring that part up later).  Ask the students what the spring is doing to the ball (to which they should reply pushing it up)

Then, set the ball on top of soft foam, and again ask what the foam is doing.  Then set it on some firm foam.  Next, set it on top of 2 meter sticks (elevated at each end by some blocks) so that the students can see the meter sticks flex in the middle.  Finally, place the ball on top of table by itself.  In each case, ask what the "base" is doing to the bowling ball.  If they still don't get it, ask what the table was doing to the spring at the beginning of the sequence.

At this point, ask the student to draw a FBD of the ball resting on the table.  At this point, now call the upward force of the table on the ball, the Normal force.  Ask what would happen to this force if the table surface was rotated (incline plane), and lead students to the fact that it is always perpendicular to the surface.

Jon then went on to describe how he uses surgical tubing ("borrowed" from the chem teacher) and student sitting/standing on a homemade hovercraft (here are the directions to make it*)(You can use on office chair if you don’t have hovercraft).  Here's a picture of the setup with an office chair {I guess Jon didn't want to bring his hovercraft from Minnesota, how rude}

*Modifications Jon made to the procedure:
Blue tarp works fine, don’t need that pattern of holes – he just put 30 small triangular holes throughout
Duct tape around between small disc and big disc
Use the biggest fender washer @home depot you can find instead of the coffee lid
Make the hole (at the very end) as close to the size of shopvac nozzle as you can (need a tight seal)

Take the class into the hallway, and ask for 2 volunteers.  One sits/stands on chair/hovercraft and holds a meterstick at his/her waist.  The second you tell to pull the rubber tubing to a fixed distance.  You tell the person to pull the other victim volunteer such that the distance the tubing is stretched does not change.  Let the carnage begin.  If you want to maintain some sense of safety have the other students line the hallway to help keep the demonstration moving down the hall instead of into doorways and other obstacles.

You can take the sequence to the next level by now asking what would happen if the person seated in the chair/standing on hovercraft were to throw a medicine ball?  (Demonstrate if you have one).  Now ask what would happen if you had a magic contraption that dropped unlimited medicine balls so you could constantly throw them?  Tell them, let's not imagine it. let's do it.  Grab a $CO_2$ fire extinguisher and release the trigger while sitting/standing.  (Jon said he removes any hose/nozzle, and that he worked out a deal with a local supply company to get an old extinguisher, and get ~$10 refills.  He said one full extinguisher will work for all his classes.)  At this point bring the class back inside and have them summarize what all has happened, using FBDs as needed.  Guide the students to the idea of Newton's 3rd Law: If "A" exerts a force on "B" to the "right," then "B" exerts a force on "A" to the "left."


From there, we moved on to individually, complete Unit IV wkst 3
(Jon told us that he doesn't use this sheet as written, but modifies it for his 1st yt students)

{Has students do the FBD’s but modifies to do progressions in steps, not all at once}
{chris inserts a week or two of material from the math modeling curriculum to review trig concepts.}
{does math review before this unit not at beginning of the year like most teachers}

After completing the worksheet, we whiteboarded our results.
Notes from WB:
#4 – group made error on purpose – switching sine & cosine
(Acting as students saying that cos is always the  horizontal component of a vector)
Jon's series of questions: Which leg of the triangle is the longer leg, so which one should be bigger?
  • What on the diagram will be equal to the Vertical leg? (Answer: weight)
  • What will be equal to the Horizontal leg? (Answer: T1)
  • Based on triangle, which should be the bigger force? (Since vert. leg>horizontal leg, Weight)
  • Does you answer match that fact?

#8 – Jon – Giancoli has a great problem w/ lawn mower
{Which in looking through my copy looks like #26 in chapter 4}
One question they asked the group (mainly to have some fun at their expense)
If floor is frictionless, how does he push the broom?
At that point someone mentioned this Cartoon over at xkcd
               http://xkcd.com/669/
Next we Whiteboarded sections of Hake “Socratic Pedagogy in the intro phys lab
Due to time constraints, Jon showed us a trick if we ever need to move things along:
If running short on time – have all students display boards, then ask if anyone has questions.
  Address the questions as needed, and move on.

Here a link to SDI labs as provided by Chris

From there we moved on to another Demo to continue to explain Newtons $3^{rd}$ Law:
Equipment: 2 spring scales & 2 volunteers
Scales attached between the 2 people, 1 person pulls while the other just holds on, then they switch, lastly both pull on the scales.
(If you don't have large spring scales, use 2 bathroom scales/ or vernier force plates)
For bathroom scales (have a "reader" looks over each shoulder & call out values)

Next they set up 2 vernier carts each w/ force sensor attached, on  cart track track
(Jon mentioned that Steiner (sp?) has variations of worksheets in the modeling website, probably under password wall for those that attended the workshop)
(Before you begin, zero the sensors and make sure one has direction flipped, or you won't see both sets of data in the plot)
            1st Trial- both cars moving with equal mass & approx same speed
            2nd Trial - add standard masses to one car, so the collision has uneven mass
            3rd Trial - One stationary vs one moving
            4th Trial - One moving fast, the other slow
            5th Trial - Cars start together and explosion with cart “spring”
{Obviously (?) you could keep going if you feel the need 

Next, they took the sensors off the cars, and attached them at the hooks, and plotted real-time data of the students pulling the sensors apart.

Unit IV: Worksheet 4
(Due to the complexity, Jon has his students first just answer the A/B/C part of the problems and has students whiteboard their answers. Then he has them draw the FBDs, however, they only need to depict the interactions of block A on B and B on A (no other forces yet), and again, they quickly whiteboard their answers.  He then walks them through one or two of the problems, and assigns the rest for homework.  Whiteboard results at the start of the next class)

We again finished the unit we feedback. Chris said they were going to limit the discussion to 15 minutes.

What we liked:
Wkst 3 – we liked FBD  & crunching numbers (we're physics teachers, what do you expect)
Wkst 4 – we also liked how this helped to solidify Newt’s 3rd law
We liked the progression of demos for 3rd law
Especially the Laser reflection based on pushing the wall
For the most part, talking about Forces with little math (have yet to bring up $a=\frac{F}{m}$)

What we didn't like:
Would like for this unit to have more lab and less time on complicated worksheets
(Demos are good, but students are watching not doing)
{someone mentioned possibly using force table labs to introduce 2D/trig}
We felt that Worksheet 1 would be too big of a jump our students and would have like to see what Chris did
      to get his kids ready for it.
 A few had concerns that their students would never be able to ever do some of this work
          
Chris also said that for his AP class he has a summer assignment, which is primarily a math review

Modeling Unit 3

Unit III: Uniform Acceleration Particle Model

We began the "Cart on an Incline Plane Lab."  After talking to Jon and Chris about Brian Frank's Blog during our lunch break, Jon and Chris altered the first question to begin the cycle by asking "What do you see/notice?"  Again, we moved through "What can you measure?" and "What can you manipulate?" before arriving at the purpose: "to determine the mathematical and graphical relationships between position and time for a cart on an incline plane at a fixed angle.  As a group, we seemed to struggle with this process this time.  I'm not sure if we are taking our role in "student mode" too seriously and confusing ourselves in the process.  We didn't seem satisfied to look at this relationship and many wanted to add more quantities such as mass and angle into the procedure.  One good suggestion was to focus the students back on the first question, "What do you see?"  By using what is already on the board, we can steer the students to the necessary target of this unit.  I might add that we should include some help to our students to focus on the actual demonstration we are doing (cart rolling down a fixed ramp) and try to dissuade them from altering the set up.  Possibly reminding them that our job is to create the experience that will teach them the necessary component of physics, and we chose this exact one for a reason. 

After we were settle on the debate, Jon told us to use the motion detector to acquire "clean data" for the cart.  When asked what he meant, he said, "You'll see what I mean."  He put on the board for us to then manually calculate 10 values of "average speed" over the range of our data (he originally put instantaneous, but later corrected it).  He also remembered later that he usually has the file "01a Graph matching.cmbl" from the physics file loaded onto the computers, so that the velocity will not be automatically calculated for the students.  For the average velocity, he tells the students to use the position and clock readings from just before and after the point we are using to calculate the average velocity.  Jon also mentioned that during the acquisition of data, and the subsequent creation of the whiteboards, he would talk to the groups about the significance of the data produced (if you started the cart after the motion detector, what do the initial data points mean?  points after the cart hit the bottom of the track?).


We next analyzed the graphs we made from the cart on an incline plane lab to derive the kinematic equations. Although this only takes about 10-15 minutes, it made this post too long.  So I made a separate post to show the process.  Although most texts give these equations, many omit the entire process.  For the sake of helping your students foster their connection between the graphs and the equations, Jon recommends spending the time to show these derivations.  {My guess is that you could either do this during whiteboarding, or as a mini-lecture (for those that aren't quite ready to give up the reins, and want to be a sage on the stage again).}

After showing all the derivations, we moved on to Lab Extension: Speeding Up and Slowing Down.  {As I've noted at least once before, we were given version 3 of this worksheet.  However, I'm only seeing version 2 on the modeling website.  I guess that's one more reason you need to go to the workshop and not just read my blog.}

Jon told us that he gives the students all the equipment except for the motion detector.  Jon said that after the individual groups show him the completed worksheet, he provides the motion detector.  After the students have all completed acquiring the data/graphs, he has them white board what they got for a given problem.  Chris does it a little differently.  He never gives them the detector, but rather has the students make the predictions for HW, and then the groups whiteboard their predictions at the beginning of class.  He then projects the actual results after the class has come to agreement for the each given problem. {My $0.02 on this is that I like Chris's approach better (sorry Jon).}

By the way, I had never seen motion maps that showed both velocity and acceleration at the same time.  For those like me, you plot the velocity above the displacement vector and acceleration below.  Have the points that represent the same time line up vertically.  I've tried to show what the map for #1 would look like below:



The blue vectors represent the velocity and the red vectors represent the acceleration for an object accelerating from rest.
{I'm honestly not sure how to draw the first point for the acceleration portion, whether they should be inline with the arrow overlapping the second point, or as shown with the first point slightly above the second.  I'm guessing how I have it is correct.  And no, I didn't waste the time to make sure the arrows were to scale.  Remember motion maps are qualitative, not quantitative.}

A couple points made by Jon and Chris:

#3 is the first instance for the students where an object is speeding up even though it has a negative acceleration.  You need to socratically question the students (What is happening to the magnitude of the velocity?   What then is the sign of the acceleration?  Can a negative acceleration increase the velocity?).  According to both Chris and Jon, this is a confusing idea, since they are used to describing a negative acceleration as a deceleration (a term you should dissuade the students from using).

#4 is a similarly confusing example in that the acceleration is positive but the object is slowing down.  Again, use Socratic questioning to lead the students to this idea.

#6 Jon omits this problem as changing the origin doesn't really come up later in the curriculum.  He said that it's up to you and your students.  Do you want/have time to spend on this?
{My thoughts are that I might leave this out for standard level, buy include it for the honors level of my classes.  If I have more than 6 lab groups in honors (which I did this past year ('10-'11)), I might make additional problems with the adjusted origin so each group whiteboards their own problem.}

From there we worked on Worksheet 2Worksheet 2a, and a supplementary worksheet.

2a: #3 Jon mentioned that students tend to struggle with all the technical vocabulary in this problem.

2a:#5 Chris asked the group presenting: “I remember a problem from the earlier work, where the negative velocity and it was speeding up.  Why is this different?” {Your trying to get the kids to focus on the speeding up when acceleration is in the same direction as motion, (and slowing down when opposite) not based on +/- sign}

Wkst III:
1 c&d Jon mention that these problems are very tricky for students. 

We next moved on to another experiment using a Vernier Photogate and the Vernier Picket Fence. (note: you may need some of the accessories to attach the photogate to a ringstand).  We used the "picket fence" file provided by vernier.

We were asked to get one measurement of "g" for the picketfence by itself, and one value while a hanging weight was attached to the picketfence.  Jon and Chris made this a competition among groups to see who could get the closest value to the accepted (9.80665 $m/s^2$) for each set of measurements.  
{I'm not sure if I would tell my students the correct value or not.  I would probably just calculate the class average and then ask the students to explain our error.  One side note, one of my pet peeves is "human error."  To me that is a student being lazy and not wanting to think about what they did wrong.  I would push my students to say that the picket fence was rotated one way or another, photogate wasn't level, etc.}

From there, we then did another "competition" lab where we were provided the motion detectors, a rubber ball (similar to traditional dodgeball that could actually leave a mark, not the foam ones given now.)  {Don't get me started on that one.}, and a metal filing shelf (similar to this, only it was one level not two). The shelf was used over the top of the detector to help protect it from the ball.  The basic procedure was to toss the ball above the motion detector and have it fall towards the detector.  Again, the group with the closest value to "g" received a prize.  We used the "ball toss" file provided by vernier.
{I think I might introduce video analysis at this point, either have the students do it in their groups, or run this as a demo, videotaping the students tossing the ball.  Then I would show on the smartboard how to use video analysis.  I would probably use the tool in LoggerPro, however, seeing Rhett Allain use VideoTracker throughout his blog, makes me think it might be worth it to have the students download and use that programHowever it might be worth leaving video analysis until we get to 2D motion.}

We ended the day by whiteboarding sections of the assigned reading from the previous night.  Instead of giving a summary of the summary, I would just say we read Aron's book and discussed 2.7 - 2.16 (excluding 2.14).  It builds off most of the concepts already discussed yesterday.  For those that haven't read it, it's a great text that explains many of the students' misconceptions and strategies to help overcome them.

We started today by finishing our whiteboard summaries of Ch 2 from Aron's book.  Since I didn't go into detail on the Day 5 post, I'll omit them here as well.

From there, we wrapped up Unit III with some feedback to Jon and Chris:

What worked:
  • The worksheet "stacks of kinematic graphs" - we felt that it was a great tool for helping students convert from one type of kinematic graph to another.  Chris mentioned that if/when you have students whiteboard this, to make sure that they display the graphs vertically.
  • Worksheet: Speeding up/slowing down - we liked that this allowed us/students to predict what they thought would occur, then later them seeing the results. 
  • We liked that there were multiple labs that were short, as you could get more hands on time, but not use multiple days to do different activities.
  • We liked seeing the graphical proof of kinematic equations
  • We liked the reading from Aron's book, especially the misconceptions he mentioned, and tools to help overcome them.
What didn’t work:
  • We said that we would like more insight into the "mechanic" of implementation the modeling cycle
    • What does the day to day flow look like
    • When do learning objectives come into play (some are at schools that must display the objectives for that day's lesson at the start of class)
    • Pacing of course
  • Some of us that aren't familiar with the content want more time to complete activities, and we also recognize that we need tools to overcome what we see in the workshop; some people are done with nothing to do, while others are struggling to keep up.
  • Some asked, "What to do if we don’t have loggerpro/equipment?"
  • One other thing we liked in the first cycle that didn't occur here was the division of Labor/variation of control variables.  {I'm not sure how you would fit that in, but that's what came up in discussion}
 {To those in the workshop (merely reading) that want to see the pacing of a class, one website I found was Mark Schober's Website.  Another great blog that you might find useful is Action-Reaction, one especially nice feature is that he organized his blogroll for different subjects (I'll try to get to that at some point).}
Miscellaneous Questions:
  • How often do the students need to do formal lab reports, and how do those "Work?"
  • As already mentioned, what are some ideas for extensions of labs for “faster” students
For the first question, Jon referred us to some of the resources at the beginning of the modeling binder (here, here, and here).
For the second question, Jon mentioned that he often splits up the groups that are done and have them help the groups that are going slower.

One other point that came up, was that if you need help keeping everyone engaged, assign each person in the group a roll. {When I need to do this, I use "Leader," "Secretary," "Technician," and "Gofor."  The leader in is charge of making sure the group is on task.  The Secretary is in charge of recording all necessary information/procedures/equipment/etc.. The technician is in charge of running the actual experiment.   The gofor (some call it the Yeoman) is the person in charge of "going for" stuff.  He/she gets the equipment at the beginning, is in charge of cleaning up at the end, and the assistant for all other jobs.}

One other conversation that came up was to make sure that everyone in the group knew one anothers' names.  Jon mentioned that he was surprised how many problems could be avoided if they knew that one simple fact.  He makes it a point to quiz students each others' names at beginning of new lab groups.

When Chris got a chance to address the question about objectives, he said he often uses some of the resources from the modeling curriculum to make review's

Kelly O'Shea has a blog that I love, which focuses a great deal on Standards Based Grading.  (One oversimplification of SBG is you report grades based on learning objectives of the unit. ) (Here are her objectives for Honors Physics, by the way).  When I asked her when she reveals her objectives to her students, she said:
Usually try to hand them out at the start of the unit. I would say few students look at them before they are preparing for an assessment. Some probably don’t look at them until they get the test back and look at their scores.
Jon mentioned that he often uses the provided Unit Objectives sheet to create a review.  Chris said that he often has the 3 ring-binder out when groups are whiteboarding, and often asks questions right out of the teacher notes (post lab discussions especially)

This was a lengthy discussion, but some great ideas came out of it.