# 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 unknowingly 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 yr. 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