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 and the force of Earth on the puck (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 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

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?**

**purpose**: To determine the graphical and mathematical relationship between the force of the earth on the object and mass.

*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:

*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)*

^{st}yr. students)

{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:

(Acting as students saying that cos is always the horizontal component of a vector)

- 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?

{

*Which in looking through my copy looks like #26 in chapter 4*}

If floor is frictionless, how does he push the broom?

http://xkcd.com/669/

If running short on time – have all students display boards, then ask if anyone has questions.

Address the questions as needed, and move on.

(Jon mentioned that Steiner (sp?) has variations of worksheets in the modeling website, probably under password wall for those that attended the workshop)

^{st}Trial- both cars moving with equal mass & approx same speed

^{nd}Trial – add standard masses to one car, so the collision has uneven mass

^{rd}Trial – One stationary vs one moving

^{th}Trial – One moving fast, the other slow

^{th}Trial – Cars start together and explosion with cart “spring”

{Obviously (?) you could keep going if you feel the need

**What we liked**:

^{rd}law

^{rd}law

**What we didn’t like**:

(Demos are good, but students are watching not doing)

{someone mentioned possibly using force table labs to introduce 2D/trig}

to get his kids ready for it.