FIU Modeling Workshop – Day 7

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
Unit V: “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
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