## Wednesday, July 13, 2011

### FIU Modeling Workshop - Day 12

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:

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

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