There is clearly a square root relationship here. I had them set the boards aside.
The next question is, "What, if any, relationship exists between the energy stored in the stretchy string and the vertical height up a ramp?" They took the same set up and just lifted the far end of the ramp.
The more energy they put into the string (by stretching it farther back) the higher up it goes.
This one shows a linear relationship. Again I had them set their boards aside.
Lastly we asked, "What, if any, relationship exists between the energy stored in the string and the slide distance?"
They took the original set up and substituted a wooden block for the low friction cart.
The more energy they put into the string the farther it slides. This is somehow related to the energy relesased to the surroundings.
This relationship is also linear.
The real question is, when you have all of these boards with the correct relationships, how do you get to the actual equations?
This takes a bit of hand waving and it pretty much teacher led. But what is the actual point? For the students (or participants) to get a sense of the energy transfer and conservation. The mathematical equations are only one part of the whole energy model and I don't think they should be the main focus for anything.
So what did we do? We looked them up on Google! Yep - I used the Google to verify that what they got in the lab actually matches the accepted equations for the different storage mechanisms for energy!
Once we were finished with the white boards they started unit 7 worksheet 3b.
Unfortunately we were on the second to last day and we skipped white boarding and discussing the worksheet :(
I wanted to get to a practicum challenge however. Here is what we did. For each group we set up a clamp on a table and put a long rod in the clamp. I used a 90 degree clamp to attach a short rod to the long vertical rod. I hung a spring on short horizontal rod and gave each group an object of known mass. I also gave each group a small drinking cup with aluminum foil on the top covering the opening.
The task was to adjust the height of your rods to that when you released the mass, from the height of your choosing, it would touch the foil without breaking through.
The video above shows a winner! The rest of the groups were very close - I mean within a few centimeters.
After that was all done we needed to so a circular motion intro. I started by swinging a rubber stopper attached to the end of a string above my head in a horizontal circle. The questions were:
- how do you find speed?
- is it accelerating?
I had them all draw the system schema for the stopper and then the force diagram.
Traditional physics students always try to put an outward force on the stopper. However, with the system schema in place there are only two forces and no one seemed to be confused.
The last question was - in what direction is the unbalanced force?
This is a three dimensional representation of the force diagram for the stopper at four different locations. They were easily able to see that the unbalanced force always points inward toward the center.