Day 49: Testing different lab methodsPosted: November 5, 2012
Last week in our weekly Physics teachers meeting we briefly talked about the possible labs to build the Unbalanced Force Particle Model (UBFPM, AKA Newton’s 2nd law). The modeling materials use a modified Atwood machine, and I planned on doing a further modification to mount a force detector on top of the cart to directly measure the force (that way you somewhat circumnavigate the problem where you must keep the mass of the system constant, thus should transfer masses from the hanging mass to to cart and vice versa). Kelly simply stated that seemed too complicated. So I decided that on my planning day today I would test to see what worked better. I modified Kelly’s version slightly, since I don’t have cool brass knuckles. I simply varied the displacement of the spring with each trial, thus varying the force (students would have to start by first measuring the spring constant of the spring, more on that below). The results are above; it worked surprisingly well. Additionally, the inverse of the slope of the graph should be the mass of the system, and it easily matched the system mass within uncertainty. Pretty cool. The acc vs mass of cart version worked similarly well. The Atwood’s data turned out good too, though.
Both methods took me about 20-25 minutes. Both had minor setup problems, but nothing serious. I did, however, find a problem with my modified Atwood version with constant force (constant hanging mass); as the acceleration changes, so does the tension in the rope (analysis of the hanging mass yields that T=mg-ma, so as acceleration increases, Tension decreases). Should have been obvious to me, but wasn’t before trying it. It’s still within 10% for the range of my values, but I wouldn’t be happy waving my hand at it.
The result is that I will be using my modification of Kelly’s version where kids will vary the spring stretch to vary the force on the cart (which I think is more intuitive anyway), then vary the cart mass with constant stretch to get the a vs m data. I had been debating putting spring force in this unit anyway (instead of the Energy unit), this just gave me a really good reason to do so.