Friday, April 20, 2012

Momentum Transfer

Today we figured out how to incorporate gains and losses of momentum (impulse) into our model of momentum. First... let's predict how the Force vs. time and velocity vs. time graphs of a cart will look when it hits a hard bumper or a springy bumper (cue demo of cart doing this, always at the same initial v).

The whiteboards were awesome:

We went through to see what we had agreed upon and not (the "open questions"):

I was stoked about the great observations that so many of them made: the hard bumper made the cart come back more slowly, the elastic bumper was in contact longer, the velocity's sign changed (they all missed the sign of the force, but it was obvious what had happened when we saw the data from the force sensor!), the "hilly" nature of the force graph, the fact that the hard bumper exerted a higher peak force, etc.  There was even an awesome justification from one of the proponents of the "hill" (as opposed to the jump/spike in F) graphs that talked about how even the hard bumper gives a little bit (invoking a molecular "springiness" model), and so the force starts out small.  Literally - close to tears there.

You know the rest of the story - they saw that the elastic bumper transferred more momentum, even though it exerted a smaller peak force, reasoned that time was a factor, too, guessed that the area under the F vs. t graph might mean something, saw that it was just about exactly equal to the change in p (finally, some lab results worked super-well the first time :), and built our model for the change in momentum:
Or, for constant forces:

The best part was the appreciation of the analogy between work and impulse, which I think was more than a little due to the IFF diagrams - adding the initial momentum from the initial diagram to the area under the Fnet vs. t graph to get the momentum from the final diagram just makes it click for a ton of kids. We applied it to a sliding box, saw that it was easier than forces/kinematics, and talked for a free minute at the end of class about how physics used to be taught.  I described it to them (I needed to, since more than one said that she "couldn't imagine how else you could learn physics") as "throwing a bunch of equations at you and hoping that the concepts emerge from that and stick."  It worked for me, but not for most.  Reformed methods don't work for everybody either, but it's a huge increase in the proportion that really build an accurate mental model, without a doubt.