Day 56: A New DiagramPosted: November 19, 2012
Kelly O’shea tried to convince me and a couple other physics folks at our Thursday night physics teacher meeting that using tip-to-tail vector addition was the way to go for problem solving with forces. I resisted. How could that possibly be better than components? Then I saw how well it works for ramps in particular, as shown above. The first is a simple diagram of the situation where I added some lines so we could find where theta should go in the force addition diagram. The second diagram is a free body diagram in which I added the second, lower normal force at some point to show how the FBD is turned into the force addition diagram, and the third diagram is the force addition diagram complete with the huge Fnet arrow. We talked about this conceptually, such as how Fnet and acceleration have to be in the same direction, and how finding Fnet would allow us to find the acceleration through the newly discovered Newton’s 2nd Law. I must admit, this method makes ramp problems much easier. I’ll probably still show them axis tilting, as some kids will probably like it and I want to make sure they know ‘conventional’ methods still, at least until I am confident enough that they can do everything needed using the ‘unconventional’ methods in future classes. Plus this method actually gets more at the core as to why tilting the axis works. But I digress.
I introduced the new diagram using the typical pull-a-box-along-the-ground-with-a-rope-at-an-angle type example (which is actually shown in the link to the Thursday meeting above). I couldn’t believe it; the class ate it up. Audible oohs and aaahs! They really like this diagram, at least right now. We’ll see how it goes for problem solving the next couple of days.