I play pick-up basketball at lunchtime a couple of days a week (in a good week, anyway). It’s become a running joke that after a particularly long or hard-fought game, I’ll announce my intention to give a pop quiz that afternoon in class. “Just work quietly at your desks, folks. I’m going to sit here and drink Gatorade.”
I’m going to turn the joke around a little for the purposes of blogging: this week is an exceptionally busy week for me, as on top of the backlog of grading that piled up last week when I was sick, I’m teaching the junior/senior level lab course for the next two weeks, and I have a bunch of running around to do for that.
So, here’s a pop quiz to fill some time, in the same vein as the three cylinders problem at BioCurious. The figure at left represents a top view of a sort of tetherball apparatus: a ball of mass m is tied to a post of radius R with a string of length L, and set into motion with an initial speed v. The string (which is, of course, massless, fricitonless, and non-elastic) wraps around the post, and eventually the ball hits the post.
What is the speed of the ball when it hits?
Be sure to justify your answer, and show all your work. I’ll be down in the basement dealing with the unique failure modes that the students have found for the lab apparatus.