A bead slides without friction around a loop-the-loop. The bead is released at height y from the bottom of the loop, which has radius r. What is the instantaneous kinetic energy K at the top of the loop so that the bead would press the track with an upward force F=mg/2?
Express the height y in terms of K, m, and r.
The Attempt at a Solution
I drew a FBD with weight mg down and F mg/2 up. The sum was mg/2 down, which I set equal to m(v^2)/r. I arranged the equation to get v^2=gr/2, and plugged that into the kinetic energy equation, getting mgr/4 as the incorrect solution.
I was able to get the second part through energy conservation, setting mgy=2mgr + K and solving.