1. Recall the "falling chain" problem from class and assume the chain to have length X and mass m. Y 9 In terms of the distance y, the chain's kinetic energy and potential energy are given by m 47 (A y ) y , - mg 4X (A + 2xy y). - K = 4X P Show that the magnitude of the downward acceleration of the free tip of the chain is greater than g. 9 2. In a tunnel with circular cross section, a uniformly dense circular disk rolls back and forth without slipping. The inner radius of the tunnel is R and the radius of the disk is r. You want to hang a pendulum in an adjacent tunnel so that the back-and-forth motion of the pendulum is synchronized with that of the disk in other words, so that varies in the same way over time on both sides of the figure: X 0 In terms of R and r, what length A should you choose for the pendulum? You can assume the bob at the end of the pendulum stick to be a point mass and you can assume the stick itself to be massless.