Answer Happy

A recent art show titled 'The Instability of the Earth' features a solid hemisphere repre- senting the Earth fixed to the floor. The Solid hemisphere has a radius R. You have a ping pong ball (hollow sphere) of mass m and radius r that is placed on the top of the sphere that represents man's fragility....or something. The ping pong ball will soon come out of equilibrium and begin rolling down the sphere. The ping pong ball rolls without slipping, but the friction is small enough to ignore other- wise. At some point before the floor, the ping pong ball will lose contact with the sphere. a) (4 points) Draw a sketch of the ball at the very top and the ball just before it loses contact. Draw Free-Body Diagrams for both sketches b) (5 points) Using concepts from Module 2 (Forces) find an expression for the velocity the ball will have just before losing contact c) (7 points) Using concepts from Module 3 (Energy, Momentum, Torque, Angular Mo- mentum), determine which concept to use and then find a different expression for the velocity the ball will have just before losing contact d) (4 points) Find as simple of an expression (using only g, R, r, and m) for the height above the floor the ball will lose contact with the hemisphere.