Using Newtonian physics - forces and/or energy considerations - but not Lagrangian formalism, solve the following problem: A large, smooth, metal sphere of radius R sits on the ground motionless and on a stable mount. An ice cube (assume friction free) is released from the top of the sphere and slides down. Don't worry about the tiny nudge needed to get it going. Find a description for the position at which the ice cube loses contact with the surface of the sphere