Question

A small block of mass m sits on the center of a dome of radius R. (Just to be perfectly clear, a dome is an upside-down hemisphere, like the top of a silo.) It is perfectly balanced at the moment, but then a slight breeze comes along and pushes it off in one direction. The rock will pick up speed as it slides down the side of the dome, and at some point it will end up going fast enough that it will lose contact with the dome.

Assuming the dome is frictionless and that initial speed from the breeze is so small as to be negligible, at what angle will the rock lose contact, measured in degrees? Measure the angle from the vertical, so that the rock started out at 0 degrees when it was balanced at the top and increases as the rock slides along the dome.

Answer 1