Coin--vertical displacement question and other 1. The problem statement, all variables and given/known data A Perfectly hemispherical dome with a 10. meter radius is treated with a frictionless coating. A marble and a coin are released from the top of the dome simultaneously. We will assume there is no air friction. The coin will slide, not roll. The coin will hit the ground first because it has more kinetic energy. 2. Questions Show mathematically whether or not the coin will stay in contact with the dome until it reaches the ground. If it does not, what will the coin's vertical displacement be at the instant it loses contact with the dome, and how far from the base of the dome will the coin hit the ground? (be clear and include explanations where necessary) 3. Attempt at the solution This part is where I am confused. I know that when the normal force is greater then the weight (or gravitational force) the coin will lose contact with the dome. I am lost on how to show it mathematically and where to start. Please Help!