Close to the centre of a campus is a tall silo topped with a hemispherical cap.

Question

Close to the centre of a campus is a tall silo topped with a hemispherical cap. The cap is frictionless when wet. Someone has balanced a pumpkin at the highest point. The line from the centre of curvature of the cap to the pumpkin makes an angle (Theta) i = 0 with the vertical. On a rainy night, a breath of wind makes the pumpkin start sliding downward from rest. It loses contact with the cap, and flies off into the air, when the line from the centre of the hemisphere to the pumpkin makes a certain angle with the vertical. The goal of the problem is to show that this angle is 48.2 deg, independent of the mass of the pumpkin or the radius of the cap!(a) Draw a FBD for the pumpkin while it is sliding down but before it loses contact. Find an expression for the normal force on the pumpkin when it is at an angle Theta with the vertical, in terms of its speed at that location. What is the normal force on the pumpkin once it loses contact? Show that the angle at which the pumpkin loses contact is 48.2. In your solution, make sure that you clearly identify the laws of physics that you are using. Your solution should convey that you know what you%u2019re doing: be clear, systematic, and explain your reasoning.

Explanation / Answer

Use the conservation of energy
m g R cos (?i) = 1/2 m v

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