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A small disk of mass m lies on the highest point of a sphere of radius R. A slight push makes the disk start sliding down. Find the force of pressure of the disk on the sphere as a function of the angle its radius vector makes with the vertical. Where does the disk lose contact with the sphere? Friction is to be neglected. |
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Answer» `F_(2) - N =mv^(2)//R` To find the velocity apply the law of conservation of energy mgh `=mv^2//2`Since h = (1 — cos ), we obtain after some simple transformations `N = mg (3 cos alpha - 2) ` When the washwer leaves the sphere it ceases to press against it and the reaction becomes ZERO. The condition for the loss of contact is `cos alpha = 2//3 , alpha = 48^@h= R//3` 
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