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Oijl
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Homework Statement
Consider a small frictionless puck perched at the top of a fixed sphere of radius R. If the puck is given a tiny nudge so that it begins to slide down, through what vertical height will it descend before it leaves the surface of the sphere?
Homework Equations
The Attempt at a Solution
I recognize that when the normal force on the puck exerted by the sphere is zero, the puck is no longer on the sphere. Therefore, I seek to express the normal force as a function of height, or of the angle measured down from the vertical, from which the height is easily calculated.
I can't find a way to write the normal force. What would the normal force be, at a point? Looking at a solution, someone wrote:
N = mgcosø + (mv^2)/R
where ø is the angle measured down from the vertical, so that it could also be written
N = (mgh + mv^2)/R
Where does this come from? I don't see the truth in this expression of the normal force.