A Penny Falling Off a Non-moving Sphere

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Homework Statement



A penny is released from the top of a very smooth sphere of radius 1 m. The sphere is fixed to a platform and doesn't move. The penny slides down from rest and leaves the sphere at a certain point. How far will the penny fall away from the point of contact of the sphere and the platform?

Homework Equations



(1) V = Vo + at
(2) a = (V^2)/9.8
(3) V^2 = Vo^2 + 2a(x - xo)

The Attempt at a Solution



Vo = 0 m/s
r = 1 m
a = g = 9.8 m/(s^2)
x = ? => The distance the penny fell from the top of the sphere to ground.

I used (1) in order to rearrange into

t = V/g

After doing that, I was thinking that maybe I could use (2) or (3) to rearrange the equation a little more to find the solution, but I'm sure that's not right, and I'm doing too much work. I've attached a pdf of the problem.
 

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Answers and Replies

  • #2
haruspex
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(1) V = Vo + at
That's only valid for constant acceleration, which this is not. You need to find the point at which the penny leaves the sphere. Suppose the radius to that point makes an angle theta to the vertical. Use conservation of energy to find its speed there, then consider the forces on the penny at that point.
 

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