A Penny Falling of a Staionary/Fixed Position Sphere

AI Thread Summary
A penny is released from the top of a fixed smooth sphere with a radius of 1.3 meters and slides down until it leaves the surface. To determine where the penny falls off, it's essential to analyze the forces acting on it, particularly using Newton's second law and considering centripetal force. The energy conservation equation mgh = 1/2*m(V^2) is relevant, where h represents the height from which the penny falls. The key challenge is calculating the angle at which the penny detaches from the sphere, which involves understanding the forces perpendicular to the surface. Proper analysis of these forces will lead to the solution of how far the penny falls from the point of contact with the platform.
. Arctic.
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Homework Statement



A penny is released from the top of a very smooth sphere of radius 1.3 meters. 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?

The penny just kind of slides off on it's own, and what needs to be found is where exactly it leaves the surface of the sphere.

Homework Equations



mgh = 1/2*m*(V^2)
h can be found using the angle.

The Attempt at a Solution



From the drawing I drew, I had the penny start from the top of the sphere and picked a spot where it falls off. I drew a line through the center of the sphere and the point where the penny falls off, but I'm at a bit of loss of where exactly to begin.
 
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Analyze the forces acting on the penny and apply Newton's 2nd law. (Don't forget that the sphere is a curved surface.)
 
Think centripetal force.
 
I know the forces working on the penny in the y-axis are the normal F = Weight. What I've been thinking about doing is using

mgh = (1/2)m(V^2)

My problem is the h. I'm thinking about saying that the center of the sphere is 0, and that the initial height of the penny is the radius. After that, I feel like I should use

h' = h - y

with h' being the height the penny falls off. I just don't know how to get the angle I need.
 
. Arctic. said:
I know the forces working on the penny in the y-axis are the normal F = Weight.
At any point, the normal force is perpendicular to the surface. Hint: Analyze force components perpendicular to the surface. What's the acceleration in that direction?
 
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