A penny is released from the top of a very smooth sphere of radius 1 meter. The

Question

A penny is released from the top of a very smooth sphere of radius 1 meter. The sphere is fixed to a platform and doesn' tmove. The penny slides down from rest and leaves th'e sphere at a cerain point How far will the penny fall away from the point of contact oft he sphere and the plaform?

A penny is released from the top of a very smooth sphere of radius 1 meter. The sphere is fixed to a platform and doesn' tmove. The penny slides down from rest and leaves th'e sphere at a cerain point How far will the penny fall away from the point of contact oft he sphere and the plaform?

Explanation / Answer

when in penny is contact, radial Component of force F = mv^2/R

so mg cos theta - N = mv^2/R

so as the penny falls

mg cos theta = mv^2/R

using the law of concervation of eenrgy mgh = 0.5 mv^2

so

R (1-cos theta) = mgRcos theta/2

cos theta = 2/3

so on x axis it falls at x = R sin theta

x = R sin (2/3)

x = 1 sin 0.667

x = 1.16 cm

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