A marble of mass m is at rest at the apex of a hemisphere of radius R. It moves slightly and begins sliding down the side of the hemisphere. At what angle & does the marble lose contact with the surface of the hemisphere?

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Chapter1: Units, Trigonometry. And Vectors
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A marble on a hemisphere
A marble of mass m is at rest at the apex of a hemisphere of radius R. It moves slightly and
begins sliding down the side of the hemisphere. At what angle û does the marble lose contact
with the surface of the hemisphere?
R
(This problem is from Douglas Giancoli's text, Physics for Scientists and Engineers, 2nd ed.
(1989).
Note: if you solve this problem correctly, you should discover that the angle is independent of
the mass, gravitational constant, and the radius of the hemisphere – which, if you think about
it, should be the case.
Transcribed Image Text:A marble on a hemisphere A marble of mass m is at rest at the apex of a hemisphere of radius R. It moves slightly and begins sliding down the side of the hemisphere. At what angle û does the marble lose contact with the surface of the hemisphere? R (This problem is from Douglas Giancoli's text, Physics for Scientists and Engineers, 2nd ed. (1989). Note: if you solve this problem correctly, you should discover that the angle is independent of the mass, gravitational constant, and the radius of the hemisphere – which, if you think about it, should be the case.
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