A block starts from rest and slides without friction along the surface of a hemi

Question

A block starts from rest and slides without friction along the surface of a hemisphere of radius R = 1.7 m. As the block slides, eventually it loses contact with the hemisphere.

What is the height, h, when the block loses contact with the hemisphere?

A block starts from rest and slides without friction along the surface of a hemisphere of radius R = 1.7 m. As the block slides, eventually it loses contact with the hemisphere. What is the height, h, when the block loses contact with the hemisphere?

Explanation / Answer

At the point of no contact normal reaction acting on the block will be zero.

Therefore balancing the forces in the radial direction

mgcos(theta) - N = mv^2/R   (radial direction)

using conservation of energy

velocity of block = sqrt(2*g*R(1-cos(theta))

substituting in above equation and putting N = 0.

mgcos(theta) = 2mg(1-cos(theta))

cos(theta) = 2/3

Therefore height h = Rcos(theta) = 2R/3

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