A small block sits on the top of a fixed frictionlesshemisphere of radius R = 9

Question

A small block sits on the top of a fixed frictionlesshemisphere of radius R = 9 meters. If the block is given ainitial horizontal velocity of v = 7 m/s. 1. determine at which height the block will leave thehemisphere 2. determine the speed of the block at this point A small block sits on the top of a fixed frictionlesshemisphere of radius R = 9 meters. If the block is given ainitial horizontal velocity of v = 7 m/s. 1. determine at which height the block will leave thehemisphere 2. determine the speed of the block at this point

Explanation / Answer

first at a angle form vertical it will slips down then at the point of falling normal reaction due to sphere will bezero. At the point of falling it will travel a ditance of R(1-cos)so velocty at the point using work-energy theorem v*v +2gR(1-cos) = V*V so at the point of falling using equilibrium along the normal ofsurface mgcos= mV*V/R which implies that gRcos =v*v+2gR(1-cos)                         3gRcos =v*v+2gR      => H =      Rcos = 2R/3 +v*v/3gR here H is height from the center of the sphere

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