A 50g marble rolls around the inside of a circular cone. The cones outer edge is

Question

A 50g marble rolls around the inside of a circular cone. The cones outer edge is at a 60 degree angle to the horizontal. the marble rolls at a speed of 5 m/s. a)How far above the bottom of the cone is the circular path that the marble rolls along? b)After rolling for some time, the marble runs into a 5g piece of clay sitting on the cone, which sticks to the marble. Still ignoring friction, how far above the bottom of the cone is the marbles and clay's new circular path? It is safe to assume the marble doesn't go faster because it has lost come potential energy.

Explanation / Answer

a)   Here, mv2 * cos60/r      =   mgsin60

=> 5 * 5 * cos60/r = 9.8 * sin60

=>    r =   1.473 m

b)    here, v = 4.545 m/sec

=>    4.545 * 4.545 * cos60/r = 9.8 * sin60

=>    r =   1.217 m

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