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Bug on a Bowling Ball
A bug sitting on top of a bowling ball begins to slide o? with negligible friction. Conclude the angle at which the bug leaves the surface.
This problem is easily solved with the aid of the diagram
The forces on the bug include the centripetal force due to gravity, the centrifugal force due to motion along the curve and the resulting normal force.
Fn = mv2/r - mg cos θ
The get done in kinetic energy as the bug slides is provided by the loss in potential energy. Since h = r - r cos θ we have
At the instant the bug leaves the ball the normal force Fn becomes zero. We are able to now substitute the value of the centrifugal force
Fn =(mv2/r)- mgcos θ
The get in kinetic energy as the bug slides is provided by the loss in potential energy. As h = r - r cos θ we have
mv2/2 = mgh
mv2/2 = mgr(1 - cos θ)
mv2/r = 2mgr(1 - cos θ)
At the moment the bug leaves the ball the normal force Fn becomes zero. We are able to now substitute the value of the centrifugal force
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