Thursday, December 06, 2007

Making The Grade


There is a cow which weighs 1400 lbs sliding down the inside of a
spinning funnel. The coefficient of friction between the cow and the
funnel is 0.102. The funnel is spinning with an angular velocity of
10 rad/s and is sloped at an angle of 50 degrees with respect to the
horizontal plane. The cow is attached to a rope which is passed over
a massless, frictionless pulley attached to the lip of the funnel.
The other end of the rope is attached to a 200 kg mass suspended
vertically from the pulley. There is a one solar mass black hole at
the bottom of the funnel. If the diameter of the funnel is 50 m at
its widest point, how long does it take the cow to slide down the side
of the funnel? Assume the cow is spherical.

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