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Calculus-based physics-Please help solve this problem!

 
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pnwokolo



Joined: 11 Mar 2010
Posts: 11
Location: Toledo,OH

PostPosted: Sun Mar 21, 2010 1:45 am    Post subject: Calculus-based physics-Please help solve this problem! Reply with quote

Sir, I have tried to solve this problem but because there are no information, I am not sure of my answer. Can you help me please. The question is:

A solid sphere is released from rest and
rolls down an incline and then into a circular
loop of radius R. What is the minimum
height h from which the sphere has to be
released so that it does not fall off the track
when in the loop? R
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hepcj
Site Admin


Joined: 23 Jun 2007
Posts: 125

PostPosted: Sun Mar 21, 2010 1:33 pm    Post subject: Reply with quote

There are two things to consider in this problem. The first is the forces acting on the ball as it travels around the loop. There is the force of gravity and the centrifugal force generated by the ball as it travels around the loop.
At the top of the loop, to stay on the track requires that the sum of the forces of gravity and centrifugal force is zero. Remember that at the top of the loop gravitational force is in the opposite direction to the centrifugal force.

From this you will obtain an expression in v^2 and you can relate this to the potential energy of the ball and thus the height through the conservation of mechanical energy:

1/2mv^2 = mgh

Then you will be able to find the height.
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pnwokolo



Joined: 11 Mar 2010
Posts: 11
Location: Toledo,OH

PostPosted: Mon Mar 22, 2010 1:21 am    Post subject: Calculus-based physics-Please help solve this problem! Reply with quote

Dear Site Admin.
Thanks very much for the help/guidance on how to solve the posted problem.
Once again, thanks.
Patrick Nwokolo
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