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April 18, 2014

Homework Help: Physics

Posted by Alphonse on Friday, October 26, 2012 at 2:19am.

A sphere with a moment of inertia 0.465mr2 and mass m and radius r rolls without slipping along an inclined track that is followed by a circular loop (like a roller coaster) of radius R. This happens on a planet where the acceleration due to gravity is g.  It starts from rest at a height h = 3.5R (height of track, ie. y-coordinate of triangle) above the bottom of the circular loop of radius R.

(For simplicity, neglect the size of the sphere relative to the radius of the loop R and the height h, i.e. r << R, h. Also, while static friction is responsible for the rolling motion, it does no work since it acts through no displacement.)
 
a)  What is the magnitude of the normal force that acts on the sphere at the top of the circular loop as a fraction or multiple of the sphere's weight mg?
 
(Example:  If you were to find the magnitude of the  normal force is 1.85mg, then enter 1.85.  As usual, retain enough sig. digs. so that you're within 0.5% of the 'exact' answer.)

b)  If the track and incline were frictionless what would happen to your answer in the previous question and why?
Options:
-decrease since the sphere would slide instead of roll and would have a larger vcm at the top
-stay the same since acm and N at the top have nothing to do with rolling motion
-increase since the sphere would not have lost mechanical energy and would have a larger vcm at the top
-increase since the sphere would slide instead of roll and would have a larger vcm at the top
-decrease since the sphere would not have lost mechanical energy and would have a larger vcm at the top

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