Hello, I need a fairly detailed explanation of how to do this problem. If you sh

Question

Hello,

I need a fairly detailed explanation of how to do this problem. If you show me just the math then I won't award any points. I need an explanation of any step involving some physics concept (ie. tension= this because of some physics law). Since I need the problem well worked out and explanation of the physics steps, I am offering 750 points.

Problem:

A thin-walled, hollow sperical shell of mass m and radius r starts from rest and rolls without slipping down a track shown in the figure (attached image).

Points A and B are on a circular part of the track having radius R. The diameter of the shell is very small compared to h0 and R, and the work down by rolling friction is neglibible.

a) What is the minimum height h0 for which this shell will make a complete loop-the-loop on the circular part of the track?

b) How hard does the track push on the shell at point B, which is at the same level as the center of the circle?

c) SUppose that the track had no friction and the shell was released from the same height h0 you find in part (A). Would it make a complete loop-the-loop? How do you know?

d) In part (c), how hard does the track push on the shell at point A, the top of the circle? How hard did it push on the shell in part (a)?

Explanation / Answer

for circular motion speed at top of circle is sqrt(gR)

so energy at bottom = 1/2 mv^2 + 2mgR = 5mgR/2

so energy at bottom is = 5 mgR/2 = initial potentila energy=mgh

so h= 5 R/2

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