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mbrmbrg
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Homework Statement
A small solid sphere, with radius 0.25 cm and mass 0.68 g rolls without slipping on the inside of a large fixed hemisphere with radius 23 cm and a vertical axis of symmetry. The sphere starts at the top from rest. The moment of inertia of a sphere is I = 2/5 MR2.
(a) What is its kinetic energy at the bottom?
(b) What fraction of its kinetic energy at the bottom is associated with rotation about an axis through its center of mass?
Homework Equations
E=U+K=constant
U=mgh
[tex]K=\frac{1}{2}mv^2+\frac{1}{2}I\omega^2[/tex]
The Attempt at a Solution
For part (a) only:
I started to write up the energy conservation law in great and glorious detail, but then I realized that since K_i=0 and U_f=0, and the question only wants to know K at bottom, I could say
[tex]mgh=K[/tex]
[tex](.00068kg)(9.81m/s^2)(0.23m)=K[/tex]
K=0.00153J
But the correct answer is 0.152J, a rather striking difference. Where did I go wrong?