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oxymoron man
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http://i.imgur.com/0RtN9Ui.png?1
I am trying to find the linear velocity of the sphere as it leaves the cliff.
2. Homework Equations :
Moment of inertia of a sphere: I= 2/5 mr2
3. My attempt at a solution:
I know that I am supposed to solve this through the conservation of energy, but would I not have to account for friction somehow since it is rolling without slipping? I know how to find the kinetic and potential energies at both points but the solutions manual (i know, i know, i cheated) says nothing about accounting for the non-conservative force of friction that is necessary for rolling without slipping.
Either way, without friction I have
U-initial: 0
K-initial= 1/2 mv^2+(1/2)*(2/5*m*r^2)*v^2/r^2
k-initial= 1/2 mv^2+1/5 mv^2
k-initial: 7/10 mv^2
and for
U-final: mgh
K-final: 7/10 mvfinal^2
Could i just set these equal to each other and get the answer? No friction needed?