(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A uniform solid cylinder (m=0.230 kg, of small radius) is at the top of a similar ramp, which has friction. The cylinder starts from rest and rolls down the ramp without sliding and goes around the loop. Find the speed of the cylinder at the top of the loop.

2. Relevant equations

PE - potential energy

KE - kinetic energy

KEr - rotational kinetic energy

I - moment of inertia

w - omega

KE0 + PE0 + KEr0 = KEf + PEf + KErf

3. The attempt at a solution

At first I was tripped up over the small radius part, until I realized that the radius would cancel out with final height of the potential energy and I deduced that the initial rotational and kinetic energies would cancel out to get something to this fashion:

mgh0 = 1/2mv^2 + mg2R + 1/2Iw^2

mgh0 = 1/2mv^2 + mg2R + 1/2I(v^2/r^2)

mgh0 = 1/2mv^2 + mg + 1/2Iv^2

I plugged and chugged my numbers to get a velocity of 7.18, but then I realized I forgot to incorporate the friction force, so how would that fit in to the mathematical equation?

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# Homework Help: Cylinder sliding down a track

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