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Silversonic

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## Homework Statement

A massless rope is wrapped several times around a solid cylinder of radius 20cm and mass 20kg, which is at rest on a horizontal surface. Someone pulls 1m of the rope with a constant force of 100N, setting the cylinder in motion. Assuming the rope neither stretches nor slips and the cylinder rolls without slipping, what is the final angular velocity and speed at its surface?

## Homework Equations

[itex] I = MR^2/2 [/itex]

## The Attempt at a Solution

I assumed it would be simple energy conservation. The work done on the cylinder in pulling is equal to its total energy afterwards.

[itex] E = Work = F \times s = 100 \times 1 = 100J [/itex]

Then equating to the cylinder energy...

[itex] 100 = 0.5Iw^2 + 0.5mv^2 [/itex]

Using [itex] v = wR [/itex] where v is the surface speed and subbing in I, I get;

[itex] 100 = 0.75Mv^2 [/itex]

If I re-arrange this I get v = 2.58ms^-1, but my answer says 3.65ms^-1.

Can anyone get the answer they provide? Where is the mistake in my working?

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