- #1

Thorskur

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## Homework Statement

Sorry guys but uploading the image didnt work so i post it on imageshack. Here is the link: http://imageshack.us/f/208/apib.jpg/

So the quastion is:

In the image the pulley is a uniform cylindrical disk of mass m and radius r. The strings are massless and there is no friction. If the system is initially at rest, find the speed of the blocks after they have moved a distance d.

## Homework Equations

E = E + W

K = 1/2Iω^2

## The Attempt at a Solution

Let's say that the potential energy is set at 0 when the blockmoves from y=d --> y=0.

Then the starting energy becomes (m1+m2)gh = 2mgd

Translating to kinetic energy, ΔU =(1/2)(2m)v2 - (1/2)Iω2

Because our pulley also has a mass m, and I =(1/2)mr2

ΔU = mv2 -(1/4)m(r2ω2) = mv2-(1/4)mv2 (Using v =rω)

So ΔU = (3mv2)/4 = 2mgd

And my answer is:

v =√[(8gd)/3]

My book say the answer is : v =√[(4gd)/5]. So I am wondering what I am doing wrong?