# Homework Help: Atwood's machine with a cylinder

1. Mar 22, 2010

### dnp33

1. The problem statement, all variables and given/known data
a massless string of negligible thickness is wrapped around a uniform cylinder of mass m and raidus r. the string passes up over a massless pulley and is tied to a block of mass m at its other end.
the system is released from rest. what are the accelerations of the block and the cylinder? assume that the string does not slip with respect to the cylinder.
Use conservation of energy (after applying a quick F=ma argument to show that the two objects move downward with the same acceleration)

2. Relevant equations
F=ma
K=$$\frac{1}{2}$$mv2+$$\frac{1}{2}$$Iw2
P=mgd
where w=angular frequency
and I=$$\frac{1}{2}$$mr2 is the moment of inertia.

3. The attempt at a solution
I wrote an F=ma equation for each mass, and because they are the same mass should undergo the same acceleration
I wasn't sure if that was as in depth as the question required.

Then i wrote a conservation of energy equation for the system
mgd + mgd = $$\frac{1}{2}$$mv2 + $$\frac{1}{2}$$mv2 + $$\frac{1}{2}$$Iw2

and solved for velocity, where i used the kinematics equation
$$\frac{4}{5}$$g