# Homework Help: Two radii pulley lifting a pack

1. Mar 3, 2012

### getty102

1. The problem statement, all variables and given/known data

You are pulling on a rope attached to the outer radius of a pulley with a moment of inertia I=676 kgm2 as shown. The tension in the rope that you are pulling is 477.9 N. A pack of mass 30.8 kg is attached to the pulley's inner radius as shown. If the inner radius of the pulley is 0.56 m and the outer radius is 0.8 m, what is the magnitude of the linear acceleration of the pack?

2. Relevant equations

Ʃtorque=(I)($\alpha$)
ƩF=ma

3. The attempt at a solution

I found the tension due to the mass of the pack on the pulley.
Tps=mp(g-at)
p=pack, at=linear acceleration of pack

I then summed the torques, and inserted the tension due to the pack on the pulley
R(Tyr)-r(mp(g-at))=I(at/R)

solved for at=[R(Tyr)-r(mp*g)]/[(I/R)-(r*mp)]

my final at=24.233 m/s/s which is not right

2. Mar 3, 2012

### Staff: Mentor

You might want to check your expression for Tps. Make sure that the implied forces result in an acceleration in the desired direction for the pack.