- #1

getty102

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## Homework Statement

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?

## Homework Equations

Ʃtorque=(I)([itex]\alpha[/itex])

ƩF=ma

## The Attempt at a Solution

I found the tension due to the mass of the pack on the pulley.

T

_{ps}=m

_{p}(g-a

_{t})

p=pack, a

_{t}=linear acceleration of pack

I then summed the torques, and inserted the tension due to the pack on the pulley

R(T

_{yr})-r(m

_{p}(g-a

_{t}))=I(a

_{t}/R)

solved for a

_{t}=[R(T

_{yr})-r(m

_{p}*g)]/[(I/R)-(r*m

_{p})]

my final a

_{t}=24.233 m/s/s which is not right