A customer service person in a department store is wrapping packages for custome

Question

A customer service person in a department store is wrapping packages for customers. The ribbon spool she uses has 13.7 m of ribbon wound on it. The radius of the spool is 15.5 cm and its moment of inertia is 0.47 kg · m2. As the spool turns, friction forces cause a torque of 0.13 N · m to act on it. The spool is initially at rest. The service person pulls on the spool with a constant tension of 13.0 N. Determine the time it takes to unwind 5.0 m of the ribbon, assuming there is no slippage and the mass of the ribbon is negligible.

Explanation / Answer

5m of ribbon = r * theta is the net anngular distance by thespool

Net torque = I(alpha)

so 13* ( 0.155) - 0.13 = ( 0.47) * (alpha)

So alpha = 4.01 rad / s^2

5 / 0.155 = ( 1/2) ( 4.01 ) * t^2

t = 4.011 seconds

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