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 14.5 cm and its moment of inertia is 0.43 kg · m2. As the spool turns, friction forces cause a torque of 0.15 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 6.0 m of the ribbon, assuming there is no slippage and the mass of the ribbon is negligible.

Explanation / Answer

Net Torque = I = (0.43)
Hand Torque = 13.0 (0.145) = 1.885 N-m
Resistance to Hand Torque (friction torque) = 0.150 N-m
Net Torque on spool = 1.885 - 0.150 = 1.735 N-m
1.735 = (0.43)
= 4.034 rad/s²
a = R = 4.034 (0.145) = 0.5850 m/s²
d = 1/2at²
6.0 = (0.5)(0.5850)t²
t² = 3.6946
t = 4.528 s ANS

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