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 15.0 cm and its moment of inertia is 0.51 kg · m2. As the spool turns, friction forces cause a torque of 0.21 N · m to act on it. The spool is initially at rest. The service person pulls on the spool with a constant tension of 9.5 N. Determine the time it takes to unwind 7.5 m of the ribbon, assuming there is no slippage and the mass of the ribbon is negligible.
s

Explanation / Answer

apply Torque Formula T = r X F

T = 9.5 * 0.15 = 1.425 N m

net Torque T = T -Tfric = 1.425 - 0.21 = 1.215 Nm

also Torque T = I A

I is moment of inertia and A is angualr accleration

so A = 1.215/(0.51) = 2.38 rad/s^2

use theta = x/r = 7.5/0.15 = 50 rad

use the kinemtic eqn in rotationa motion as

Theta = wo t + 0 A t^2

t^2 = 2 theta/A

t^2 = 2* 50/2.38

t = 6.48 secs

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