0 1 points OSColPhys2016 10 5WA052 Tutorial. y Notes Ask Your Teacher A customer

Question

0 1 points OSColPhys2016 10 5WA052 Tutorial. y Notes Ask Your Teacher 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 the spool is 16.0 cm and its moment of inertia is 0.35 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 14.5 N. Determine the time it takes, in seconds, to unwind 5.0 m of the ribbon, assuming there is no slippage and the mass of the ribbon is negligible. Additional Materials Reading Tutorial

Explanation / Answer

Given,

L = 13.7 m ; R = 16 cm ; I = 0.35 kg-m^2 ; Tau = 0.13 N-m ; T = 14.5 N ; l = 5 m

We know that

Tau = I alpha = F r

Tau' = 14.5 N x 0.16 = 2.32 Nm

Tau-net = 2.32 - 0.13 = 2.19 N-m

alpha = 2.19/0.35 = 6.26 rad/s^2

a = R alpha = 6.26 x 0.16 = 1.002 m/s^2

from eqn of motion

S = ut + 1/2 at^2

5 = 0.5 x 1.002 t^2

t = sqrt (9.984) = 3.16 s

Hence, t = 3.16 s

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