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Question 19N.3.SL.TZ0.5c(ii)

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Date November 2019 Marks available [Maximum mark: 3] Reference code 19N.3.SL.TZ0.5c(ii)
Level SL Paper 3 Time zone TZ0
Command term Calculate Question number c(ii) Adapted from N/A
c(ii).
[Maximum mark: 3]
19N.3.SL.TZ0.5c(ii)

A flywheel is made of a solid disk with a mass M of 5.00 kg mounted on a small radial axle. The mass of the axle is negligible. The radius R of the disk is 6.00 cm and the radius r of the axle is 1.20 cm.

A string of negligible thickness is wound around the axle. The string is pulled by an electric motor that exerts a vertical tension force T on the flywheel. The diagram shows the forces acting on the flywheel. W is the weight and N is the normal reaction force from the support of the flywheel.

The moment of inertia of the flywheel about the axis is I=12MR2.

At t = 5.00 s the string becomes fully unwound and it disconnects from the flywheel. The flywheel remains spinning around the axle.

(c(ii))

At t = 5.00 s the flywheel is spinning with angular velocity 200 rad s–1. The support bearings exert a constant frictional torque on the axle. The flywheel comes to rest after 8.00 × 103 revolutions. Calculate the magnitude of the frictional torque exerted on the flywheel.

[3]

Markscheme

ALTERNATIVE 1

0=2002+2×α×2π×8000 ✔

α=«-»0.398 «rad s-2» ✔

torque = αI=0.398×0.5×5.00×0.0602=3.58×10-3 «N m» ✔

 

ALTERNATIVE 2

change in kinetic energy =«-»0.5×0.5×5.00×0.0602×2002=«-»180 «J» ✔

identifies work done = change in KE ✔

torque = Wθ=1802π×8000=3.58×10-3 «N m»✔

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