A wheel is mounted on frictionless bearings on a horizontal shaft through its ce

Question

A wheel is mounted on frictionless bearings on a horizontal shaft through its center. The moment of inertia of the wheel is 4.0 kg-m2, and its radius is 0.50 meters. A cord is wrapped around the rim of the wheel, and a steady pull of 40 N is exerted on the cord, as shown below (a) What is the angular acceleration of the wheel? (b) Show that the work done in unwinding 5.0 meters of cord equals the gain in kinetic energy of the wheel up to that point. (c) If a mass having a weight W-40N hangs from the cord, as shown below, compute the angular acceleration of the wheel. (d) Why is the answer to part (c) not the same as in part (a)?

Explanation / Answer

(A) r F = I alpha

0.50 x 40 = (4) alpha

alpha = 5 rad/s^2

(B) Work done = F.d = 40 x 5 = 200 J

wf^2 - w0^2 = 2 alpha theta

w^2 - 0 = 2 (5)(5/0.5)

w^2 = 100

KE = I w^2 / 2 = 4 x 100/2 = 200 J

(C) W - T = m a

40 - T = 4 a

and 0.5 T = 4(a/0.5)

T = 16 a

a = 2 m/s^2

alpha = a / r = 4 rad/s^2

(D) Now work done will be same but Kinetic energy will divide into kE of mass and KE of pulley.

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