13. -0.02/3 points | Previous AnswersOSColPhys1 10.P.020.WA. Ask Your Teacher My
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13.-0.02/3 points | Previous AnswersOSColPhys1 10.P.020.WA.
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A solid cylinder is mounted above the ground with its axis of rotation oriented horizontally. A rope is wound around the cylinder and its free end is attached to a block of mass 56.0 kg that rests on a platform. The cylinder has a mass of 235 kg and a radius of 0.380 m. Assume that the cylinder can rotate about its axis without any friction and the rope is of negligible mass. The platform is suddenly removed from under the block. The block falls down toward the ground and as it does so, it causes the rope to unwind and the cylinder to rotate.
Question Part Points Submissions UsedExplanation / Answer
a) on block, (Using F = ma)
56g - T = 56a ....(i)
on solid cylinder ,
torque = r x F = I x alpha
I = M R^2 /2 and alpha = (a/R)
RT = ( M R^2 /2 ) (a/R)
T = 235a/2
T = 117.5a ... (ii)
from (i) and (ii)
56g - 117.5a = 56a
a = 3.17 m/s^2
alpha = a/R =3.17 / 0.380 = 8.33 rad/s^2
b) theta = wi * t + alpha *t^2 /2
theta = 0 + 8.33*5^2 /2 = 104.16 rad
revolutions = 104.16 / 2pi = 16.58 rev.
c) L = theta * R = 104.16 x 0.380 = 39.58 m
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