A large 16.0-kg roll of paper with radius R = 18.0 c m rests against the wall an

Question

A large 16.0-kg roll of paper with radius R=18.0cm rests against the wall and is held in place by a bracket attached to a rod through the center of the roll . The rod turns without friction in the bracket, and the moment of inertia of the paper and rod about the axis is 0.260kg?m2. The other end of the bracket is attached by a frictionless hinge to the wall such that the bracket makes an angle of 30.0? with the wall. The weight of the bracket is negligible. The coefficient of kinetic friction between the paper and the wall is ?k=0.25. A constant vertical force

Explanation / Answer

F on rod cos theta=u x F normal + F frictional + W
F on rod sin theta= F normal
set the two equations equal to each other and solve for F normal

a)
F on rod = W + F frictional / cos theta - u x sine theta=((16 kg * 9.8) + 40 N)/ (cos(30) - (0.25*sin(30))))= 266 N

b)

? = (40 * 0.18 - 0.18 * 266 * sin(30) *.25) / .260 = 4.67 rad/sec^2

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