a large 17 kg roll of paper with radius r=19cm rests against the wall and is hel

Question

a large 17 kg roll of paper with radius r=19cm 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 0.27 kg/m2. the other end of the bracket is attached by a frictionless hinge to the wall such that the bracket makes an angle 30 degrees with the wall the weight of the bracket is negliable. the coefficient of kinetic friction between the paper and the wall is 0.25. a constant vertical force f=50 is applied to the paper, and the paper unrolls.

a. what is the magnitude of the force that the rod exerts on the paper as it unrolls.

b. what is the magnitude of the angular acceleration of the roll

Explanation / Answer

a)

N =(F+mg)/(cos30-uk*sin30)

N =(50+17*9.8)/(cos30-0.25*sin30)

N=292.3 N

b)

fk=uk*N1*sin30=292.3*0.25*sin30

fk=36.54 N

a =R(F-fk)/I =0.19(50-36.54)/0.27

a=9.47 rad/s^2

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