A textbook of mass 2.03 kg rests on a frictionless, horizontal surface. A cord a

Question

A textbook of mass 2.03 kg rests on a frictionless, horizontal surface. A cord attached to the book passes over a pulley whose diameter is 0.150 m , to a hanging book with mass 2.95 kg . The system is released from rest, and the books are observed to move a distance 1.24 m over a time interval of 0.780 s . What is the tension in the part of the cord attached to the textbook? What is the tension in the part of the cord attached to the book? What is the moment of inertia of the pulley about its rotation axis?

Explanation / Answer

Using the equation of motion,

s = ut + 0.5*at^2

where s = distance moved = 1.24 m

t = 0.78 s

u = initial velocity = 0

So, 1.24 = 0 + 0.5*a*0.78^2

So, a = 4.08 m/s2

So, So, tension in the part of the cord attached to textbook, T1 = m1*a = 2.03*4.08 = 8.28 N

Tension in the part of the crod attached to the book, T2 = m2*(g-a) = 2.95*(9.8 - 4.08) = 16.9 N

Moment of inertia of the pulley = (T2 - T1)*R^2/a = (16.9-8.28)*(0.15/2)^2/4.08 = 0.0119 kg.m2

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