A textbook of mass 1.91kg rests on a frictionless, horizontal surface. A cord at

Question

A textbook of mass 1.91kg rests on a frictionless, horizontal surface. A cord attached to the book passes over a pulley whose diameter is 0.200m , to a hanging book with mass 3.06kg . The system is released from rest, and the books are observed to move a distance 1.15m over a time interval of 0.770s .

a) What is the tension in the part of the cord attached to the textbook?

b) What is the tension in the part of the cord attached to the book?

Take the free fall acceleration to be g = 9.80m/s^2 .

c) What is the moment of inertia of the pulley about its rotation axis?

Take the free fall acceleration to be g = 9.80m/s^2 .

Explanation / Answer

y = vo*t + 0.5*a*t^2

a = 2y/t^2

a = (2*1.15)/(0.77*0.77) = 3.879 m/s^2

a) T1 = m1*a = 1.91*3.879 = 7.40889 N

b) T2 = m2*g - m2*a = m2*(g-a)

T2 = 3.06*(9.9-3.879)

T2 = 18.42426 N

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c) (T2 - T1)*R = I*alfa = I*a/R

I = (T2-T1)*R^2/a

I = ((18.42426-7.40889)*0.1*0.1)/3.879

I = 0.0283 kg m^2

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