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

Question

A textbook of mass 1.91 kg rests on a frictionless, horizontal surface. A cord attached to the book passes over a pulley whose diameter is 0.130 m, to a hanging book with mass 2.90 kg . The system is released from rest, and the books are observed to move a distance 1.11 m over a time interval of 0.820s.

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

Put M_1=1.91 kg , d=0.130 m , m_2 = 2.90 kg , s = 1.11m , delta t =0.820s

First the acceleration of the system comes from s = 1/2*a*(?t)^2

so a = 2*s/(?t)^2

Now summing forces about M_1 we have T1 = M_1*a = M_1*2*s/(?t)^2

2. Now summing about m_2 we get m_2*g - T2 = m_2*a

so T2 = m_2*(g - 2*s/(?)^2)

3. Now summing torques about the pulley we get (T2 - T1)*d/2 = I*? but ? = a/d/2

so (T2 - T1)*d/2 = I*2*s/(?t)^2/(d/2)

So I = (T2 - T1)*(d/2)^2*(?t)^2/2 = (T2 - T1)*d^2/8*(?t)^2

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