A textbook of mass 1.94 kg rests on a frictionless, horizontal surface. A cord a

Question

A textbook of mass 1.94 kg rests on a frictionless, horizontal surface. A cord attached to the book passes over a pulley whose diameter is 0.200 m , to a hanging book with mass 3.09 kg . The system is released from rest, and the books are observed to move a distance 1.13 m over a time interval of 0.840 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

x = (1/2)at^2
acceleration = (2.26 m)/(0.840 s)^2 = 3.2029 m/s^2

(a) T = (1.94 kg)(3.2029 m/s^2) = 6.2137 N

(b) T = (3.09 kg)(9.8 m/s^2 - 3.2029 m/s^2) = 20.385 N

(c) The unbalanced force on the pulley is 14.172 N,
applied at 0.1 meter from its center, so the torque is 1.4172 Nm, and it brings about an angular acceleration of
(3.2029 m/s^2)/(0.1 m) = 32.029 rad/s^2;
hence

the moment of inertia is
torque/alpha = 0.04424 g*m^2.

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