A textbook of mass 2.08kg rests on a frictionless, horizontal surface. A cord at

Question

A textbook of mass 2.08kg 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 3.10kg . The system is released from rest, and the books are observed to move a distance 1.27m over a time interval of 0.850s

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?
Take the free fall acceleration to be g = 9.80m/s2

What is the moment of inertia of the pulley about its rotation axis?
Take the free fall acceleration to be g = 9.80m/s2 .

Explanation / Answer

x = (1/2)at^2
acceleration = (22.54 m)/(0.850 s)^2 = 3.515 m/s^2

(a) T = (2.08 kg)(3.515 m/s^2) = 7.3112 N
(retaining lots of digits until part c)

(b) T = (3.10 kg)(9.8 m/s^2 - 3.515 m/s^2) = 19.4835 N
(retaining lots of digits until part c)

(c) The unbalanced force on the pulley is 12.123N,
applied at 0.1 meter from its center, so the torque is 1.2123 Nm, and it brings about an angular acceleration of
(3.515 m/s^2)/(0.1 m) = 35.15 rad/s^2;
hence the moment of inertia is
torque/alpha = 0.03449 kg*m^2.
round to 0.0345 kg*m^2

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