A textbook of mass 2.10 rests on a frictionless, horizontal surface. A cord atta

Question

A textbook of mass 2.10 rests on a frictionless, horizontal surface. A cord attached to the book passes over a pulley whose diameter is 0.180 , to a hanging book with mass 2.92 . The system is released from rest, and the books are observed to move a distance 1.29 over a time interval of 0.760 . the rension of the part of he cord attached to the textbook is 9.38 N, and the tension in the part of the cord attached to the book 15.6 N. please find the mmoent of inertia of the pulley about its rotation axis?

Explanation / Answer

Assume the system has uniform linear acceleration (a) with initial vel u = 0 d = ½at² .. .. a = 2d / t² .. (2 x 1.29m) / (0.76s)² .. .. a = 4.47 m/s² 1) For m1 .. Tension is net force = m1 x a .. 2.1kg x 4.47m/s² .. .. ?T1 = 9.387 N 2) For m2 .. Net force = (m2 x a)? = m2g? - T2? .. T2 = m2(g - a) .. 2.92kg(9.80 - 4.47) .. .. .. ?T2 = 15.56 N 3) Assuming pulley is frictionless .. Accelerating force applied at rim = T2 - T1 = (15.56 - 9.387)N .. .. F = 6.1766 N Accelerating torque acting on pulley Tq = F x r = 6.1766N x 0.09m .. .. Tq = 0.555 Nm Tq = I a .. (angular equiv of F = m x a) (I= mom of inertia, a= angular accel in rad/s²) a = a / r = 4.47m/s² / 0.09m .. .. a = 49.66 rad/s² I = Tq / a = 0.555 / 49.66 .. .. ?I = 0.0111 kg.m²

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