A textbook of mass 1.90 kg rests on a frictionless, horizontal surface. A cord a

Question

A textbook of mass 1.90 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 3.00 kg . The system is released from rest, and the books are observed to move a distance 1.22 m over a time interval of 0.830 s .

Part A

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

Part B

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

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

Part C

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

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

Explanation / Answer

Assume the system has uniform linear acceleration (a) with initial vel u = 0
d = ½at² .. .. a = 2d / t² .. (2 x 1.22m) / (0.83s)² .. .. a = 3.54 m/s²

1) For m1 .. Tension is net force = m1 x a .. 1.90kg x 3.54m/s² .. .. T1 = 6.72 N

2) For m2 .. Net force = (m2 x a) = m2g - T2 ..
T2 = m2(g - a) .. 3.00kg(9.80 - 3.54) .. .. .. T2 = 18.78 N

3) Assuming pulley is frictionless ..
Accelerating force applied at rim = T2 - T1 = (18.78 - 6.72)N .. .. F = 12.06 N
Accelerating torque acting on pulley Tq = F x r =12.06N x 0.065m .. .. Tq = 0.7839 Nm

Tq = I .. (angular equiv of F = m x a) (I= mom of inertia, = angular accel in rad/s²)
= a / r = 3.54m/s² / 0.065m .. .. =54.46 rad/s²

I = Tq / = 0.7839 /54.46 .. .. I = 0.01439kg.m²

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