A textbook of mass 1.92 kg rests on a frictionless, horizontal surface. A cord a

Question

A textbook of mass 1.92 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 2.94 kg. The system is released from rest, and the books are observed to move a distance 1.29 m over a time interval of 0.820 s.

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

2. 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.

3. 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 velocity u = 0

d = at^2/2

a = 2d/t^2 = 2*1.29/0.82^2 = 3.84 m/s^2

1]  For m1,

Tension is net force = m1*a

= 1.92*3.84 = 7.37 N

2]  For m2,

Net force = m2*a = m2g - T2

T2 = m2*(g-a)

= 2.94*(9.8 - 3.84) = 17.52 N

3]  Assuming pulley is frictionless

Accelerating force applied at rim = T2 - T1 = (17.52 - 7.37) = 10.15 N = F

Accelerating torque acting on pulley Tq = F * r = 10.15*0.1 = 1.015 N/m

Tq = I*a'

where, a' is angular acceleration

I moment of inertia

a' = a/r = 3.84/0.1 = 38.4 rad/s^2

I = Tq/a = 1.015/38.4 = 0.026 kg m^2 answer

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