A textbook of mass 2.03 kg rests on a frictionless, horizontal surface. A cord a

Question

A textbook of mass 2.03 kg rests on a frictionless, horizontal surface. A cord attached to the book passes over a pulley whose diameter is 0.180 m , to a hanging book with mass 2.99 kg . The system is released from rest, and the books are observed to move a distance 1.23 m over a time interval of 0.850 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

1.

using d = ut + at^2 /2

1.23 = 0 + a(0.850^2)/2

a= 3.40 m/s^2

from newton's 2nd law ( F =ma) on textbook,

T1 = ma = 2.03 x 3.40

T1 = 6.91 N

2. ) now in book,

F = mg - T2 = ma

2.99x9.80 - T2 = 2.99 x3.40

T2 = 19.12 N

3) on pulley,

torque =I x alpha

r(T2 - T1) = I ( a/r)

0.180 ( 19.12 - 6.91) = I ( 3.40 / 0.180)

I = 0.116 kg m^2

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