A textbook of mass 1.95 kg rests on a frictionless, horizontal surface. A cord a

Question

A textbook of mass 1.95 kg rests on a frictionless, horizontal surface. A cord attached to the book passes over a pulley whose diameter is 0.100 m , to a hanging book with mass 2.96 kg . The system is released from rest, and the books are observed to move a distance 1.27 m over a time interval of 0.780 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

part a )

x = ut + at^2/2

u = 0

x = 1.27 m

t = 0.780 s

a = 4.175 m/s^2

T1 = m1a1

T1 = 1.95 * 4.175 = 8.14 N

T2 = m2(g-a)

T2 = 16.65 N

part c )

t = rF = (T2-T1)*R

R = 0.100/2

t = I*alpha

alpha = a/R

I = (T2-T1)*R/alpha

I = 5.096 x 10^-3 kg-,m^2

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