A textbook of mass 2.09 kg rests on a frictionless, horizontal surface. A cord a

Question

A textbook of mass 2.09 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 3.07 kg. The system is released from rest, and the books are observed to move a distance 1.20 m over a time interval of0.800 s. What is the tension in the part of the cord attached to the textbook? 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/s^2. What is the moment of inertia of the pulley about its rotation axis? Take the free fall acceleration to be g = 9.80 m/s^2.

Explanation / Answer

r = radius of pulley = diameter/2 = 0.18 /2 = 0.09 m

M = mass of pulley =

a)

consider the motion of textbook on horizontal surface

X = displacement = 1.20 m

a = acceleration

t = time of travel = 0.8 sec

Vo = initial velocity = 0 m/s

using the equation

X = Vo t + (0.5) a t2

1.20 = 0 (0.8) + (0.5) a (0.8)2

a = 3.75 m/s2

for textbook on horizontal surface , force equation is given

T1 = m1 a                       

T1 = 2.09 x 3.75

T1 = 7.84 N

b)

for book, force equation is given as

m2g - T2 = m2 a

T2 = m2g - m2 a                  

T2 = (3.07) (9.8 - 3.75)

T2 = 18.6 N

c)

Torque equation for the pulley is given as

T2 - T1 = I a/r2

18.6 - 7.84 = I (3.75)/0.092

I = 0.0232 kgm2

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