A textbook of mass 2.07 kg rests on a frictionless, horizontal surface. A cord a
ID: 1395637 • Letter: A
Question
A textbook of mass 2.07 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 2.91 kg . The system is released from rest, and the books are observed to move a distance 1.30 m over a time interval of 0.850 s .
A. What is the tension in the part of the cord attached to the textbook?
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 .
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
Given
M1 = mass of the book on the surface = 2.07 kg
M2 = mass of the hanging book = 2.91 kg
R = radius of the pulley = 0.200 m
d = distance fallen = 1.30 m
t = time fallen = 0.850 s
g = acceleration by gravity = 9.81 m/s^2
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acceleration of the system a
s= ut +1/2*a*t^2
d= 1/2*at^2
1.30 = 1/2*a*0.850*0.850
a=3.598 m/sec^2
using netons second law of motion on M1
T1 = M1*a
T1= 2.07*3.598
T1= 7.449 N
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newtons 2nd law of motion on M2
M2*g-T2 = M2*a
M2(g-a) =T2
T2 = 2.91*(9.81-3.598)
T2= 18.07N
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principle of torque on the pulley.
T2
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