please solve the part C question A textbook of mass 1.95 kg rests on a frictionl

Question

please solve the part C 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 0.120 m , to a hanging book with mass 3.02 kg. The system is released from rest, and the books are observed to move a distance 1.21 m over a time interval of 0.810 s . 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/s^2. Significant Figures Feedback: Your answer 18.4 N was either rounded differently or used a different number of significant figures than required for this pa item, keep all the digits and round as the final step before submitting your answer. Part C What is the moment of inertia of the pulley about its rotation axis? Take the free fall acceleration to beg= 9.80 m/s^2

Explanation / Answer

For textbook T1 = m1*a.......(1)

for book m2*g - T2 = m2*a

initial speed is u = 0 m/s

distance travelled is s= 1.21 m

time taken is t = 0.81 S

apply S = 0.5*a*t^2

a = S/(0.5*t^2) = 1.21/(0.5*0.81^2) = 3.68 m/s^2

then T1 = 1.95*3.68 = 7.19 N

T2 = m2(g-a)

T2 =3.02*(9.81-3.68) = 18.5 N

net torque is T = (T2-T1)*(diameter/2) = (18.5-7.19)*(0.12/2) = 0.6786 N-m

T = I*alpha

alpha is angular accelaration = a/R = 3.68/0.06 = 61.3 rad/s^2

moment of inertia is I = T/alpha = 0.6786/61.3 = 0.01107 kg*m^2

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