In the Atwood\'s Machine shown in t he adjacent Figure the masses of the blocks
ID: 2178478 • Letter: I
Question
In the Atwood's Machine shown in t he adjacent Figure the masses of the blocks are m1 = 3.0 kg and m2 = 2.0 kg. The moment of inertia of the frictionless about its axis is lc =0.60 kg.m2 and its radius is Rc = 0.20 m. There is no shipping between the rope and the pulley. Find the acceleration of the blocks and the angular acceleration of the pulley after the system is released from rest. (Include the free-body diagrams for the pulley and the two masses) Find the tension (T1 and T2) in the rope on both sides of the pulley Find the angular velocity of the pulley at t = 4.0 s. Through what angle did the pulley turn between t = 0 and t = 4.0 s? Express your result in revolutions. Express first your answers in parts and in terms of any or all of the variables m1, m2, Ic, Rc and (acceleration due to gravity), and then their numerical values.Explanation / Answer
m1g - T1 = m1a
(T1- T2)R = I
T2- m2g = m2a
m1g - m2g = (m1+m2)a + I
a = R
a = (m1-m2)g/(m1+m2+I/R)
(3-2)/(3+2+0.6/.2) = 0.125 M/S^2
=a/R = 0.125/0.2 = 0.625 rad/s^2
T1 = m1g-m1a = 3(9.8-0.125) = 29.025 N
T2 = m2(g+a) = 2(9.8+0.125) = 19.85N
W2 = W1 + t
w2 = 0 + 0.625*4
= 2.5 rad/sec
= w1t+0.5*t^2
= 0 + 0.5*0.625*4^2
= 5 rad
6.28 rad = 1 rev
5 rad = 0.796 rev