Atwood\'s machine, shown below, consists of a cord around a pulley of rotational
ID: 1446215 • Letter: A
Question
Atwood's machine, shown below, consists of a cord around a pulley of rotational inertia I, radius R, and mass M, with two block (masses m_1 and m_2) hanging from the ends of the cord. Assume the pulley is free to turn without friction and that the cord does not slip. Ignore air resistance. The masses are released from rest and mass m_2 rises while mass m_1 falls Assuming that the cord does not slip as it passes around the pulley, what is the relationship between the angular acceleration of the pulley (alpha) and the magnitude of the linear acceleration of the blocks (a)? (Use any variable or symbol stated above as necessary.) What is the net torque on the pulley about its axis of rotation in terms of the tensions T_1 and T_2 in the left and right sides of the cord? (Use any variable or symbol stated above as necessary.)Explanation / Answer
a)use the reltaion,
a = R*alfa
==> alfa/a = 1/R
b)
from figure, T1 = m1*g - m1*a
T2 = m2*g + m2*a
net Torque acting, T = T1*R - T2*R
= (m1*g - m1*a)*R - (m2*g + m2*a)*R
= (m1-m2)*g*R - (m1+m2)*a*R
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