3) An ood\'s machine consists of two masses (2.0 kg and 4. kg) connected by a ma

Question

3) An ood's machine consists of two masses (2.0 kg and 4. kg) connected by a massless inelastic cord that passes over the top of a ey. (The two masses hang vertically.) The pulley is a uniform disc of radius 4.0 cm and mass of 1.0 kg. Assume the pulley is bject to friction from a motionless finger that is touching the surface of the pulley. Initially the heavier mass has a downward speed of 0.2 m/s. It comes to rest in 2.0 seconds. What is the magnitude of the torque on the pulley, about its axis of rotation, from the frictional force of the finger, during those 2.0 seconds?

Explanation / Answer

given
m = 2 kg
M = 4 kg

Mp = 1 kg
r = 4 cm

vi = 0.2 m/s
t = 2 s
vf = 0 m/s

so deceleration = -a
hence
vf= vi - at
a = 0.2/2 = 0.1 m/s/s

now let the torque be T
tension in the ropes bve T1 and T2

then from force balance
T1 - Mg = Ma
T1 = 39.64 N
mg - T2 = ma
T2 = 19.42 N

from torque balance
(T1 - T2)*r - T = 0.5*Mp*r*a
T = 0.8068 Nm

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