Determine the acceleration of the hanging masses of M and 2M in an Atwood’s machine. Mass of the pulley is 3M
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Determine the acceleration of the hanging masses of M and 2M in an Atwood’s machine. Mass of the pulley is 3M

[From: ] [author: ] [Date: 11-12-25] [Hit: ]
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Determine the acceleration of the hanging masses of M and 2M in an Atwood’s machine.
Mass of the pulley is 3M and I =3 M r²/2

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Difference in mass = 2M-M = M
Mg is the force causing the masses (M+ 2M) to move with acceleration a and to give an angular acceleration α to the pulley of mass m such that α = a / r
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If T is the net tension on the pulley Tr = I α
T = I a / r² and substituting for I =3 M r²/2
T =3 M a /2
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Hence Mg = (M a+2M a +T) or
Mg = (M +2M +3M/2) a

a =2 g / 9= 2.2 m/s²
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http://en.wikipedia.org/wiki/Atwood_mach…

a = g*(m2 - m1)/(m1 + m2 + I/r^2)

I'll leave the rest of it up to you.
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