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
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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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
-------------------------
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
==================
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.
a = g*(m2 - m1)/(m1 + m2 + I/r^2)
I'll leave the rest of it up to you.