An Atwood\'s machine consists of two masses, m A and m B , which are connected b

Question

An Atwood's machine consists of two masses, mA and mB, which are connected by a massless inelastic cord that passes over a pulley, see the figure. If the pulley has radius R and moment of inertia Iabout its axle, determine the acceleration (a) of the masses mA and mB, and compare to the situation in which the moment of inertia of the pulley is ignored (a0). [Hint: The tensions FTA and FTB are not necessarily equal. We discussed the Atwood machine in Example 4-13, assuming I = 0 for the pulley.] (Use m_1 for mA, m_2 for mB, R_0 for R0, and g and I as appropriate.)

Explanation / Answer

here net clockwise moment as +ve and anti clockwise moenmts as -ve

let A be the accleration of both the bodies

then

Ta - Ma g =   Ma A

and

(Tb-Ta) = AI/R

so

then

Accleration A = Ta/Ma   -g

for B:

A = (Tb-Ta) /Mb

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