How Does a Double-Pulley Modified Atwood Machine Work?

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The discussion focuses on the mechanics of a double-pulley modified Atwood machine, specifically analyzing the forces acting on two masses, m1 and m2. It establishes that the total forces acting on both masses are zero, indicating a state of equilibrium. The tension in the string is uniform, leading to the conclusion that for mass m1, the upward force is 2T, while for mass m2, it is T. This analysis assumes no friction and neglects the mass of the pulleys and connecting components.

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1. For the modified Atwood machine of this problem, assume that the two masses do move. Also assume that there is no friction, and that gravity is the only force acting. Also assume that you can ignore the mass of the pulleys and of the connecting rod and string. Notice that mass m1 is rigidly attached to the smaller pulley.
Do this problem in 3 stages, by answering the following questions.

1. The total force acting on mass m1 and that acting on mass m2 areboth zero TF
2. in the same direction TF
3. equal in magnitude TFhttp://b.imagehost.org/0304/lerner3_53.gif
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3. my guess is that since the tension force is the same everywhere on this massless string, then the total force acting on mass m1 and m2 should be both zero... but its known whether the pulleys are in motion or not so...
 
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Look 2 chords are pulling up on the mass m1 and only one on the mass m2

So for mass m1 it becomes 2T up and m1g down and for other T up and m2g down
 

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