Tensions with 3 blocks on a single pulley

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PAstudent
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Homework Statement



The diagram shows two blocks, each of mass m, connected by cord A, and the top block of mass m connected to the block of mass M by cord B. Both cords are of negligible mass. Cord B passes over a frictionless peg that is fixed in place. The system of blocks and cords is released from rest from the position shown, and because 2m<M, block M descends under constant acceleration the distance h in a time T. Derive, in terms of m, M, h, T, and the acceleration due of gravity g, expressions for the tensions in the cords A and B during that time T
Diagram of a frictionless pulley with cord B over it, block M on the right side and a hanging stack of two blocks labelled m on the left, joined by cord A, with height h marked below block M.
[/B]


Handwritten free-body diagrams for three blocks: top block with upward tension F_TA and weight mg, middle block with upward F_TB and downward mg, and block M with upward F_TB and downward Mg, with Newton's second law equations beneath each.

Homework Equations

The Attempt at a Solution


The picture shows my work. And I was wondering if I drew the FBD correctly and my equations were correct[/B]
 
(1) In your FBD for mass 2, you left out the tension from the cord below it.
(2) When writing your equations, take care to use a consistent sign convention for the acceleration.
 
PAstudent said:
So tension A= m(a+g)
And
Tension B= M(g-a)
Those are correct.