Setting up Newton's 2nd law for a two-mass pulley system

[I'm Awesome]

I have a problem which reads:

A frictionless pulley with zero mass is attached to the ceiling, in a gravity field of 9.81 m/s2 . Mass M2 = 0.10 kg is observed to be accelerating downward at 1.3 m/s2

and I have a solution which tells me to solve the problem use Newton's 2nd law:

m1a1 = T1 - m1g

m2a2 = T2 - m2g

We also have an acceleration (constraint/constant??) a1 = a2 = a, and by Newton's 3rd law, T1 = T2

=> m1 (a+g) = m2 (g-a) => m1 = [(g - a)/(g + a)]m2

and then from this we just plug in numbers.My question is, how do we arrive to the conclusion of creating this equation? I'm really confused about how to actually set up the equation. Also is a1 and a2 the same acceleration just in opposite directions?

 

[Dale]

how do we arrive to the conclusion of creating this equation?

Just draw the free body diagram for each mass. Everything else follows from those and the constraints you mentioned.

 

[Doc Al]

Also is a1 and a2 the same acceleration just in opposite directions?

Yes. The acceleration constraint should be a1 = - a2. Let "a" be the magnitude of that acceleration.