Solve Two Connected Masses for Acceleration

[Juggernaut06]

Homework Statement

Two masses are tied together by a string over a massless pulley so that they can both move vertically. Their masses are 1 kg and 3 kg. What is the acceleration of the 1 kg mass?

Homework Equations

F=ma
W=mg

The Attempt at a Solution

I have the 3 kg mass's summation of forces as ma-T. (In my free body diagram, the 3kg mass is the one closest to the pulley.)

The 1 kg mass's summation of forces are mg-T.

I'm unsure if my diagram is correct and I don't know where to go from here.

 

[tiny-tim]

Welcome to PF!

Hi Juggernaut06 ! Welcome to PF!

Two masses are tied together by a string over a massless pulley so that they can both move vertically. Their masses are 1 kg and 3 kg. What is the acceleration of the 1 kg mass?
…
I have the 3 kg mass's summation of forces as ma-T. (In my free body diagram, the 3kg mass is the one closest to the pulley.)

The 1 kg mass's summation of forces are mg-T.

No, both wrong …

both masses have both a and mg.

And of course a is equal (and opposite) for both.