I don't understand conceptually how something accelerating down weighs less. For example, the elevator example of course if you have something with a string and a weight and the acceleration of the elevator increases upward as positive, you get
T - mg - ma = 0
and for acceleration down, you get
T - mg + ma = 0
This to me doesnt make sense, because shouldnt the equations be switched around because ma is + going up and - going down??