why is m*a in m*a=T-W treated as negative?

Question

lets say a block is being pulled up by a rope with a constant acceleration a. When we write the net forces equation we get Sum in y direction = T-W where T and W are the tension in the rope and the weight of the block. Then going further, the Sum in the y direction becomes mass \* acceleration. if the acceleration vector is upward then why is the mass \* acceleration treated as opposite from the tension T even if they are on the same side of the block, both in the positive y direction?

In: Physics

Answer 1

I’d say they’re not.
T – W = ma so the tension is assumed positive (upward) and the acceleration is also positive (upward).

Nitpick, you can either write T – W and then just put 9.81m (or 32.2m) for the weight, or you can say T + W and then insert the negative yourself to recognize that gravity is oriented downward. Both ways work.