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

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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

2 Answers

Anonymous 0 Comments

The block is being pulled up by the tension and pulled down by gravity. The net force will therefore be their difference, with the sign being the direction the block is moving (positive = up, negative = down)

Anonymous 0 Comments

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.