Why is tension T=m(g-a) and not m(g+a)?

[soljaragz]

There is a problem I am looking at and in its explanations for the answer it says

"...We know the sum of forces acting on m is T-mg which is equal to ma. Therefore, T=m(g-a)..."

um...Shouldn't T=m(g+a)?

 

[Andrew Mason]

There is a problem I am looking at and in its explanations for the answer it says

"...We know the sum of forces acting on m is T-mg which is equal to ma. Therefore, T=m(g-a)..."

um...Shouldn't T=m(g+a)?

Yes, provided the signs of g and a are opposite. This is explicit in T = m(g-a), where g and a are the magnitudes of the vectors $\vec{g} \text{ and } \vec{a}$.

AM

 

[0rthodontist]

Doesn't make sense to me. a should be oriented so that + is in the direction of the tension and - is in the direction of gravity. It shouldn't be an absolute value. Anyway if they want to use it as an absolute value in the second part they should have been doing that in the first part.