Equation Q: Ma=T-W & Ma=W-T | Tension Differences

[charlie_luna]

i have a couple of examples i am working through and i only need to know the differences between 2 equations. this deals with tension. one equation is ma=t-w and the other is almost the same, ma=w-t. my instructor uses both of these but why would you use t-w and then use w-t? one of the examples is a weight being lowered with a rope and the other is using 2 weights one each side of a pulley.

 

[Doc Al]

one equation is ma=t-w and the other is almost the same, ma=w-t. my instructor uses both of these but why would you use t-w and then use w-t?

Both are just examples of applying Newton's 2nd law. Often folks like to use "a" to represent the magnitude of the acceleration. Thus if the acceleration is upward, it's +a; if downward, -a. That leads to two versions of the final equation:

For acceleration upward:
ΣF = T - W = ma

For acceleration downward:
ΣF = T - W = m(-a)
or:
W - T = ma

Don't memorize these results; instead, understand how they come about.

 

[Archosaur]

I've never seen these equations before, but I'm going to guess that they are Mass*Acceleration=tension-weight (and weight-tension) correct?

Your instructor is not treating t and w as vectors.
He is subtracting their magnitudes only.
the eq he uses and the final direction of the net force depends on which is bigger (t or w).
He switches eqs so you always end up with a positive number.

He's undoubtedly doing it because he's not sure you know how to add vectors.
If you know how to add vectors, definitely do it that way, because his method only works when the forces are in opposite directions.

This is just another example of teachers cutting corners and teaching stuff that you will have to unlearn later. It drives me crazy.

Your intuition is correct.

F=ma

F is the net force; the sum of all the force vectors.

Your instructor is not teaching you a shortcut, he is sabotaging your education.

...Sorry. It really irks me.