Question Concerning F=ma and FBDs.

[lawtonfogle]

Ok, I know that, using a FBD, one is susposed to use $$\sum F = m a$$
My question is what order do you put the forces that $$\sum F$$ equal
An example might help me explain my question.
Lets take a block of wood that is supported by a string. The only forces acting on it are $$mg$$ and $$T$$
So...
$$\sum F = ma$$
$$T - mg = ma$$
or
$$mg - T = ma$$.
I know if $$a = 0$$ it does not matter, but how does one decide what order to put th forces in when there is acleration?

 

[lawtonfogle]

The $$\sigma$$ should be a capital sigma.I fixed it.

 

[Päällikkö]

It depends on how you choose the positive and negative directions.
T - mg = ma₁, you've chosen the positive direction upwards.
mg - T = ma₂, you've chosen the positive direction downwards.

T - mg = ma₁ = -(mg - T) = -ma₂

In the case that mg is greater than T, the acceleration's negative when you've chosed the positive direction upwards, and positive when you've chosen the positive direction downwards. The magnitude does not change.

 

[lawtonfogle]

So on an Atwood machine, I should chose it so that both masses are the same way written (both T - mg, or vice versa), or so that the greater force is first.