# Calculating Free Body Diagram Forces

• B
On EngineersEdge.com they have a free body diagram of a scissor lift

https://www.engineersedge.com/mechanics_machines/scissor-lift.htm

Can anyone explain how the Fy, Fx components are determined? What is specifically confusing to me is how Fy is opposite in direction given the system.

To me it would make sense that those could just as easily be swapped and the choice is arbitrary.

Merlin3189
Homework Helper
Gold Member
The calculation follows to determine Fy etc.

But if you mean, how did they decide what direction to draw the Fy arrows on the FBD, then I would say it is an arbitrary decision.
You know that w acts downwards (at A and D) and that Rx acts inwards (at B and C, in the first setup), from your understanding of the operation of the device.
But you may not have a clear idea of which way Fy and Fx are acting at E. So you just have a guess and mark them in. If you are right, then they work out to be positive. If you are wrong, they work out negative, meaning they actually point in the opposite direction.
That's why you have to be clear in your calculations to add and subtract forces strictly according to the direction you've marked on the diagram. You'll notice that in the calculations, they mark the direction in which they are summing forces. So, for eg., w initially appears as -w, because they are summing forces upwards and w points downward.

sophiecentaur
Gold Member
2020 Award
So you just have a guess and mark them in. If you are right, then they work out to be positive. If you are wrong, they work out negative, meaning they actually point in the opposite direction.
I don't think you want to imply a 'quality judgement' here. It's not a matter of right or wrong but a totally arbitrary choice of initial direction and the resulting sign of the answer. It might even be a good idea to decide that you would always choose the F to be in a positive x or y direction and that would take away any possibility of getting mixed up on the way through the calculations. In the context of displacement, we usually choose 'up and to the right' for our axes. The obvious exception to this is the dropped object problem where we tend to choose down as the y axis with a positive g but that, in itself, often causes sign confusion.

Merlin3189
Homework Helper
Gold Member
Absolutely agree with Sophie. I wondered about using that way of saying it, but didn't worry enough about possible misunderstanding.

Okay, this makes perfect sense now.

So in very simple terms the middle joint has forces that cancel out, hence the Fy in opposite directions because it does not move. It is supporting forces in both directions and therefore must sum to 0 net force.

Thank you!