Equilibrium under the action of concurrent forces

[jimmyly]

Homework Statement

Hello all, I just finished a question on equilibrium. I wish I could upload a diagram or something but I don't know how to get it from my Microsoft oneNote to here. But basically there is a mass held In equilibrium by two ropes. on the left is mass 2 and on the right is mass 3. mass 3 = 200N...0.....0
.../\50°.|.30°/\
.../...\...|.../...\
...m2...\...|.../.. m3(200n)
...\.../
....V
...m1

Homework Equations

ƩF = 0

The Attempt at a Solution

I have solved everything and got everything correct. But that isn't the problem
what I did was I got the Y-components and X components

so here is my question
Fx2 - Fx3 = 0 ------> these are the x-components and I know the sum must be zero to be in equilibrium.( my question applies to y-component as well)
why is it that we must Subtract the two?

is it because they are in opposite directions? i.e. <----(-)----0------(+)------->
or is it because weight cannot be negative? cause if I add them together I get - Newtons

Thanks for the help!

 

[ehild]

The net force on m1 has to be zero in equilibrium. That is valid for both the x and y components. If F2x and F3x are the x components of the forces exerted by the ropes, F2x+F3x=0. But these forces are opposite, and their magnitude is equal to the tension multiplied by the cosine of the given angle. The tension itself is positive. So F2x=-T2 sin(50°) and F3x=T3 sin(30°)

_{To upload picture, go to "go advanced" "manage attachment" "browse" and "upload"}

ehild

 

[jimmyly]

aahhhh makes sense now. thanks a lot!