# Equilibrium under the action of concurrent forces

1. Feb 21, 2013

### jimmyly

1. The problem statement, all variables and given/known data
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
2. Relevant equations
ƩF = 0

3. 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!

2. Feb 21, 2013

### 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°)

ehild

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• ###### threemass.JPG
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3. Feb 22, 2013

### jimmyly

aahhhh makes sense now. thanks a lot!