Force components of two strings tied to a painting at 45 degree angles

[Mr Davis 97]

Homework Statement

Find the equation of the horizontal components of two strings tied to a painting at 45 degree angles with the horizontal.

Homework Equations

F_net = 0

The Attempt at a Solution

Since the painting is in equilibrium, I found that, in the horizontal direction, F_net = 0 = S_1x - S_2x, where S_1x S_2x are the horizontal components of the force by the strings. What I don't understand is why S_1x = S_2x. This naturally follows as a result, but aren't these two quantities equal and opposite, since they have the same magnitude but are in opposing directions? Shouldn't it be S_1x = -S_2x?

 

[haruspex]

Find the equation of the horizontal components of two strings tied to a painting at 45 degree angles with the horizontal.

The set up is not at all clear. Is the painting at 45 degrees or the strings? Where are the strings attached to the painting? Etc.

 

[PhanthomJay]

Homework Statement

Find the equation of the horizontal components of two strings tied to a painting at 45 degree angles with the horizontal.

Homework Equations

F_net = 0


What I don't understand is why S_1x = S_2x. This naturally follows as a result, but aren't these two quantities equal and opposite, since they have the same magnitude but are in opposing directions? Shouldn't it be S_1x = -S_2x?

you assumed that one comp acts left and the other right. The fact that s1= s2 means means you assumed the correct directions, provided, however, that each comp pulls away from the picture, not toward it. Plus and minus signs get very tricky.