Equilibrium with the string in the center exactly horizontal

[Mcmenhweilleisi]

Homework Statement

Find
Tension T1
Tension T2
Tension T3

Relevant Equations

Obtain on the left weigs 40N and on the right 50N

 

[PeroK]

For homework help you have to show us your best attempt at solving the problem yourself. See the guidelines:

https://www.physicsforums.com/threads/homework-help-guidelines-for-students-and-helpers.686781/

 

[Delta2]

A few things to get you started:

Consider the piece of string in the middle and apply the equilibrium conditions for it. So it will be
$$\sum F_x=0$$$$\sum F_y=0$$ $$\sum M=0$$
So you will have 3 equations and 3 unknowns ($T_1,T_{3x} , T_{3y}$. You can find angle by $\tan\theta=\frac{T_{3x}}{T_{3y}}$.

I think that $T_2$ will be equal to $T_{3x}$ or ($T_{1x}$ ) not very sure about this.

 

[Frabjous]

Shouldn’t you just sum the forces on each side of the second string. 4 eqs and 4 unknowns (T1, T2, T3, θ). I have no idea what a moment means for a string

 

[kuruman]

Shouldn’t you just sum the forces on each side of the second string. 4 eqs and 4 unknowns (T1, T2, T3, θ). I have no idea what a moment means for a string

Actually, the 4 equations are decoupled. One can find T₁ and T₂ from the FBD of the knot on the left and then find the rest from the FBD of the knot on the right.

@Mcmenhweilleisi : Please show us your work to get more help.

 

[Delta2]

Shouldn’t you just sum the forces on each side of the second string. 4 eqs and 4 unknowns (T1, T2, T3, θ). I have no idea what a moment means for a string

Well you apply the moment equation as the string was some sort of rigid body (since it is taut).

I think the two ways are equivalent, because the way I see the moment equation it is essentially a force balance equation e.g $$T_{3y}l-50l=0$$ where l the length of the second string.

 

[haruspex]

I think the two ways are equivalent

Quite so.
We have one set of forces acting at one knot, and another set at the other knot.
Writing that the resultant of one set has no moment about the other knot is the same as writing that that resultant has no component normal to the string.