Equilibrium of frame with two masses

[VHAHAHA]

Homework Statement

I need to find the tension T, γ and β in part 2 of this question.
The question is attached.

Homework Equations

First of all, the frame is a right angle triangle because (3L)^2 + (4L)^2 = (5L)^2
take torque about the point O
we got 2LF + mg(4Lcosγ) = Mg(3Lsinγ)
from the balance of force, we got
Tcosβ=(m+M)g + F cos γ
Tsinβ = Fsinγ

The Attempt at a Solution

I have listed these 3 equations but I don't know how to solve them
Please give me some help

 

[tiny-tim]

Hi VHAHAHA!

Hint: if there were only three forces, they would all have to go through the same point.

 

[VHAHAHA]

Hi VHAHAHA!

Hint: if there were only three forces, they would all have to go through the same point.

But i think that there are 4 forces

 

[VHAHAHA]

Do u mean that i have to combine 2 gravitational force into 1 combined force so that there is 3 force?

 

[tiny-tim]

(just got up :zzz:)

Do u mean that i have to combine 2 gravitational force into 1 combined force so that there is 3 force?

Yup!

The two gravitaitonal forces are known, and they're easy to add …

so go for it! ​

 

[VHAHAHA]

the combined g force = (m+M)g
how do go to the same point? i can't see any common point

btw
Why 3 force will meet at a point if it is at eqm.
It there any proof? thanks

 

[tiny-tim]

the combined g force = (m+M)g
how do go to the same point? i can't see any common point

Just use the resultant.

(It goes through the point where you'd have to put the fulcrum if you wanted to balance it)

btw
Why 3 force will meet at a point if it is at eqm.
It there any proof? thanks

Suppose only two forces go through a point …

then, if you take moments about that point, the moments of those two forces will be zero, and the moment of the third force won't!

 

[VHAHAHA]

I don't understand
If we see part 1
T=(M+m)g
but these 3 force don't have the common point
they are parallel

 

[tiny-tim]

… part 1
…
but these 3 force don't have the common point
they are parallel

ah, they have a common point "at infinity"

alternatively, my argument only applied when …

Suppose only two forces go through a point …

… and in part 1, two forces don't go through a point (except "at infinity")!

 

[VHAHAHA]

Thank you.
But i still don't understand
There are 4 forces! How to use this rule in part 2 =