# Equilibrium of frame with two masses

## 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

#### Attachments

• 24.1 KB Views: 298

Related Introductory Physics Homework Help News on Phys.org
tiny-tim
Homework Helper
Hi VHAHAHA! Hint: if there were only three forces, they would all have to go through the same point. 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

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

tiny-tim
Homework Helper
(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! the combined g force = (m+M)g
how do go to the same point? i cant 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
Homework Helper
the combined g force = (m+M)g
how do go to the same point? i cant 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! 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
Homework Helper
… 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")! Thank you.
But i still don't understand
There are 4 forces! How to use this rule in part 2 =