Equilibrium of frame with two masses

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Homework Help Overview

The discussion revolves around the equilibrium of a frame with two masses, focusing on the calculation of tension (T), angles (γ and β), and the forces acting on the system. The problem is set within the context of static equilibrium and involves analyzing forces and torques in a right-angle triangle configuration.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the equations of torque and force balance, questioning how to solve for the unknowns. There is exploration of the concept of combining gravitational forces and the implications of having multiple forces acting on the system.

Discussion Status

The conversation is ongoing, with participants providing hints and questioning the assumptions regarding the number of forces and their points of application. Some guidance has been offered regarding the combination of forces, but clarity on the geometric arrangement and equilibrium conditions remains a topic of inquiry.

Contextual Notes

There is a noted confusion regarding the application of equilibrium principles when multiple forces are involved, particularly in relation to their points of concurrency and the concept of forces acting "at infinity." Participants are grappling with the implications of these concepts in the context of the problem.

VHAHAHA
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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
 

Attachments

  • question.png
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Hi VHAHAHA! :smile:

Hint: if there were only three forces, they would all have to go through the same point. :wink:
 
tiny-tim said:
Hi VHAHAHA! :smile:

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

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?
 
(just got up :zzz:)
VHAHAHA said:
Do u mean that i have to combine 2 gravitational force into 1 combined force so that there is 3 force?

Yup! :biggrin:

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

so go for it! :wink:
 
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
 
VHAHAHA said:
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. :smile:

(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! :wink:
 
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
 
VHAHAHA said:
… part 1

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

ah, they have a common point "at infinity" :wink:

alternatively, my argument only applied when …
tiny-tim said:
Suppose only two forces go through a point …

… and in part 1, two forces don't go through a point (except "at infinity")! :smile:
 
  • #10
Thank you.
But i still don't understand
There are 4 forces! How to use this rule in part 2 =
 

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