Equilibrium of frame with two masses

  • Thread starter VHAHAHA
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  • #1
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
 

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Answers and Replies

  • #2
tiny-tim
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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:
 
  • #3
VHAHAHA
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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:

But i think that there are 4 forces
 
  • #4
VHAHAHA
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Do u mean that i have to combine 2 gravitational force into 1 combined force so that there is 3 force?
 
  • #5
tiny-tim
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(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! :biggrin:

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

so go for it! :wink:
 
  • #6
VHAHAHA
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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
 
  • #7
tiny-tim
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the combined g force = (m+M)g
how do go to the same point? i cant 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:
 
  • #8
VHAHAHA
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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
 
  • #9
tiny-tim
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… 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 …
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
VHAHAHA
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Thank you.
But i still don't understand
There are 4 forces! How to use this rule in part 2 =
 

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