- #1
Jason Ko
- 21
- 6
- TL;DR
- I found this theorem in D. Morin's book on mechanics. How to prove it mathematically? Does it have a name?
The direction of three forces acting on a line has to be concurrent?
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Discussion Overview
The discussion revolves around the conditions for equilibrium in a system subjected to three forces, specifically whether the lines of action of these forces must be concurrent. The focus appears to be on theoretical implications and proofs related to this concept.
Discussion Character
- Debate/contested
Main Points Raised
- One participant asserts that if the third line of action of a force does not intersect the point where the other two lines cross, a net torque is created, indicating that the system cannot be in equilibrium.
- Another participant expresses a sense of realization about their previous misunderstanding, suggesting a reconsideration of their stance.
- A further reply indicates that there may be a "simple" proof in the textbook that supports the initial claim about the concurrency of force lines, although this proof has not been read by some participants.
- Another participant expresses agreement with a specific viewpoint, referencing Morin, which may imply support for the idea that the lines of action must be concurrent.
Areas of Agreement / Disagreement
Participants do not appear to reach a consensus, as there are differing interpretations of the conditions for equilibrium and references to proofs that have not been universally acknowledged or read.
Contextual Notes
Some assumptions regarding the definitions of equilibrium and torque may be implicit in the discussion. The reference to a textbook proof suggests that there may be additional context or limitations not fully explored in the thread.
- #2
- 22,823
- 14,863
Take the point of crossing of two of the force lines of action. If the third line of action does not pass through that crossing, there is a net torque and therefore this cannot happen for a system in equilibrium.
- #3
Jason Ko
- 21
- 6
Thanks! I was being stupid
- #4
- 15,894
- 9,061
Probably you didn't read the "simple" proof provided below the statement that you highlighted in the textbook.Jason Ko said:
- #5
- 22,823
- 14,863
Nor I. Good thing I agree with Morin though …kuruman said:
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