- #1
songoku
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- 401
- Homework Statement
- Please see below
- Relevant Equations
- Equilibrium
Thanks
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The discussion centers on understanding the correct vector diagram of forces acting on a hinge in static equilibrium. The force on the hinge has both horizontal and vertical components, with the horizontal component directed to the right to balance tension. The vertical component can be either upward or downward, but clarification is sought on why it should be downward in this scenario. The importance of considering resultant torque at different pivot points is emphasized for accurate analysis. The conversation also touches on the implications of replacing the hinge with a slider, which would require an external downward force to maintain equilibrium.
Thanks
- #2
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Hint: What are the conditions for static equilibrium of such an object?
- #3
songoku
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I get the hint. I need to consider resultant torque at different pivot.robphy said:
Thank you very much for the help robphy
- #4
Lnewqban
Homework Helper
Gold Member
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If you replace that hinge with a slider, which is free to move up and down that wall, an external down force would be needed to counteract the moment that W induces about the point of connection of the cable to the trapdoor.
My attempt:
Initial total M.E = PE of hanging part + PE of part of chain in the tube. I've considered the table as to be at zero of PE.
PE of hanging part = ##\frac{1}{2} \frac{m}{l}gh^{2}##.
PE of part in the tube = ##\frac{m}{l}(l - h)gh##.
Final ME = ##\frac{1}{2}\frac{m}{l}gh^{2}## + ##\frac{1}{2}\frac{m}{l}hv^{2}##.
Since Initial ME = Final ME. Therefore, ##\frac{1}{2}\frac{m}{l}hv^{2}## = ##\frac{m}{l}(l-h)gh##. Solving this gives: ## v = \sqrt{2g(l-h)}##. But the answer in the book...
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