Rod in equilibrium, and find its angle to the vertical plane

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To analyze a rod in equilibrium, begin by creating a free body diagram to visualize the forces acting on the rod. Identify the forces such as gravity, tension, and any applied forces, ensuring to represent their directions accurately. Apply the conditions for equilibrium, which state that the sum of forces and the sum of moments must equal zero. Use trigonometric relationships to determine the angle of the rod with respect to the vertical plane. This systematic approach will lead to finding the rod's angle effectively.
jmao15
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Homework Statement
The diagram shows a uniform rod AB resting in the angle between a vertical plane and a plane inclined at 60° to the vertical. Find the angle theta if: (a) both planes are smooth, (b) the inclined plane is smooth but the vertical plane is rough, A is on the point of slipping down and μ =0.5
Relevant Equations
Lami's theorem??
Literally, don't know how to start.
IMG_20210530_172134.jpg
 
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jmao15 said:
Literally, don't know how to start.
Always start with a free body (force) diagram.
 
Thread 'Chain falling out of a horizontal tube onto a table'

Thread 'Chain falling out of a horizontal tube onto a table'

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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