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The discussion revolves around a physics problem involving simple harmonic motion and energy calculations after a collision, specifically where the energy is expressed as mgh/2. The original poster is struggling to formulate the energy equation post-collision and is seeking assistance with the actual calculations. Forum members emphasize the importance of demonstrating prior effort in solving the problem to receive help. They also encourage the use of LaTeX for clarity in presenting equations. Adhering to homework guidelines is crucial for effective assistance.
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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