Galactic Dynamic Homework （Problem 2.1 of B&T)

Thread starter Chamarel Elna
Start date Feb 25, 2023
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Dynamic Homework

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The condition "limρr^5/2=0" is crucial for preventing infinities in potential energy (PE) calculations within the context of Galactic Dynamics. This requirement is stricter than merely avoiding infinities in mass, ensuring a more stable mathematical framework. By imposing this condition, it helps maintain the physical realism of the model being analyzed. Understanding its usefulness aids in accurately modeling gravitational interactions in astrophysical systems. Overall, this condition is essential for achieving meaningful results in the study of galactic dynamics.

Feb 25, 2023

Chamarel Elna

Thread moved from the technical forums to the schoolwork forums

TL;DR Summary: Why the topic give the condition "limρr^5/2=0“？What is the usefulness of this condition？ Thanks!

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Feb 25, 2023

Frabjous

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You are trying to prevent infinities from popping up in the PE. This is more strict than trying to prevent infinities from popping up in the mass.

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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