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So recently I get my question closed. While it is entirely up to the community to decide whether a question is on topic or not, I got really confused by the feedback:

Homework-like questions and check-my-work questions are considered off-topic here, particularly when asking about specific computations instead of underlying physics concepts.

I followed the two links and here is what I found for the definition of homework-like questions:

A "homework question" is any question whose value lies in helping you understand the method by which the question can be solved, rather than getting the answer itself.

Yet I failed to see why my question is a homework like question, as otherwise the underlying method would be a general solution of a generic type of question, with my question be a specific case. However I don't think the underlying method can be generalized, as $L=T-V$ is already a generic case, and trying to generalize the method to prove that $L=4T-\sqrt{3}V$ is proper is just pure nonsense.

Also I don't think the question is remotely similar to a check-my-work question, and I got quite confused for my question to be closed for this reason. I have thought that maybe it would be closed for being to broad, or as a duplicate, yet homework close reason was a surprise for me.

My question So would anyone explain why my question is homework-like or check-my-work, and how can I improve it and avoid making future mistakes?

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    $\begingroup$ Note: the question got three "homework-like" close votes, and two "duplicate" close votes. $\endgroup$
    – rob Mod
    May 10, 2020 at 20:53
  • $\begingroup$ @rob Note: I've been on this site for years and contributed many answers, and I find the homework close reason not only confusing but blatantly self-contradicting. See this post. $\endgroup$
    – DanielSank
    Aug 28, 2020 at 15:09

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I don’t understand your question. BTW there may have been multiple close reasons and the system takes the one with the more votes (I think), and I may have voted to close because it was unclear.

From your question:

How can this proof be generalized to a multiple-object system, considering the forces between those objects are conservative?

Why can’t you take $T$ to be the total kinetic energy and $V$ to be the total potential energy? That and simply repeating the steps of your question will yield (basically) $f=ma$, albeit in component form and in a possible sub-efficient coordinate system. That’s what textbooks and homework questions require you to do.

Moreover, your question is now linked to this question and near-duplicate of it so it could also have collected close votes as a duplicate.

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  • $\begingroup$ err... Why doing so won't work is explained in edit 1. $\endgroup$
    – user12986714
    May 10, 2020 at 16:44
  • $\begingroup$ so the potential is a function $V(q_1,q_2)$. So what else? Just take the appropriate partials. We must be talking at cross purposes here... $\endgroup$
    – ZeroTheHero
    May 10, 2020 at 17:25

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