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A rope with length $L$ and mass density per unit length $ρ$ is suspended vertically from one end. Find the tension as a function of height along the rope

I just don’t understand the way the functions have been used in the solution of the question (this from Morin’s classical mechanics book)

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    $\begingroup$ Welcome to Physics Stack Exchange! If you could be a little more precise about what you're having trouble understanding(...the way functions have been used... is not very clear), it would be easier to provide an answer. $\endgroup$
    – python128
    Commented 2 days ago
  • $\begingroup$ You should explain which functions you do not understand. The key insight in the solution is probably that the tension at each point along the rope must be sufficient to support the weight of the rope below that point. $\endgroup$
    – gandalf61
    Commented 2 days ago
  • $\begingroup$ You might find this Veritasium video helpful - I Rented A Helicopter To Settle A Physics Debate... $\endgroup$
    – mmesser314
    Commented 2 days ago

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