Mastering Equation Solving: m(dv/dt)=mg-bvn | Step-by-Step Guide

  • Context: High School 
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Discussion Overview

The discussion revolves around the equation m(dv/dt) = mg - bvn, exploring its meaning, implications, and potential corrections. Participants analyze the equation in the context of differential equations, forces acting on a falling body, and dimensional consistency.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant presents the equation m(dv/dt) = mg - bvn and seeks clarification on its meaning.
  • Another participant suggests a possible correction to the equation, proposing m(dv/dt) = -mg - bvn instead, questioning the original formulation.
  • A third participant interprets the equation as a differential equation and raises concerns about dimensional consistency, speculating on the meanings of the symbols involved.
  • Another participant identifies the equation as related to a falling body with a resistance force modeled as bv^n.
  • One participant introduces a different equation, dx/dt = 1 - axn, suggesting that the original equation may have additional complexities that are not fully understood.

Areas of Agreement / Disagreement

Participants express differing interpretations of the original equation, with no consensus reached on its correctness or meaning. Multiple competing views remain regarding the formulation and implications of the equation.

Contextual Notes

There are unresolved questions about the assumptions behind the symbols used in the equation, as well as concerns regarding dimensional analysis and the relationship between the proposed equations.

Opressor
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Member warned that homework posts must show some effort and be posted in a HW section
m (dv / dt) = mg-bvn
 
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Opressor said:
m(d2v/dt2)=-mg-bvn
This equation doesn't make sense if the symbols have their usual meanings. Did you mean m(dv/dt)=-mg-bvn ?
 
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What does it represent? It is a differential equation (second derivative of velocity?) equals -(mass)(gravity?) - (some number b) times (velocity?)^n
If I am even close, it does not look like the dimensions match.
 
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is the equation of a falling body having as resistance force bv ^ n
 
It looks like you are asking about solutions to dx/dt = 1 - axn? For a and n = constants you can just integrate it, so I guess there is more to your equation than we understand?
 
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