What is the Terminal Velocity with Linear Drag?

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SUMMARY

The discussion centers on determining the terminal velocity of an object moving horizontally through a liquid under the influence of a linear drag force represented by F = -cv. The equation m(dv/dt) = -cv is derived, leading to the expression vf = v0 * e^(-ct/m). However, the participant questions the physical interpretation of this result, noting that as time approaches infinity, vf approaches zero, which contradicts the expected behavior of terminal velocity. The confusion arises from a misunderstanding of the limit process in the context of drag forces.

PREREQUISITES
  • Understanding of Newton's Second Law (F=ma)
  • Familiarity with linear drag force concepts
  • Basic knowledge of differential equations
  • Experience with exponential decay functions
NEXT STEPS
  • Study the derivation of terminal velocity in fluid dynamics
  • Learn about the effects of different drag coefficients on motion
  • Explore the concept of limits in calculus, particularly in physical contexts
  • Investigate the behavior of objects under varying initial velocities in drag scenarios
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Students in physics, engineers working with fluid dynamics, and anyone interested in the mathematical modeling of motion through fluids.

PsychonautQQ
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Homework Statement


An object moves through a liquid horizontally against a linear drag force given by F = -cv
What is the terminal velocity? Initial Velocity is V_0


Homework Equations


F=ma


The Attempt at a Solution



m(dv/dt) = -cv
-->
(dv/v) = (-c/m)dt
ln(vf/v0) = -ct/m
vf=v0*e^(-ct/m)

which says that as time goes to infinity that vf will equal v0 but that doesn't make any sense physically... what did I do wrong here?
 
Physics news on Phys.org
Take the limit incorrectly? ##V_f## approaches 0 as ##t \to \infty##, no?
 
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