Differential Equation and Newtons 2. law

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SUMMARY

The discussion focuses on deriving a differential equation for the movement of an object in a fluid, utilizing Newton's Second Law (F = ma). The force acting against the object is defined as F = -b*e^v, where b is a constant and v represents the object's velocity in m/s. The objective is to separate the variables so that velocity (v) is on one side and time (t) is on the other, allowing for a solution to the differential equation. Participants emphasize the need to equate the resistive force to the mass times acceleration to progress in solving the equation.

PREREQUISITES
  • Understanding of Newton's Second Law (F = ma)
  • Knowledge of differential equations and separable equations
  • Familiarity with exponential functions and their properties
  • Basic concepts of fluid dynamics and resistive forces
NEXT STEPS
  • Study the derivation of differential equations from Newton's Second Law
  • Learn techniques for solving separable differential equations
  • Explore the behavior of exponential functions in physical systems
  • Investigate the effects of resistive forces in fluid dynamics
USEFUL FOR

Students in physics or engineering, mathematicians interested in differential equations, and anyone studying fluid dynamics and motion under resistive forces.

Atilla1982
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In a fluid, there's an exponential force F = -b*e^v working against the direction of movement. B is constant, and v is the objects velocity in m/s.

They want me to use Newtons 2. law to find a differential equation for the movement of an object with mass m. The equation is separable, separate so v is found on one side of the = and t on the other side.

Could anyone please point me in the right direction here?
 
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Atilla1982 said:
In a fluid, there's an exponential force F = -b*e^v working against the direction of movement. B is constant, and v is the objects velocity in m/s.

They want me to use Newtons 2. law to find a differential equation for the movement of an object with mass m. The equation is separable, separate so v is found on one side of the = and t on the other side.

Could anyone please point me in the right direction here?

what's F = ma in terms of a differential equation?

(i take it that we want it in terms of velocity.)

after you get that step, you equate it to that resistive force, and ... there you go.
 

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