Classical Mechanics: linear resistance

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Homework Help Overview

The problem involves a rocket experiencing a linear resistive force, with the goal of deriving an expression for its speed under specific conditions, including mass loss at a constant rate. The subject area is classical mechanics, focusing on dynamics and forces.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the need to integrate the governing equation and question the implications of mass changing over time. There is uncertainty about the origin of specific terms in the derived expression.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem and the necessary steps to take. Some guidance has been offered regarding the need for integration and the relationship between mass and time, but no consensus has been reached on the next steps.

Contextual Notes

There is a noted lack of clarity regarding the integration process and the derivation of specific terms in the final expression. Participants are also grappling with the implications of the rocket's mass changing over time.

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Homework Statement


Consider a rocket subject to a linear resistive force, f= -bv but no other external forces. Using the equation mv'= -m'*vext+Fext show that if the rocket starts from rest and efects mass at a constant rate k= -m' then its speed is given by v=(k/b)vex[1-(m/m0)^b/k]

The Attempt at a Solution


so i thought maybe I was suppose to integrate both sides of the equation
mv'= -m'*vext+Fext, but then i really didn't know where to go from there. Any help?
 
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I think your missing piece of information is to realize that the mass of the rocket depends on time:

[tex]m(t) = m_0 - kt[/tex]
 
Do I not need to integrate then? I just don't know where the power of b/k comes from.
 
You still need to integrate, but the integral is different.
 
I still can't get this one to work out. Am I still missing information? I tried starting with the equation mv'= -m'*vext+Fext. I solved for v'. and then substituted in the equation m0-kt. But then I didn't know where to go from there.
 
help, I'm still stuck, can anyone help me?
 

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