What is the formula for variable mass systems and rockets?

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SUMMARY

The formula for variable mass systems and rockets is defined as v = u * ln(M0/M), where v represents the rocket's velocity after time t, M0 is the initial mass, M is the mass after time t, and u is the velocity of the ejected gas relative to the rocket. This equation is crucial for understanding the dynamics of rockets as they lose mass through fuel consumption at a constant rate, described by r = -dM/dt. Mastery of this formula is essential for anyone studying rocket propulsion and variable mass systems.

PREREQUISITES
  • Understanding of basic calculus, specifically integration
  • Familiarity with the concepts of variable mass systems
  • Knowledge of rocket propulsion principles
  • Basic physics of motion and forces
NEXT STEPS
  • Study the derivation of the Tsiolkovsky rocket equation
  • Learn about the principles of conservation of momentum in variable mass systems
  • Explore advanced integration techniques relevant to physics
  • Investigate the effects of thrust-to-weight ratio on rocket performance
USEFUL FOR

Aerospace engineers, physics students, and anyone interested in the mechanics of rocket propulsion and variable mass systems will benefit from this discussion.

UchihaClan13
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Okay guys
I am studying variable mass systems and rockets,as such
I was introduced to the formula v=u*ln M0/M
where v is the velocity of the rocket after a time t
M0is the initial mass of the rocket,M is the mass of the rocket after time t
u is the velocity of the ejected gas w.r.t to the rocket
The mass is being lost(in the form of fuel being used up to propel the rocket and provide it the required upward force) at a constant rate r=-dM/dt
Could any of you guys help me with the derivation of this "useful" equation?
I just started learning integration
Hence i can't figure out the integrand so easily
Thanks in advance!:)
UchihaClan13
 
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UchihaClan13 said:
Could any of you guys help me with the derivation of this "useful" equation?
If you give us a link to a specific derivation and tell us exactly where you get "stuck", someone can probably help you.
 
Okay I will
Thank you:)
 

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