Unusual difficult kinetic problem

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The discussion revolves around solving a complex kinetic problem related to a rocket's mass and momentum. The initial mass is denoted as M, and after using qm energy, the mass changes to M-m. Participants suggest using an integral form of energy balance, specifically the equation ∫ m(t) v d v = qm, but express uncertainty about how to begin. The conversation emphasizes the importance of considering the exhaust gases and applying conservation of momentum to derive a differential equation. This approach aims to clarify the relationship between the changing mass of the rocket and its momentum.
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Homework Statement


http://img80.imageshack.us/img80/1797/20799357.png

Homework Equations


General kinetics formulas

The Attempt at a Solution


Actually I don't know how to start. The initial mass is M when qm energy is used the mass is M-m. If I use an energy balance I must use the integral version, right?

\int m(t) v \mbox{d}v = qm

But I don't know how to start.
 
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I myself have never done this before, but I will try to help you. I think my way should get the required formula.

Consider the exhaust gases (a small amount 'dm') at time 't'.

Initial momentum pt= dm*ve

Final momentum pt+dt = dm(vR-ve)

Rocket:

pt=(M-dm)vR
pt+dt= (M-dm)(vR-ve).

Now use conservation of momentum here: Loss in change of momentum in gas = change momentum gained by rocket

Using this, you should now be able to get a differential equation to solve (remember, 'dm' is infinitesimally small)
 

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