# Work Energy Theorem for Variable Mass Systems

by MuIotaTau
Tags: energy, mass, systems, theorem, variable, work
 P: 82 How do we know that the work-energy theorem holds for variable mass systems? Or rather, since I'm sure that we can at least know it to be true experimentally, what is the mathematical basis for the work-energy theorem? I know for fixed mass systems, a rather simple derivation comes from integration Newton's second law over an infinitesimal displacement, but I've never seen any sort of derivation of the relationship for variable mass systems, only the assumption that it holds. So purely out of curiosity, does any such demonstration exist?
 PF Gold P: 953 Could you please give an example of a 'variable mass system'?
 P: 82 The stereotypical examples that come to mind are a rocket, or perhaps a moving traincar leaking water.
 Sci Advisor HW Helper PF Gold P: 12,016 Work Energy Theorem for Variable Mass Systems Well, you can set up an equation for the energy flux, obviously, where the rates of work (i.e power transferred) on the system combined with the rate by which energy leaves the system bymeans of energy carrying material will equal the rate of change of the kinetic energy in the system.
 PF Gold P: 953 Thank you for this clarification. The work-energy theorem will apply to all the particles in the system, provided that you enlarge your system to include not just the particles in the rocket or the train car, but those that have left it (exhaust gases, leaked water). I suspect this is too general a remark to be of much use. I'll try and come up with something more specific, but let's hope someone else supplies what you want sooner than I will.

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