"The net work done on an object is equal to its change in kinetic energy."

Let's say that a rocket is moving upwards while expelling gas and is thus losing mass. (Non-constant mass)
As the object loses mass, it gains even more kinetic energy.

Is the work-energy theorem still applicable?


1 Answer 1


I believe the problem lies with how you are stating the work-energy theorem.

Every good reference to it I can find states something along the lines of:

"The work done on a particle is equal to it's change in kinetic energy"

(emphasis mine) The word particle is extremely important here (sometimes they also use "rigid body"). For a single particle or rigid body, it cannot really do much beyond move as a reaction to forces. When you have an object that is made up of multiple interacting particles (such as a rocket ship expelling fuel), you cannot treat it as a rigid body, and so the interactions between work and energy aren't as direct as "work done is the change in kinetic energy" on the macroscopic scale of the spacecraft itself.

Work done can also change potential energy, thermal energy, or electrical energy, depending on how it interacts with the system. In this case, there are changes in the potential energy and thermal energy as a result of the fuel combustion, and this is able to increase the kinetic energy of the parts of the spacecraft we want to increase the kinetic energy of (i.e. the payload). (a bit more elaboration can be found here)


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