# Work done as a function of time

Hey guys, can the work done on a body be described as the function of time during which a force acts upon it?

mfb
Mentor
You can do this.
It might be more useful to consider power, but that depends on the setup.

I mean in a situation like where you hold an object against, say, gravity for some time would there be any work done? From what we know, until there is no motion, the work done is zero. But would it be possible to look at this problem from the "time" point of view?
For example you have a mass 'm' being attracted to another mass 'M'. You want to keep 'm' from getting to 'M'. So, say you use a rocket to push 'm', against the direction of its motion. If you manage to stop it and hold it against the gravity of 'M', would any work be done? If yes, work against what?

mfb
Mentor
Power is force times velocity, and power is the derivative of work done. With zero velocity, power is zero and therefore work done does not change.

A rocket has to do work in your setup, but that is used to accelerate its reaction mass.

Reaction mass?

mfb
Mentor
That stuff which gets ejected. In chemical rockets, it is the same as its fuel. In other designs (like ion drives), it can be different.
See this explanation for details.

Thanks. So basically the work done to throw the reaction mass is the work done to hold the 'm' in its place?

mfb
Mentor
Well, it is work done by the rocket to counter some force (here: gravity) - this just shows that rockets are a bad idea if you want to hold something in a fixed distance. A simple connection gives the same result and does not have to do work.