Finite force, infinite work?
Hey everyone, I was thinking about how work is defined in physics (W = F · d) and had a question about physics in ideal conditions.
- In space (or a perfectly frictionless environment), if you apply a constant force to an object, it should keep accelerating forever, right? Or atleast keep constant velocity
Since there’s no friction or drag, the displacement (d) would increase indefinitely over time.
Does this mean that, given enough time, the work done (W) by that force would actually become infinite?
I think, this makes sense because W = F · d and d → ∞.
- But does infinite work imply infinite energy input? Or is the power (rate of work) what matters?
Is this a valid interpretation, or am I missing something?
Jus sorry if this was already posted before but I was unable to find it.
Comments
Well, it would take infinite time to do infinite work. Also as things get faster (closer to the speed of light), time slows down, so then you need even more time to do the same work.
The key phrase is “given enough time”… it would take an infinite amount of time to do infinite work, which would mean that an infinite amount of energy was input.
Of course, at that point you can no longer use classical kinematic formulas, which break down due to relativistic limits. And there will be a point where special relativity is not enough of a description.
Then there’s the engineering side of the problem. How exactly is one going to apply a force limitlessly to an object?
If by “ideal conditions”, you mean there’s isn’t a limit like the speed of light, yes, in such a place objects could be accelerated indefinitely.
F x d only applies to a distance over which you’re applying the force. No force, no work.