I’m still in school so this might sound like a bit of a stupid question. I know that work done = force x distance, so if I were to apply a force to an object in an environment where it would not be opposed by any other forces (such as space), the distance travelled would theoretically be infinite. Would this mean that the work done is also infinite? At what point do we stop measuring the distance travelled?

In: Physics

Work is only being done while a force is still being applied to the object. Even though the object may travel forever, you stop putting a force after the initial push and the work being done drops to 0 at that point. The total work done would only be the product of the force applied times the distance it was applied over. Once you let go, work stops being done.

Work done is the force multiplied by the distance **over which the force is applied**.

If you push something for 1meter and are applying 1N of force to it, then the work done was 1 Joule, whether or not the object comes to a rest or continues indefinitely doesn’t matter to the amount of work you have done on it.

The distance is also important, if you have a force which is always at a right angle to the direction of motion (e.g in a circular orbit, force is always at 90 degrees to the direction of motion) then the work done will be 0.

You measure the distance that you applied force over, not the distance traveled. If you only push the object for a meter, then let go, the distance is 1 meter, even if the object slides off to infinity once you let go.