Does work depend on a point of reference?

Question

Imagine there is me, Earth and some other guy. Me and a guy move parallel to each other at the speed of 1000m/s relative to Earth.

I am so fit that my mass is 0.5kg, so when a force of 1N in the direction of my movement acts on me for 1s, I accelerate to 1002m/s and in that time I travel 1001m (all relative to Earth).

The work is force multiplied by displacement, so 1N*1001m=1001J

But from the guys perspective I was still, and after the force I moved just 1m relative to him.

And here the work is just 1N*1m=1J.

So is it that the work depends on the reference point, or the work is the difference between displacement and displacement if there was no force?

Work depends on the frame of reference. See https://physics.stackexchange.com/q/353187/195949 — Claudio Saspinski, Sep 18 '23 at 22:52
I still don't understand. How much work was done in my example? And in the car and bench example, is there even any work from the sitting in the car point of view? If the object is already moving very fast, then any little force applied would do insane work, that just doesn't seem right. — Богдан Красновид, Sep 19 '23 at 00:28
Does this answer your question? If motion relative to a frame of reference is purely relative, how do we account for the work done to move relative to the frame of reference? — Dale, Sep 19 '23 at 01:29
This might help - How is energy "stored in an electric field"? — mmesser314, Sep 19 '23 at 01:55

score 0 · Answer 1 · answered Sep 19 '23 at 00:49

I am so fit that my mass is 0.5kg, so when a force of 1N in the direction of my movement acts on me for 1s, I accelerate to 1002m/s and in that time I travel 1001m (all relative to Earth).

All this 1001m displacement does not come due to the application of the external force. Most of it would have happened even without the need for a force (as the body already has prior some velocity).

Work done can be seen as the change in energy of the object (in this case, kinetic energy). Assuming that the mass on which the force is being acted is the same in both frames (more on this below), the change in kinetic energy is just proportional to the change in the velocities. The latter will be the same for both observers in Newtonian physics.

However, in relativity, this problem of acceleration is more complex. Here, the mass of the object (not the rest mass), as well as the time for which the force acts, would be perceived differently by the two different frames of reference. Nevertheless, the net work done should result in the same value owing to the conservation of total energy.

Does work depend on a point of reference?

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