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I performed a thought experiment.

Consider a body $A$ and another body $B$.

Body $B$ is moving at velocity $v$ in direction $x$ with respect to $A$. This implies that body $A$ is moving at velocity $v$ in direction $-x$ with respect to $B$.

If work is done on body $B$, its velocity increases to $(v+dv)$ with respect to $A$ but the direction does not change.

Now, $B$ is moving in direction $x$ with velocity $(v+dv)$ with respect to A and A is moving with velocity $(v+dv)$ in direction $-x$ with respect to $B$.

$B$ says that work is done on $A$ whereas $A$ says that work is done on $B$.

This means that even workdone is relative. Is my reasoning correct?

Edit:- I am making this question more general. Since velocity is relative, does this mean that quantities arising from it like force, kinetic energy/workdone, momentum, acceleration, magnetic effects due to the movement of charges etc. relative?

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    $\begingroup$ Yes, energy ("workdone") is relative, not only in special relativity but also in classical Newtonian mechanics $\endgroup$
    – user341440
    Commented Apr 22, 2023 at 18:11

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This means that even workdone is relative. Is my reasoning correct?

Yes, work is relative. That means that in order to correctly specify the work you must clearly identify the reference frame.

does this mean that quantities arising from it like force, kinetic energy/workdone, momentum, acceleration, magnetic effects due to the movement of charges etc. relative?

Most quantities that depend on velocity are indeed relative for the same reason. This includes KE, momentum, speed, etc.

There are some quantities that are a little more difficult. For instance, force and acceleration are relative to the reference frame in relativistic physics. But in Newtonian physics they are the same in all inertial frame. So sometimes the answer depends on the physical theory you are using.

Other quantities, like action or proper time, depend on velocity, but in a specific combination with other quantities that makes them not relative

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    $\begingroup$ Isn't that what I was saying yesterday? Today you got it right. In the meantime I was thinking about how to do this right in terms of teaching. Maybe we should introduce the concept of the momentum vector and the energy-momentum vector sooner into the high school curriculum. I think this might illustrate the reference frame dependence of kinetic energy better than the usual way of keeping velocity and energy separate. $\endgroup$
    – FlatterMann
    Commented Apr 23, 2023 at 3:29
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    $\begingroup$ @FlatterMann if you want to have a conversation then please post to physicsforums.com Your argument is incorrect today and yesterday $\endgroup$
    – Dale
    Commented Apr 23, 2023 at 3:34
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    $\begingroup$ @FlatterMann why did you bother to comment here then? Your comments are wrong both yesterday and today. It is a bit frustrating to me because most of your posts are reasonable, but not only are you clearly wrong on this I have provided the math showing it to you. I think you should pursue this, but you need a different venue than PSE comments $\endgroup$
    – Dale
    Commented Apr 23, 2023 at 3:43
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    $\begingroup$ @FlatterMann maybe. I think that one of the challenges with Galilean relativity is that we teach it with displacement and velocity vectors and not forces, momenta, work, energy, power, acceleration, etc. We just stop too early $\endgroup$
    – Dale
    Commented Apr 23, 2023 at 3:51
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    $\begingroup$ I think we are in full agreement on that. I am glad I am not the only person who thinks that. $\endgroup$
    – FlatterMann
    Commented Apr 23, 2023 at 4:06
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Work done = force*distance. Force is not relative because it can be measured using a device such as spring balace. Whatever this device registers is agreed upon by all reference frames. You can always determine in which frame the force was applied by checking where spring balance registered a non-zero value. This way you can tell where the work was done.

However, you can't determine where the work was done just by looking at velocities because they're relative, so is kinetic energy.

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