Consider an object which has been given a speed $v$ on a rough horizontal surface. As time passes, the object covers a distance $l$ until it stops because of friction. Now,
Initial kinetic energy = $\frac{1}2mv^2$
And final kinetic energy is zero. Therefore, work done by friction on the object is equal in magnitude to $\frac{1}2mv^2$.
Now here is the part that I found weird: Consider another frame moving with a speed $v_0$ in the same direction with respect to the ground frame. Now, kinetic energy of the original object with respect to this new frame is $\frac{1}2m(v-v_0)^2$.
And, the final kinetic energy is equal to $\frac{1}2mv_0^2$.
So this means that the work done by frictional force, in this case, will have a magnitude of $\frac{1}2m[(v-v_0)^2-v_0^2]$, which is obviously different from the value which we get with respect to a stationary frame.
And this part seems very unintuitive to me. How is it possible for the same force to do different amounts of work in two different inertial frames? (I would consider it unintuitive even if we consider non inertial frames, after considering pseudo forces).
And if we were to do more calculations based on the two values of the work done by friction, we would land on different values of some quantities which aren't supposed to be different in any frame. For example, the coefficient of friction would be different, as the amount of frictional force is constant, acting over a distance $l$. We can say that Work done by frictional force is $\alpha$$mgl$, where $\alpha$ is the coefficient of friction and $g$ is the acceleration due to gravity. We can clearly see that $\alpha$$mgl$ equals two different values.
So, is this just how physics works, or is there something wrong here?