mechanical power in moving coordinate system

Question

Suppose I have an object resting on top of a table. There are two forces acting on the object: gravitational pull and the supporting force from the table. It is pretty obvious, that the table is doing no work, because the supporting force has no displacement. However, in a moving coordinate system the point where the force acts actually has displacement, therefore the table does work on the object. Now a table obviously cannot transfer energy by itself. My question is how do I determine the actual work done by the table, on what basis do I differentiate between the resting and moving coordinate system to calculate the work being done?

The question arose when I was taking an escalator and moving up the stairs. Assuming that I'm moving with the same relative velocity compared to the escalator do I need to invest the same amount of power as if the escalator was stationary?

Answer 1

Thank you for asking this question.

Yes, the displacement with a stationary coordinate is different from the displacement with a moving coordinate. And the works done are different.

In your case, the net force (i.e. gravity + reaction force) is zero. So the net work is zero with whatever displacements you may have.

What about if you let an object free fall where there is only gravity force and you observe it with a stationary coordinate and with a moving coordinate? The works done by gravity force are different with two different coordinates as the displacements are different. So the energy changes are different. In this example, the kinetic energy changes will be different. Because the mass is constant, the velocity changes are different. This is fine because with a moving coordinate, the two velocities should be different.

Now, there arises a question, if we can convert the energy to heat, is that we can get more or less energy on a moving coordinate system. This is a relativity question. For example, an object sitting on the earth surface next to you. To you, this object have zero kinetic energy and you can not get any energy from it. But if you sit on an astroid moving fast passing this object sitting on the earth, this object has a significant kinetic energy.