# Meaning of kinetic energy and non-contact forces

My textbook gives the following physical interpretation for kinetic energy:

The kinetic energy of a particle is equal to the total work that particle can do in the process of being brought to rest.

This makes perfect sense to me if the only forces involved are contact forces, as in order to bring a body to rest, work equal to the negative of its present kinetic energy has to be done on it.

From Newton's 3rd law , each force acting on that body will have a reaction force, which corresponds to said body doing work on the other object(s), and the displacement is the same.

However, imagine now an apple strapped to some sort of propulsion system, which perfectly counteracts gravity such that the apple is floating above the earth with $$0$$ velocity (unsure about reference frame here). It follows that the apple's kinetic energy is $$0$$ as well.

Now, does the apple not exert a gravitational force on the Earth as well?

This means that the apple is doing work on the Earth (assuming the apple is the only body interacting with the Earth), as it moves slightly, even though $$K = 0$$, which contradicts the interpretation given at the beginning (as the possible work done by the apple should be 0 according to it). Therefore I ask, does it only apply to contact forces?

Now, does the apple not exert a gravitational force on the Earth as well?

Yes it does.

This means that the apple is doing work on the Earth (assuming the apple is the only body interacting with the Earth), as it moves slightly, even though K=0

First, an important issue is that force is not energy. I can push against a wall with all my strenght; as long as I do not move it I have added no energy at all. Another exemple is if I were to do push-ups; during the exercise I do exert a lot of force (at least by my standards) but after I am done and lay on the ground, I have the same (kinetic and potential) energy that I would have had if I had done no push-ups.

In any case, the important factor you are missing here is the chemical energy that you are constantly spending in order to fuel your rocket to raise your apple and keep it over the ground.

• I know that force alone isn't energy, but if the apple were the only body exerting a force on the Earth, meaning the Earth accelerates, there's a displacement, and thus work is done by the apple.
– user332598
Commented Apr 10, 2022 at 8:57
• Yes. In fact one proposed method for deflecting dangerous asteroids would involve putting a massive rocket near an asteroid. But the answer to your question is "chemical energy". Commented Apr 10, 2022 at 9:10
• So the apple is doing work even though its kinetic energy is 0, right? But the interpretation I gave says K is equal to the work the body can do in the process of being brought to rest, which should be 0 in this case (as K = 0), yet it does work regardless. Isn't this a contradiction?
– user332598
Commented Apr 10, 2022 at 9:12
• Why this obsession with K? There are lots of other types of energy. Since there is a gravitatory field from the apple, the Earth has a potential energy in relation to that field. That is the energy that would push it towards the apple. In the same way that the potential energy of the apple in Earth's gravitatory field is what accelerates it towards Earth. Commented Apr 10, 2022 at 9:17
• I understand all of that, I'm just confused about the physical interpretation I gave, as it seems to contradict the fact that the apple is able to do work without having any kinetic energy.
– user332598
Commented Apr 10, 2022 at 9:22