Everyone knows kinetic energy is converted to potential energy in the body when it moves up against the earth's opposing gravitational force. But I am facing some problem with this.
What I learnt about Newton's third law of motion and … :
From the answer and comment of my another question written by @Floris, I have learnt that Newton's 3rd law of motion is a direct consequence of law of conservation of energy. When a body moves in a certain direction and an opposing force acts on it , it does exert a reacting force (by Newton's law) on that agent doing positive work on the agent and by law of conservation of energy the agent gains that energy which the moving body spends while doing work on the agent. Hence, the body loses its kinetic energy.
Problem in the case of the body moving up against the earth's gravitational force:
When a body starts moving up from the earth, it immediately faces the opposing gravitational force . So the body will also exert reactive force on the earth,the agent of the gravitational force. Thus using the concept what I have learnt , the body must do work on earth which will eventually make it to lose energy and by the law of conservation of energy,the lost energy will be taken by the agent upon which the body exerts reactive force ie. earth .
But nothing does happen like that. During its ascent,kinetic energy is converted to potential energy which is stored in the body,not in the earth.
I have some loophole in my understanding. But where have I done the mistake? Where is my intuition incorrect? Please clear my confusion.
Best Answer
If I understand you correctly, your mistake is in using friction as an analog to gravity.
Because friction is a non-conservative force the work done is dependent on the path taken. Furthermore the energy "lost" due to friction is stored in a way that is not spontaneously reversible within the system (e.g. heat, plastic deformations, etc.). Gravity on the other hand is conservative so the work done by gravity is not dependent on the path taken, and is dependent only on the distance between the two objects.
To say an object does work on another object is also slightly incorrect because the work is done by a force. In this respect gravity does work on both objects, because the force applies to both of them as understood through Newton's Third Law,and Newton's Law of Gravitation.
Alternatively looking at different reference frames might help. e.g. In an "earth-centric" reference frame I would push off the earth with my feet, and lift the ball relative to the earth with my hand. In a "ball-centric" reference frame I would push off the ball with my hand, and lift the the earth relative to the ball with my feet.