I'm trying to grasp basic concepts of energy and I have a question regarding conservation of energy.
According to Feynman's book and Wikipedia, the law of conservation of energy states that isolated physical systems (physical systems with no resulting force being exerted on them, only internal forces) have their energy conserved.
But then I picture some object at some point above the surface of earth (disregarding air resistance). It is clearly not an isolated physical system (gravity is being exerted on it) but somehow, while it's freefalling, its energy is being conserved (its potential energy, based on its position relative to earth, is being transfered to its kinetic energy).
I know the earth-object system can be thought of as an isolated system, but what I'm curious is that for some non-isolated systems (the mass above the earth), energy is being conserved.
So, it seems like the conservation law of energy sometimes works only for isolated systems, but sometimes for non-isolated systems.
So, to what kinds of system does the law of conservation of energy really apply? Or equivalently, what are "isolated physical systems", really?
Best Answer
As you quoted,
the Law of Conservation of Energy states that Isolated Physical systems have their energy conserved.
But, nobody says that a non-isolated system cannot have its energy conserved.
The mass above the Earth is acted upon by a field which is conservative, the gravitational field. In a conservative field the total energy of a body is conserved, while only transforming, reversibly from one form to another. In your case, the gravitational potential energy transforms into kinetic and back. I.e. by falling on the Earth, if the collision of the object with the Earth is completely elastic (no loss of energy), the object would bounce back, then fall again, and so on.
Absolutely isolated systems don't exist, only approximately isolated. The Universe is full of bodies, s.t. any object is subjected to the attraction of other objects. In our labs we do all sort of experiments in vacuum but we can never realize absolute vacuum.
About the conservation of energy, in the classical physics we can say that it always holds, on condition that we take in consideration all the forms of energy involved in the process under examination. For instance, if when examining your object moving in the gravitational field of the Earth we take in consideration the friction with the air, the conservation of the mechanical energy doesn't hold anymore. But if we add the energy lost by friction, the total energy remains constant.