Basic but important physics questions: What does it mean to say Energy is conserved?
Ok, here’s a question I’ve been thinking a bit about. In my classes we learn about the principle of energy conservation as the idea that there is this fundamental quantity, energy, that we can account for in a system. If the system is completely isolated, this quantity doesn’t change, and when this system is interacting with its surroundings (via work, heat or radiation) we can account for the changes in the energy of this system.
But it’s gotten me thinking of a question I find myself asking a lot—”Is the energy of this system conserved?” I think most of my students hear that as “does the energy of this system stay the same?” But now I’m thinking that if my notion of conserved is “can be accounted for” then the answer to this question should always be yes (we can always figure out how to calculate the energy flowing in/out of the system), unless we’re working on problems dealing with the total energy of the universe and dark energy or something.
Wikipedia seems to say that a conserved quantity is constant along the trajectory of a system, and thus is sounds like for the system of a ball falling to the ground (where K is increasing), energy would not be conserved.
So if this is true, must I say something like the energy of the ball system is not conserved, but we can account for the change in the energy of the system by calculating the work done by the gravitational force? And is this an application of the principle of energy conservation?