# 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?

I say the balls energy is not constant, but the energy is conserved (can be accounted for). I teach these two terms and then instead of just asking is energy conserved, I ask is energy constant? And then, is energy conserved? I expect the answer to always be yes to the second one (that we aren’t violating the conservation law.) And if the answer to the first is no, the we know energy has been added or removed from the system through one of the processes you mentioned.

I saw Eric Mazur talk about this very topic once in a talk about how bad physics textbooks are. IIRC, his point was that most books use constant and conserved interchangeably, and that’s wrong. A conserved quantity can’t be created or destroyed: there’s a fixed amount in the universe. That’s very different from whether the amount of that quantity is constant in a given system. Again, IIRC, it’s wrong to try to apply the idea of conservation to a system. Energy is always conserved (can’t be created or destroyed). A conclusion we can draw from this fact is that the amount of energy in a closed system is constant.

Wouldn’t it be an application of the work-energy theorem? Fg does work on the ball, causing a change in its K…but if you look at the ball-Earth system we could say the mechanical energy is constant. In either case, energy is conserved because it can be accounted for.

From AP Physics 1 Course Description (pg. 128), under Big Idea 5, Enduring Understanding 5.A: “Certain quantities are conserved, in the sense that the changes of those quantities in a given system are always equal to the transfer of that quantity to or from the system by all possible interactions with other systems.” and (Essential Knowledge 5.A.2) “For all systems under all circumstances, energy, charge, linear momentum and angular momentum are conserved. For an isolated or closed system, conserved quantities are constant. An open system is one that exchanges any conserved quantity with its surroundings.”

NGSS / Framework also seems to take this view of conservation: “The total change of energy in any system is always equal to the total energy transferred into or out of the system. This is called conservation of energy. Energy cannot be created or destroyed, but it can be transported from one place to another and transferred between systems. Many different types of phenomena can be explained in terms of energy transfers. “

Like Chris said above, energy is always conserved. What changes is OUR definition of a system – if we’re clever, we can design a system that all of the energy transfer happen inside of (a closed system). Or, we can choose our system so that the same energy transfers happen, but energy crosses that system boundary (an open system).

My students spend a lot of time talking about how to pick a system – how to figure out what energy is stored, as what kind/flavor/color, and in which objects. If you can teach them to follow the energy transfers, THEN define the system (so they can choose open/closed), I’ve found a lot of misconceptions (like what work is) just fall away.

Great post!