Question

When energy is conserved, does that mean its conserved to potential energy always? Or to another form?

Answer 1

You need to specify:

"When MECHANICAL energy is conserved, does that mean its conserved to potential energy always? Or to another form? "

Then the answer is: Yes it is an exchange between KE and different forms of potential energy.

Answer 2

I thought generally energy would be conserved to potential energy...
@Vincent-Lyon.Fr

Answer 3

Energy, in the broad sense, is conserved too. But when you brake, this conservation means that KE is converted to thermal energy. So mechanical energy itself is not conserved.

It all depends at what level you are reasoning, and if you take into account microscopic forms of energy or not.

Answer 4

In short, conservation of energy just means that when you add all the energies up in a system you define, you'll always get the same constant value where the point being emphasized is that energy can neither be created nor destroyed.

Answer 5

It can certainly all be collected as potential energy. But it need not be.

Answer 6

Generally energy is conserved. In what form? It depends of the situation, the system, many many factors as always. I keep forgetting you can't get a simple answer out of physics because many many factors relies on that answer :)

@Vincent-Lyon.Fr @s3a @Carl_Pham

Answer 7

It's pretty simple at the microscopic level. Just thinking non-relativistically for the moment, all you usually have is kinetic energy and the energy due to electric forces (magnetic forces enter into the kinetic energy). Gravity is usually neglible at the microscopic level, and nuclear and weak forces are (1) rare unless you're in a nucleus or center of a star, and (2) put you into relativistic regions immediately anyway.

Energy swings back and forth between kinetic and electrical potential, as particles come closer or further away from other charges. When they dip into regions of strong attractive force, kinetic energy increases (they speed up) and potential decreases, and if the region is of repulsive forces, kinetic energy decreases (they slow) and potential increases.

Where it gets complicated is really at the macroscopic level, because a lot of energy is invisible to us -- it is contained in the microscopic movements and forces of atoms and molecules. But the consequences of the flow of energy among the microscopic degrees of freedom, and to and from macroscopic observable degrees of freedom, are important, and give rise to the enormous complexity of our macroscopic "forms" of energy, as well as the complexities of thermodynamics. The reason essentially because if we want to understand macroscopic degrees of freedom without knowing about the microscopic dynamics underlying it, we have to construct much more complicated force and energy laws.

An analogy: suppose we want to describe the motion of your car on the highway. One way is to describe your motion and the motion of all other cars. Then we can probably write down a pretty simple rule of motion for your car: you accelerate to a steady 65 MPH if you can, you move around other cars, passing them if they are going slower, and you brake when you can't pass. Simple dynamical laws, because they apply to all the degrees of freedom -- you and all other cars.

But now suppose we want dynamical laws that describe your motion *without* using the trajectories of all other cars. We want to put into one side of the laws just your motion at time t, and get out your motion at time t+dt -- without putting in the locations and velocities of all others cars.

We can do this, at least in an average way, by carefully averaging over the dynamics of all other cars. For example, when you pass near a major on-ramp, where another freeway merges into yours, generally there is a lot of traffic, so we can expect you to slow down, on average. Maybe do a lot more lane-changing. We could build that into the dynamical laws: when you pass the I-5/I-605 interchange, jiggle lane randomly and slow down. We can invent fictitious "forces" that account for these effects -- a force that jiggles your lane and slows you down, and which increases in strength as you come near the intersection.

And so on. But as you can see, we have to build a much more complicated dynamics for you, if we want to have that dynamics depend only on your position and velocity, and average over the behaviour of all other cars. That's essentially what we do when we try to build macroscopic physics of visible objects. We want to describe the dynamics of macroscopic objects using only their positions and velocities, and averaging over the dynamics of all the microscopic particles that make them up. But that necessarily means we come up with much more complicated dynamics, with all kinds of complicated fictitious (or better yet "effective") forces, and much more complicated ways to evaluate your energy.

Answer 8

@Carl_Pham very very interesting post! Thank you!