Notes from Richard Feynman's Caltech lectures on Physics, Book 1, Chapter 4 in the book
We don't really understand what energy is, nor the mechanisms behind the movement of energy (or the conservation of energy). We just understand the numbers behind it all, and that they work.
Ultimately, all energy comes from three sources: the sun, hydrogen or uranium.
Think of energy as children’s toy blocks. Each block is immutable -- it can’t be changed. But it can be moved around. It is the job of the physicist, playing the role of the parent here, to keep count of all these blocks. In Feynman’s example, there are 28 blocks. One day there are 27 -- one is behind the bed. The next day there are 29 -- a friend brought over a block. The next day there are 26. The child left two outside.
The job of keeping track of the blocks can involve some thought and calculation. If the child hides the blocks in a box, you have to figure out how to weigh the box, so you can estimate how many are inside. If he throws them in the bath water, then you work out a way to measure the displacement of water in the tub, etc.
When it comes to energy, physics is like this. Except, instead of blocks, we think of energy in numbers. We don’t know what those numbers mean, really. We do know energy has man forms (in the box, under the water, etc), and there are formulas for figuring them out in those conditions.
But how does energy move from one place to another? It is equally as simple, and at the same time, as mysterious. We do not understand the conservation of energy, but we do know how it works.
Gravitational energy is the potential energy of an object, or its ability to do work. The potential energy of each object can be calculated with the weight of an object multiplied by the height at which it is located, or the distance at which it could fall. Gravitational energy is the based on the the gravitational pull of the earth itself.
There are other forms of potential energy, in addition to gravitational energy. Electrical energy operates on the same principal though with electrical charge rather than gravitational force. The electrons (and on the proton side leptons and baryons) move about, but are not destroyed or created in the movement of electrical energy.
There is also kinetic energy, or the movement of force. To better understand the dif between gravitational and kinetic energy, think of a swinging pendulum, a weight hung at the bottom of a string attached to a fixed point that can move freely. As the string is pulled to its side and released, gravitational energy propels it along. Once it hits the bottom of its arc, then it is not the downward force but the momentum -- the kinetic energy -- that propels it further up into the air.
Kinetic energy can be calculated by the weight of the object multiplied by the velocity squared / the constant force of gravity. The formulas for both gravitational and kinetic energies are approximate and grow less precise. In the case of gravitational energy, the further from the earth, the less pull gravity has, while with kinetic energy, relativistic corrections kick in.
Other forms of energy include radiant energy, or light. A photon has the energy of Planck's Constant multiplied by its frequency. Chemical energy is part electrical energy and part kinetic energy. There is mass energy, which is just the energy you get by existing. This is the latent energy of the electrons and protons together, which can produce energy when combined. Knowing the mass of the object will give you the amount of energy it will produce. Nuclear energy is the arrangement of particles inside the nucleus -- it is not entirely electrical, kinetic, or chemical, so we are not entirely sure what it is.
There is also elastic energy, of the energy of a string moving back and forth when tied between two points. Here, you may wonder where the energy is dissipates to. It is lost to the molecules of the string jiggling. Vibration of atoms leads to heat as they jostle against each other.
Weirdly enough, even though nature does enforce the conservation of energy, it does not actually harness a lot of it, Feynman pointed out. Only one of 2 billion parts of light from the sun even hits the earth. And, in any given situation, the amount of available energy on the whole is much lower than the available energy. There is a lot of movement in the ocean, for instance, though it would take an immense amount of work to coordinate all the motion into a single force.