What Is Energy?
There is a law in nature for which no exception has ever been found: conservation of energy. It states: there exists a numerical quantity (energy) whose total remains unchanged regardless of what happens in nature. This is not a description of a specific mechanism, but an abstract mathematical principle.
"Building Blocks Analogy": Like counting all the visible and hidden blocks in a room — the total never changes. Energy works the same way: it has many "forms," and all forms must be accounted for to maintain conservation.
Common forms: gravitational potential energy, kinetic energy, thermal energy, elastic energy, electrical energy, chemical energy, radiant energy, nuclear energy, mass energy.
🪜Gravitational Potential Energy: Derived from "No Perpetual Motion"
Using the idea of a "reversible lifting machine" (perpetual motion is impossible), one can show that all reversible machines have the same optimal efficiency, leading to the gravitational potential energy formula:
Potential Energy (near surface) = Weight × Height
More generally, energy change = force × distance. This idea also applies to electric potential energy, etc.
Inclined Plane
Use energy conservation to quickly find equilibrium conditions (no need to decompose forces).
Screw Jack
Handle travel × force = load rise height × weight.
Virtual Work Principle
Assume infinitesimal displacements, keep "weight × height" sum constant, solve for static equilibrium.
🏃Kinetic Energy: Defined by "How High It Can Rise"
The kinetic energy of a pendulum at its lowest point equals the gravitational potential energy corresponding to the "height it can still rise":
K.E. = W · h(V) = W · V² / (2g)
Where W is weight and g is gravitational acceleration. This formula is approximately valid at low speeds and near the surface; relativistic corrections are needed at high speeds.
🔄Other Forms and Transformations
Elastic energy: Stretching/compressing a spring stores energy, exchanging back and forth with kinetic energy; losses convert to thermal energy (increased atomic "jiggling").
Electrical/radiant energy: Work done by charges; light is oscillating energy of the electromagnetic field.
Chemical energy: Originates from electron kinetic energy and electric interaction energy (essentially reducible to electrical and kinetic energy).
Nuclear energy: Energy released by changes in internal nuclear structure (strong interaction; details beyond electricity and gravity).
Mass-energy relation: E = mc²
Particle-antiparticle annihilation releases a definite amount of radiant energy; rest mass itself contains energy.
Conservation law family: Energy, linear momentum, angular momentum. They are closely tied to "spacetime symmetries" (more precise under quantum mechanics).
Conservation reduced to "counting": Charge conservation, baryon number conservation, lepton number conservation.
🔥Available Energy and Energy Sources
What's conserved is total energy; available energy is limited by thermodynamics and entropy. The thermal motion of seawater is enormous, but it's hard to organize it into useful work.
Natural Energy Sources
The Sun (rain/wind/biomass/coal), uranium, hydrogen fusion (if controllable).
Vision
If controlled fusion is achieved, a tiny amount of water could satisfy enormous energy demands.
✨Key Points
Energy is an abstract "ledger" — forms can change, but the total stays constant.
Gravitational PE: weight × height; KE: W·V²/(2g).
Energy methods unify the analysis of inclined planes, levers, jacks, and static equilibrium.
Available energy is limited by thermodynamics and entropy; energy development depends on physics breakthroughs.