Classical Mechanics · Energy & Work
You never see energy directly — you see rocks fall, fires burn, muscles flex. But underneath every transformation is a number that never changes. Conservation of energy is the deepest accounting system in all of physics.
There is a fact, or if you wish, a law, governing all natural phenomena that are known to date. There is no known exception to this law — it is exact so far as we know. The law is called the conservation of energy. It states that there is a certain quantity, which we call energy, that does not change in the manifold changes which nature undergoes.
Idea 1 · What is Energy?
Feynman opened with a striking admission: we don't actually know what energy is. It isn't a fluid, a substance, or a thing. It is an abstract quantity — a number — that stays constant no matter what physical processes occur.
Think of a child's "Dennis the Menace" blocks. Mom can always account for all the blocks, even when some are in a box, some in the water, some hidden under the rug. Energy is like that. The universe can store it in different "hiding places" — but the total never changes.
Total Energy = Kinetic + Potential + Heat + Electrical + Chemical + Nuclear + ...
This total is always the same. Nature never creates or destroys energy — only converts it between forms.
One joule is the energy needed to lift an apple (≈100g) one meter upward against Earth's gravity. A food calorie (kcal) equals 4,184 joules. A lightning bolt delivers about 250 kJ. The Sun radiates 3.8 × 10²⁶ joules every second.
Conservation of energy isn't arbitrary — it follows mathematically from the fact that the laws of physics are the same today as they were yesterday. Time-translation symmetry implies energy conservation. Emmy Noether proved this in 1915.
Idea 2 · The Two Master Forms (and their children)
Every moving object has kinetic energy. It grows with the square of velocity — double the speed means four times the KE. This is why highway crashes are so much more destructive than parking lot fender-benders.
An object held above the ground has potential energy stored in the gravitational field. When released, gravity converts it to kinetic energy. h is height above a chosen reference point — you can choose any reference, since only changes in PE matter.
Idea 3 · Work — Transferring Energy Through Force
Work is energy transferred to or from an object by a force acting over a distance. The angle θ is between the force direction and the direction of motion. Only the component of force along the motion does work.
The net work done on an object equals the change in its kinetic energy: W_net = ΔKE = ½mv² − ½mv₀²
Power is how fast energy is transferred. Unit: the Watt (W = J/s). A 100 W lightbulb consumes 100 joules every second. A Tour de France cyclist outputs ~400 W sustained. A horse: ~750 W (1 horsepower).
No real machine converts energy perfectly. Some always becomes heat (friction, air resistance). Efficiency = (useful output energy) / (total input energy) × 100%. A car engine: ~25%. A human muscle: ~25%. An LED: ~80%.
Thermodynamics limits it. The Second Law says that in every energy conversion, some energy "spreads out" into heat — increasing entropy. A perfectly efficient engine would violate the Second Law of Thermodynamics.
Idea 4 · Conservative vs. Nonconservative Forces
A force is conservative if the work it does is independent of the path taken — only the starting and ending positions matter. Examples: gravity, springs (Hooke's Law), electric force (Coulomb's Law).
For a conservative force, you can define a potential energy function. Going around a closed loop returns you to the same energy state.
Friction, air resistance, tension — these are nonconservative. The work they do depends on the path; taking a longer path means more energy lost to heat. You can't recover that energy as potential energy — it has spread into thermal motion.
KE_initial + PE_initial + W_nonconservative = KE_final + PE_final
The nonconservative work term (friction, drag) accounts for energy converted to heat. Total energy is still conserved — it just moves into forms we can't easily use.
Every conservative force has a potential energy field — a map of stored energy in space. Gravity: PE = mgh. Electric: PE = kq₁q₂/r. Spring: PE = ½kx². Objects "roll downhill" in these fields toward lower potential energy.