Energy is transferred, never created or destroyed
Principle of conservation of energy — Energy cannot be created or destroyed. It can only be transferred from one store to another, and the total in a closed system stays constant.
Energy is not a substance and it is not a fuel that gets used up. It is a quantity that can be counted before and after any process, and the two counts always agree. What changes is where it is stored and what form it takes.
The useful way to think about it is in stores and transfers. A stretched catapult holds energy in an elastic store. Release it and that energy is transferred to the kinetic store of the stone. The stone rises, and energy moves from the kinetic store to the gravitational store. Nothing is made or lost at any point.
When people say energy is "wasted", they mean it has ended up somewhere useless — usually spread out as internal energy in the surroundings, warming the air by an unmeasurably small amount. It is still there. It is simply no longer available to do anything.
| Store | What holds it | Everyday example |
|---|---|---|
| Kinetic | anything moving | a moving car |
| Gravitational potential | anything raised up | water behind a dam |
| Elastic (strain) | anything stretched or compressed | a drawn bow |
| Internal (thermal) | the random motion of particles | a hot cup of tea |
| Chemical | bonds between atoms | food, fuel, a battery |
| Nuclear | the nucleus itself | uranium fuel |
Kinetic and gravitational potential energy
Two stores dominate mechanics problems, and both have equations you must be able to use in either direction.
Kinetic energy depends on the square of the speed. That squaring has real consequences: double the speed of a car and you quadruple its kinetic energy, which is why stopping distances grow so alarmingly with speed and why a crash at 60 km/h is four times as severe as one at 30.
Gravitational potential energy depends on the change in height, not on the height above some absolute zero. Only differences matter, so you are free to measure from whatever level is convenient — usually the ground or the lowest point of the motion.
- KE
- kinetic energyJ
- m
- masskg
- v
- speedm s⁻¹
- g
- gravitational field strengthN kg⁻¹
- Δh
- change in heightm
A 0.20 kg ball is dropped from a height of 5.0 m. Calculate its speed just before it lands, ignoring air resistance. Take g = 9.8 N kg⁻¹.
- All the gravitational store becomes kinetic store, so
mgΔh = ½mv².Conservation of energy — nothing is lost with no air resistance. - The mass cancels from both sides:
gΔh = ½v².A heavier ball would land at the same speed, which is worth noticing. v² = 2gΔh = 2 × 9.8 × 5.0 = 98.v = √98.v = 9.9 m s⁻¹.
9.9 m s⁻¹, independent of the mass
Watch the two bars trade height while the total stays flat. Switch friction on and the total bar sinks — that energy has not vanished, it has left as internal energy in the air and the pivot.
Work done by a force
Work done — The energy transferred when a force moves its point of application along the direction of the force, W = Fs. One joule is one newton-metre.
Work is simply another name for energy transferred mechanically. If a force moves something, it does work on it, and the energy transferred equals force multiplied by the distance moved in the direction of the force.
That last phrase is doing real work in the definition. Carry a heavy suitcase horizontally across a room and you do no work against gravity at all, because the upward force you apply and the horizontal movement are at right angles. Your arms ache, but that is your muscles working internally, not work done on the case.
When the force and the movement are at an angle to each other, only the component of the force along the direction of motion counts.
- W
- work doneJ
- F
- forceN
- s
- distance movedm
- θ
- angle between them°
Power and efficiency
Power is the rate of energy transfer — how fast the work is done, not how much. Two cranes that lift the same load to the same height do the same work; the one that does it in half the time has twice the power.
Efficiency compares what you wanted with what you paid for. No real machine reaches 100%, because some energy always ends up in stores you did not want — usually internal energy from friction, and sound.
Efficiency is never greater than 100%. If a calculation gives more, something has gone in upside down: check that the useful output is on top and the total input underneath.
- P
- powerW
- W
- work doneJ
- t
- times
- v
- speedm s⁻¹
A motor raises a 50 kg load 8.0 m in 10 s. It draws 5.0 kW from the supply. Calculate the useful power output and the efficiency. Take g = 9.8 N kg⁻¹.
- Useful work
= mgΔh = 50 × 9.8 × 8.0 = 3920 J.The useful job is raising the load. - Useful power
= W/t = 3920 / 10 = 392 W. - Input power
= 5.0 kW = 5000 W.Convert before dividing. - Efficiency
= 392 / 5000 = 0.0784. = 7.8%.Low, but plausible for a small hoist — most of the input becomes heat.
useful power 392 W, efficiency 7.8%
Key points
- Energy is conserved: count it before and after and the totals match.
- Kinetic energy goes as
v²— double the speed, quadruple the energy. - Work done equals energy transferred,
W = Fs. - No work is done when the force is at right angles to the motion.
- Power is energy per second; efficiency is useful out over total in.