Physics › Mechanics › Conservation of energy
Conservation of energy
Energy is never made and never destroyed, only moved between stores, and two stores dominate mechanics: kinetic and gravitational potential. Add the work done against resistive forces and every mechanics energy problem becomes the same piece of bookkeeping.
Builds on Work, energy and power.
IN THIS TOPIC
- State the principle of conservation of energy and use it as an accounting identity.
- Calculate kinetic energy and changes in gravitational potential energy.
- Balance energy budgets that include work done against friction or drag.
WHAT YOU PROBABLY THINK
Energy gets used up.
The principle, and the two big stores
The principle of conservation of energy: energy cannot be created or destroyed, only transferred from one store to another. “Using” energy means moving it somewhere less useful, never reducing the total. Mechanics runs almost entirely on two stores. Kinetic energy, the energy of motion:
and the change in gravitational potential energy when a mass moves through a height:
The square in Ek deserves respect: doubling the speed quadruples the kinetic energy, which is the physics behind stopping distances growing so alarmingly with speed.
Frictionless exchanges
With no resistive forces, the two stores simply trade. A pendulum converts potential to kinetic on the way down and back again on the way up; a thrown ball does the same in one exchange.
The exchange gives a fast route through problems that would be tedious with forces: equate mgΔh to ½mv2, and speeds and heights fall out without a single force diagram. The mass frequently cancels, which is why a heavy and a light pendulum released from the same height arrive at the bottom with the same speed.
When friction takes its cut
Real systems leak, and the leak has a name: work done against resistive forces. The energy is not destroyed; it is transferred to internal energy of the surfaces and the air, warming them. Conservation then reads as a budget with three lines:
Energy in equals useful energy out plus energy to the resistive forces, every joule accounted for. AQA sets these both ways: given two of the three lines, find the third; or given all three, confirm the books balance. Either way the method is the same sentence: write the stores at the start, write them at the end, and let the difference be the work done against resistance.
THE EXAM BIT
- Open energy questions with the accounting sentence: energy at the start = energy at the end + work done against resistive forces. The structure itself carries method marks.
- ΔEp uses the vertical height change. On a slope, that is the drop, not the distance travelled along the surface.
- “Where did the energy go?” has one acceptable answer: transferred to internal energy of the object and surroundings by the resistive force. “Lost as heat” is tolerated; “lost” alone is not.
- The mass often cancels in pure Ep-to-Ek exchanges. If a question asks why two different masses land at the same speed, that cancellation is the answer.
- Doubling v quadruples Ek. Any question comparing speeds through energy hinges on the square.
CHECK YOURSELF
A child of mass 30 kg starts from rest at the top of a slide 2.5 m high and reaches the bottom at 5.0 m s−1. How much energy was transferred to the surroundings by friction? Take g = 9.8 m s−2.
Show a hint
Write the budget: potential in, kinetic out, friction takes the difference.
Show the answer
Potential energy given up: ΔEp = mgΔh = 30 × 9.8 × 2.5 = 735 J.
Kinetic energy gained: Ek = 12mv2 = ½ × 30 × 5.02 = 375 J.
The books must balance, so friction took 735 − 375 = 360 J, now internal energy in the slide, the child and the air.
Energy is never used up.
It is moved, and you can always audit the move.
No animated video for this topic yet; these notes stand alone. InkPhysics on YouTube.