Conservation of Energy
Conservation of Energy
- Energy can move between stores and objects, but the accounting total does not disappear.
- Most exam problems become easier when you compare one clear initial state with one clear final state.
Keep the total, track where it goes
Definition
1 markWhat is meant by the principle of conservation of energy?
Model answer: Energy cannot be created or destroyed; it can only be transferred or transformed from one form to another.
GPE decreasesKE increases- With negligible air resistance, a falling object's GPE loss equals its KE gain.
- Mass cancels in a fall from rest, so objects dropped through the same height reach the same speed when air resistance is negligible.
- The mass does not cancel when the question asks for the energy itself. A heavier object has more GPE and more KE.
Worked example
A fall with no resistance
A ball falls from rest through 5.0 m. Find its speed.
- Set GPE lost equal to KE gained: .
- Cancel mass, then solve for speed.
- .
Answer
Add every destination when resistance acts
high GPE
low KElow GPE
high KElower return height
with energy dissipation
energy dissipated
to surroundingsball still gains KEFollow 100 J through a fall
Change one condition. The three bars must still total 100 J.
GPE lost is split between kinetic energy and energy dissipated to the surroundings.
GPE remaining50 J
Kinetic energy40 J
Dissipated10 J
Total100 J
- Friction and drag transfer energy into internal energy of the object and surroundings. We call this energy dissipatedbecause it spreads out and is less useful.
- “Energy lost” is shorthand for energy no longer in the mechanical store being tracked. It is not destroyed.
Write the energy equation in words first: initial energy = useful final energy + energy dissipated. Then insert formulae.
Your turnExam-style
A 2.0 kg object falls from rest through 8.0 m. It reaches 10 m s⁻¹. Calculate the energy dissipated by air resistance.
Show worked answer
Worked answer: GPE lost = . KE gained = . Energy dissipated = .