Conservation of Energy
Simple Explanation
The law of conservation of energy states that energy cannot be created or destroyed — only transferred from one form to another, or from one object to another. The total energy in an isolated system always stays exactly the same.
Why Do We Need It?
This is one of the most powerful laws in all of physics — it lets you predict the outcome of incredibly complicated processes (like a rollercoaster ride, or a bouncing ball) just by tracking where the total energy goes, without needing to analyze every force in detail.
Worked Example
Find the speed of a falling object using energy conservation
A 2 kg ball is dropped from a height of 5 m. Using g = 9.8 m/s², find its speed just before hitting the ground (ignoring air resistance).
Why Does This Work?
Since no energy is lost to friction or air resistance in this idealized case, whatever GPE the ball loses by falling must reappear entirely as KE — setting the two expressions equal is a direct application of the conservation law, and elegantly avoids needing kinematics equations at all.
Real-Life Example
A rollercoaster
A rollercoaster car is slowly pulled to the top of the first hill, then released to complete the ride under gravity alone.
The GPE stored at the top continuously converts back and forth into KE as the car speeds up going downhill and slows going uphill — with a little energy steadily lost to friction and air resistance, which is why the car can never quite return to its original height.
Practice
A 0.5 kg ball is dropped from a height of 3.2 m. Using g = 9.8 m/s² and ignoring air resistance, find its speed just before landing. (Round to 1 decimal place.)
HardCommon mistake
Assuming energy conservation means an object always keeps moving forever — real systems always lose some useful energy to friction, air resistance, or heat, so while the TOTAL energy is conserved, USEFUL (kinetic or potential) energy usually decreases over time.
Quick Review
- Total energy in an isolated system is always conserved (never created or destroyed).
- Energy transforms between forms — e.g. GPE to KE — but the total stays constant.
- Real systems lose useful energy to friction/air resistance as heat, even though total energy is still conserved.