Conservation of Energy: Law, Formula & Real-Life Examples
One of the most important laws in physics: Energy cannot be created or destroyed — it only changes form. Learn the principle, formulas, derivations, and how it applies to roller coasters, pendulums, and everyday life.
What is the Law of Conservation of Energy?
The law of conservation of energy states that the total energy of an isolated system remains constant. Energy can neither be created nor destroyed — it can only be transformed from one form to another or transferred from one object to another.
This is one of the fundamental principles of physics and forms the basis of the First Law of Thermodynamics.
Mechanical Energy & Its Conservation
Mechanical energy is the sum of Kinetic Energy (KE) and Potential Energy (PE).
Kinetic Energy (KE)
KE = ½ m v²
Energy due to motion. Depends on mass and velocity.
Gravitational Potential Energy (PE)
PE = m g h
Energy due to position/height. g = 9.8 m/s².
Total Mechanical Energy = KE + PE
E = ½mv² + mgh
Conservation of Mechanical Energy
When only conservative forces (like gravity) act and there is no friction or air resistance:
Initial Mechanical Energy = Final Mechanical Energy
This is the key equation we use to solve many physics problems without needing forces or acceleration.
Real-Life Examples
1. Roller Coaster
At the top of the hill: Maximum gravitational potential energy, zero kinetic energy.
At the bottom: Potential energy converts to kinetic energy → maximum speed.
Total mechanical energy remains constant (ignoring friction).
2. Simple Pendulum
At highest point: Maximum PE, zero KE.
At lowest point: Maximum KE, zero PE.
Energy continuously converts between potential and kinetic.
3. Falling Object
As an object falls, its potential energy decreases while kinetic energy increases by the same amount.
Solved Practice Problems
Problem 1: A 2 kg ball is dropped from a height of 10 m. What is its speed just before hitting the ground? (g = 10 m/s²)
Solution: mgh = ½mv² → v = √(2gh) = √(2×10×10) = 14.14 m/s
Problem 2: A roller coaster car starts from rest at 50 m height. What is its speed at 20 m height? (Ignore friction)
Solution: mg(50) = mg(20) + ½mv² → v = √(2g×30) ≈ 24.5 m/s
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