3.3MechanicsCore

Conservation of Energy

A pendulum swinging back and forth, a rollercoaster car climbing and falling, a ball bouncing lower with every bounce — all of them are governed by a single, unbreakable rule: energy is never created or destroyed, only transferred from one form to another or moved between objects.

35 min Video by Physics Online Module 3.3 Work, energy and power

Conservation of Energy — A Level PhysicsWatch the full walkthrough before the notes below.

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What you'll be able to do

State the principle of conservation of energy
Apply conservation of energy to mechanical systems involving kinetic and gravitational potential energy
Account for energy "lost" to resistive forces such as friction and air resistance
Solve problems involving energy transfers along a path, not just between two points

The principle of conservation of energy

The principle of conservation of energy states that energy cannot be created or destroyed — only transferred from one form to another, or transferred between objects. In an idealised mechanical system with no resistive forces, the total mechanical energy (kinetic plus gravitational potential) stays exactly constant throughout the motion.

E_{k} + E_{p} = constant

Total mechanical energy is conserved in the absence of resistive forces.

1All the gravitational PE lost converts entirely into kinetic energy:

m g h = \frac{1}{2} m v^{2}

2The mass cancels:

g h = \frac{1}{2} v^{2}

, so

v = 2 g h

v = 2 \times 9.81 \times 4.0 = 78.48

Answer

v \approx 8.86

m s⁻¹

Tip — Notice the mass cancels completely in a free-fall speed calculation — this is exactly why (ignoring air resistance) a heavy object and a light object dropped from the same height hit the ground at the same speed.

Energy transfers in a swinging or rolling system

For a pendulum, rollercoaster or any system that rises and falls, mechanical energy continuously exchanges between kinetic and gravitational potential energy, while their sum stays constant (again, ignoring resistive forces). This lets you find a speed at any point in the motion just from height differences, without needing to know anything about forces or the shape of the path taken.

1At the highest point, all energy is gravitational PE (relative to the bottom of the swing); at the lowest point, all of it has converted to kinetic energy.

m g h = \frac{1}{2} m v^{2} \Rightarrow v = 2 g h

v = 2 \times 9.81 \times 0.15 = 2.943

Answer

v \approx 1.72

m s⁻¹

Tip — When resistive forces are present, energy is not lost from the universe — it is transferred to internal (thermal) energy of the surroundings, via friction or air resistance. "Lost" mechanical energy always has to go somewhere.

Equation recap

Δ E_{k} = - Δ E_{p}

In an ideal system, kinetic energy gained equals gravitational PE lost.

v = 2 g h

Speed after falling (or rising) through height h, from conservation of energy.

Common mistakes to avoid

Assuming energy simply "disappears" when friction or air resistance acts.

Energy is never destroyed — resistive forces transfer mechanical energy into thermal (heat) energy of the object and its surroundings.

Believing a heavier object always falls faster than a lighter one.

Ignoring air resistance, mass cancels out of v=√(2gh) — all objects reach the same speed after falling the same height, regardless of mass.

Forgetting to account for energy dissipated by resistive forces when a problem states some energy is "lost".

If a percentage of energy is dissipated, only the REMAINING fraction converts into kinetic energy — don’t use the full initial energy value in that case.

Key takeaways

Energy cannot be created or destroyed — only transferred between forms or objects.
In a system with no resistive forces, total mechanical energy (Ek + Ep) stays constant.
Falling/swinging speed (no air resistance): v = √(2gh) — independent of mass.
Where friction or air resistance acts, the "missing" mechanical energy is transferred to thermal energy, not destroyed.

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Conservation of Energy

35 min Video by Physics Online Module 3.3 Work, energy and power