Conservation & Dissipation of Energy

Energy Conservation Principle

The principle of conservation of energy states that energy cannot be created or destroyed. Instead, energy can only change from one form to another within a system. This means the total amount of energy in a closed system remains constant at all times.

For example, when a pendulum swings, its energy continuously changes between kinetic energy (energy of motion) and gravitational potential energy (energy stored due to height). Although the form changes, the total energy stays the same, assuming no energy is lost to the surroundings.

This principle is fundamental in physics and helps us understand how energy flows and transforms in everyday processes.

For instance, if a ball is dropped from a height of 5 metres, its gravitational potential energy at the top is converted into kinetic energy as it falls. The total energy remains constant (ignoring air resistance).

Gravitational potential energy at the top: $E_p = mgh$, where $m$ is mass, $g$ is gravitational field strength (9.8 N/kg), and $h$ is height.

Kinetic energy just before hitting the ground: $E_k = \frac{1}{2}mv^2$.

Because energy is conserved, $E_p = E_k$ (if no energy is lost).

Energy Dissipation

Although energy is conserved, not all energy in a system remains useful. Some energy spreads out and becomes less useful for doing work. This process is called energy dissipation.

Dissipated energy is often transferred as thermal energy (heat) to the surroundings, which cannot be used to do useful work in the system. For example, when you rub your hands together, mechanical energy is dissipated as heat, warming your skin.

Energy dissipation reduces the efficiency of machines and systems because some energy is wasted and cannot be harnessed for the intended purpose.

For example, in a moving car, friction between the tyres and road, and air resistance, cause some of the car's kinetic energy to dissipate as heat and sound. This energy is wasted from the perspective of moving the car forward.

Energy Transfers and Losses

Energy is transferred between different energy stores in a system. For example, chemical energy in fuel can be transferred to kinetic energy in a moving vehicle.

However, during these transfers, some energy is lost due to friction and other resistive forces. Friction converts useful energy into thermal energy, which dissipates into the surroundings.

Sound energy is another common form of wasted energy. For example, when a machine operates, it often produces noise, which is energy lost from the system.

Consider a cyclist braking to a stop: the kinetic energy of the moving bike is transferred to thermal energy in the brake pads due to friction, which dissipates into the air as heat. Some energy is also lost as sound from the brakes squealing.

Understanding these energy transfers and losses helps in designing systems that minimise wasted energy and improve performance. For instance, lubricating moving parts reduces friction, so less energy is dissipated as heat, making machines more efficient (see Improving Efficiency topic for more).

Example: A toy car with a mass of 0.5 kg is pushed along a surface. It initially has 10 J of kinetic energy. After moving, friction causes 3 J of energy to dissipate as heat. How much useful kinetic energy does the car have left?

Useful kinetic energy = Initial kinetic energy 6 Energy dissipated

Useful kinetic energy = $10 \text{ J} - 3 \text{ J} = 7 \text{ J}$

So, 7 J of kinetic energy remains to keep the car moving, while 3 J has been wasted as heat.