Efficiency & Power

The Principle of Conservation of Energy states that energy cannot be created or destroyed, only transferred. Therefore, the total energy input must always equal the sum of the useful energy output and the wasted energy.

In real-world mechanical systems, friction and air resistance inevitably convert some kinetic or electrical energy into thermal energy (heat). This 'dissipated' energy is considered wasted because it does not contribute to the intended task.

Because some energy is always dissipated, the efficiency of a real machine is always less than 100%. A 'perfect' machine with 100% efficiency is a theoretical ideal that does not exist in practice.

To calculate Power ($P$), divide the total energy transferred ($E$) or work done ($W$) by the time ($t$) taken: $P = \frac{E}{t}$

To calculate Efficiency ($\eta$), use the ratio of useful output to total input. This can be calculated using either energy or power values: $\eta = \frac{\text{Useful Output Power}}{\text{Total Input Power}}$ or $\eta = \frac{\text{Useful Energy Output}}{\text{Total Energy Input}}$

To convert a decimal efficiency to a percentage, multiply the result by 100. For example, an efficiency of $0.45$ is equivalent to $45\%$.

Power vs. Energy: Energy is the total capacity to do work (measured in Joules), while Power is the speed at which that work is done (measured in Watts). A high-power machine does the same amount of work as a low-power machine but in less time.

Input vs. Output: Input refers to the total energy/power consumed by the device (e.g., electricity from a wall socket), whereas Output refers only to the energy/power that performs the intended function (e.g., the mechanical lifting of a weight).

Unit Consistency: Always ensure time is in seconds before calculating power. If a problem provides time in minutes or hours, convert it immediately ($1\text{ min} = 60\text{ s}$).

Sanity Check: Efficiency can never exceed 100%. If your calculation results in a value greater than 1 (or 100%), you have likely swapped the 'useful' and 'total' values in the fraction.

Identify 'Useful': Carefully read the scenario to determine the intended goal. For a lightbulb, light is useful and heat is waste; for a heater, heat is useful and light is waste.

The 'Lost' Energy Myth: Students often think wasted energy simply disappears. In reality, it is transferred to the surroundings, usually as thermal energy, increasing the temperature of the environment.

Power and Force Confusion: Power is not just 'strength' or force. A machine can exert a massive force but have zero power if it is not moving or transferring energy over time.

Percentage vs. Decimal: Forgetting to multiply by 100 when asked for a percentage, or using a percentage directly in a multi-step calculation without converting it back to a decimal first.