Applied Calculations Involving Efficiency, Work Done and Power

Applied Calculations Involving Efficiency, Work Done and Power

Foundations of Energy, Work Done and Power

In physics, the term energy can be defined as the capacity to do work. In other words, energy is an attribute of a system that allows it to do something or make something happen.
The measure of energy is the joule (J). It is a derived unit from other base units, defined as one newton meter.
Work done (W) is the energy transferred or converted. It can be defined as Force multiplied by Distance, it is also measured in joules.

Principles of Efficiency

Efficiency is a measure of how much useful work is done by an energy conversion process. It is defined as the ratio of useful energy output to the total energy input.
Efficiency is often expressed as a percentage, where a 100% efficiency means that all the input energy is converted into useful output and there are no losses.
In reality, no process can be 100% efficient due to unavoidable energy losses mainly as heat.

Calculations Involving Work Done

Work done can be calculated using the formula: Work Done (J) = Force (N) x Distance (m).
If the force is applied at an angle, then only the component of the force that acts in the direction of the motion does work: Work Done = Force x Distance x cos(θ), where θ is the angle.

Calculations Regarding Power

Power describes the rate of energy transfer or the rate at which work is done.
Power is calculated using the equation: Power (W) = Work Done (J) / Time (s).
Another commonly used unit of power is the horsepower (hp), particularly in the context of motor vehicles. One horsepower is approximately equal to 746 watts.

Applied Calculations of Efficiency

Efficiency can be calculated with the formula: Efficiency (%) = (Useful energy output / Total energy input) x 100.
Improving the efficiency of an energy conversion process can save energy, which is beneficial for cost reasons and also for environmental protection.
The total energy input and the useful energy output must be in the same units when inserting them into the equation.

Understanding Mechanical Advantage

In some machines, like levers and pulleys, mechanical advantage is achieved by distributing the input energy in a way that maximises the output force or speed.
Mechanical advantage can be calculated by the ratio of output force to input force or using the ratio of input distance to output distance.

Utilising Sankey Diagrams

A Sankey diagram is a tool that can be used to visualise energy transfers and efficiencies in a process.
In a Sankey diagram, the width of the arrows is proportional to the amount of energy they represent.
The input energy is shown by a single arrow leading to the box representing the device or process, and the output energy is shown by multiple arrows leading away from the box with their widths proportionate to the energy they represent.