Anything that takes input and produces output, whether its an electrical generator or a simple pulley system, can be measured for how well it uses the work put into it. The work efficiency formula helps you quantify this and judge the efficiency of any machine.
Work Efficiency Formula
The formula to calculate work efficiency is the ratio of output to input expressed as a percentage. For a machine, you can determine the work put into the machine depending on how the machine works. You can generally calculate work by multiplying the force times distance for the motion.
Make sure you appropriately calculate the input and output of the machine or object that performs the work, as well as considering other factors such as the human operating the machine.
The work efficiency formula is efficiency = output / input, and you can multiply the result by 100 to get work efficiency as a percentage. This is used across different methods of measuring energy and work, whether it's energy production or machine efficiency.
Example Work Efficiency Calculation
A pulley rope that pulls a 10 pound weight 1 foot off the ground due to a human applying 6 pounds of force to pull the pulley rope 2 feet has these specific input and output forces. The human force, the input force, performs 6 pounds times 2 feet of work, or 12 foot-pounds of work. The machine's motion, the output force, is then 10 pounds times 1 foot of work, or 10 foot-pounds of work.
The work efficiency is then the ratio of output to input in percentage form. This would be 10/12, or 0.83. Multiply this by 100 to convert to a percentage, which would give a work efficiency of 83 percent.
Work Efficiency Definition Physics
The ratio of work output to input is used as a measure of efficiency in many areas of physics and engineering. Researchers find it useful to describe the percentage of products and consumables for a process to determine how to conserve energy, power, or other limited quantities.
Determining the ratio of output to input gives you an idea of how efficient the system, process, method, pipeline or whatever is being used is.
When analyzing the thermodynamics of heat engines, for example, the useful work output that a heat engine such as a Carnot heat engine may measure the work the engine can perform as output with the high-temperature heat the engine uses as input.
Work Efficiency Formula in Practice
Physicists and engineers use work efficiency when determining how productive and energy-conservative processes are for electrical circuits (electrical efficiency), thermal heat engines (thermal efficiency), radioactive process (radiation efficiency), other processes including quantum mechanics (quantum efficiency).
The simple ratio of output to input means scientists and engineers can used their simplified, universalized mathematical formulas for whatever type of efficiency or purpose they need. For example, you may use the ratio of power an antenna radiates to the power it absorbs at its terminals when detecting radio frequencies as a measure of efficiency.
Efficiency is more commonly expressed as a percentage as it directly compares the two factors, input and output. However, there are cases in which efficiency can be measured without a percentage such as specific impulse, the momentum divided by mass for a rocket by taking into account how it uses propellant or fuel as well as air resistance and other forces. Specific impulse gives physicists and engineers to determine thrust, efficiency and measures of propellant usage when designing an engine.
About the Author
S. Hussain Ather is a Master's student in Science Communications the University of California, Santa Cruz. After studying physics and philosophy as an undergraduate at Indiana University-Bloomington, he worked as a scientist at the National Institutes of Health for two years. He primarily performs research in and write about neuroscience and philosophy, however, his interests span ethics, policy, and other areas relevant to science.