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# Efficiency of Machines

by Ron Kurtus (revised 27 June 2016)

The * efficiency of a machine* indicates how well its input energy is converted to useful output energy or work. It is a major factor in the usefulness of a machine and is the fraction or percentage of the output divided by the input.

According to the *Law of Conservation of Energy*, the total output energy or work must equal the total input energy. However, some of the input energy does not contribute to the output work and is lost to such things as friction and heat.

Examples of machine efficiency include a lever, automobile, and perpetual motion machine.

Questions you may have include:

- What is the efficiency equation?
- How do losses fit in?
- What are some examples of efficiency?

This lesson will answer those questions. Useful tool: Units Conversion

## Efficiency equation

The efficiency of a machine concerns how much energy is lost to friction and heat during its operation. Since work is the change in kinetic energy, the efficiency of a machine can be stated as the percentage of the output work divided by the input work minus the work lost from to friction and heat.

Eff = W_{O}/W_{I}

where

**Eff**is the efficiency decimal fraction**W**is the output work or energy_{O}**W**is the input or effort work or energy_{I}

Multiply **Eff** by **100%** to get the *efficiency percentage*.

## Losses

According to the *Law of Conservation of Energy*, the output work or energy equals the input work minus the work lost from to friction and heat:

W_{O}= W_{I}− W_{Loss}

Substituting for **W _{O}** in the efficiency equation:

Eff = (W_{I}− W_{Loss})/W_{I}

or

Eff = 1_{}− W_{Loss}/W_{I}

## Examples

Examples of efficiency include a lever and automobile.

### Lever

A simple lever loses about 2% or 0.02 of the input energy to internal friction at its fulcrum:

W_{Loss}= 0.02W_{I}

Thus:

Eff = 1_{}− 0.02W_{I}/W_{I}

Eff =1 − 0.02

Eff =0.98 or 98%

### Automobile

On the other hand, the efficiency of an automobile is only around 15%. About 75% of the energy is lost through wasted heat from the engine and another 10% is lost due to internal friction, including losses from tire friction.

### Perpetual motion machine

If losses to friction and heat are zero, the efficiency of the machine is:

Eff = W_{O}/W_{O}

Eff =1.0 or 100%

Such a machine is called a *perpetual motion machine* since once it was started, it would run forever. Inventors have worked for years to create such a machine, but they have been unsuccessful.

## Summary

The usefulness of a machine is determined by its efficiency. A machine converts the force provided from an input energy into output work. The Law of Conservation of Energy requires that the total input energy must equal the total output energy.

According to the *Law of Conservation of Energy*, the total output energy or work must equal the total input energy. However, some of the input energy does not contribute to the output work and is lost to such things as friction and heat.

Examples of machine efficiency include a lever, automobile, and perpetual motion machine.

Use science to make things more efficient

## Resources and references

### Websites

**The Efficiency of Machines** (PDF) - Carolina Curriculum

**Mechanical Efficiency** - Wikipedia

### Books

**Top-rated books on Simple Machines**

## Questions and comments

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## Efficiency of Machines