A major factor in the usefulness of a machine is its efficiency.

A machine converts the force provided from an input energy into motion that changes the magnitude or direction of that force. This motion against a resistive force is the work done by the machine. According to the Law of Conservation of Energy, the total input energy must equal the total output energy. However, some of the output energy does not contribute to the output work and is lost to such things as friction and heat.

The efficiency of a machine is the ratio of the input energy to the useful output work.

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 You need to know the output work or energy to determine the efficiency of a machine.

The work done by a machine is the distance the force moves the object against the restive force. This output work is designated as:

     Wo = Fd


Wo is the output work

F is the output force to move the object

d is the distance the object moves

For example, a lever will lift a weight against the restive force of gravity.

Since work is equivalent to energy expended and following the Law of Conservation of Energy, the output work should equal the input work or energy:

      Wo = Wi or Wo = Ei


Wi is the input work

Ei is the input energy

But that is true only in an ideal machine. In reality, there are losses to the output from internal friction, heat or other things that take away from the efficiency of the machine.

The real situation is:

    Ei = Wo+ EL

where EL is the energy that is lost.

For example, the energy expended in pushing a box up a ramp is greater than the work done or than the potential energy of having the box at a greater height. This is because useful energy is lost due to the friction of the box sliding along the ramp surface.

Another example is the output work available from a gasoline engine is less than the input energy of the fuel. Much heat energy is wasted and not used in the output.

The efficiency of a machine is the output work or energy divided by the input work or energy.

    Efficiency = Wo/Wi

As an illustration of the losses in all machines, a simple lever loses about 2% of the input energy to internal friction at its fulcrum, such that its efficiency is 98%. If 100 joules of work is input, 98 joules of work is the output.

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.