Editing Simple machine (section)

==Friction and efficiency==
All real machines have friction, which causes some of the input power to be dissipated as heat. If <math>P_\text{fric}\,</math> is the power lost to friction, from conservation of energy

<math display="block">P_\text{in} = P_\text{out} + P_\text{fric}</math>

The [[mechanical efficiency]] <math>\eta</math> of a machine (where <math> 0 < \eta \ < 1</math>) is defined as the ratio of power out to the power in, and is a measure of the frictional energy losses

<math display="block">\begin{align}
\eta & \equiv {P_\text{out} \over P_\text{in}} \\
P_\text{out} & = \eta P_\text{in}
\end{align}</math>

As above, the power is equal to the product of force and velocity, so

<math display="block">F_\text{out} v_\text{out}  =  \eta F_\text{in} v_\text{in}</math>

Therefore,
{{Equation box 1  |cellpadding = 0 |border = 1 |border colour = black |background colour = transparent  |indent =:
|equation = <math>\mathrm{MA} = {F_\text{out} \over F_\text{in}} = \eta {v_\text{in} \over v_\text{out}}</math>
}}
So in non-ideal machines, the mechanical advantage is always less than the velocity ratio by the product with the efficiency <math>\eta</math>. So a machine that includes friction will not be able to move as large a load as a corresponding ideal machine using the same input force.