section_path: Friction and efficiency
section_name: Friction and efficiency
paragraph_text: Friction and efficiency
  
  All real machines have friction, which causes some of the input power to be dissipated as heat. If P fric {\displaystyle P_{\text{fric}}\,} is the power lost to friction, from conservation of energy
  
  P in = P out + P fric {\displaystyle P_{\text{in}}=P_{\text{out}}+P_{\text{fric}}}
  
  The mechanical efficiency η {\displaystyle \eta } of a machine (where 0 < η < 1 {\displaystyle 0<\eta \ <1}) is defined as the ratio of power out to the power in, and is a measure of the frictional energy losses
  
  η ≡ P out P in P out = η P in {\displaystyle {\begin{aligned}\eta &\equiv {P_{\text{out}} \over P_{\text{in}}}\\P_{\text{out}}&=\eta P_{\text{in}}\end{aligned}}}
  
  As above, the power is equal to the product of force and velocity, so
  
  F out v out = η F in v in {\displaystyle F_{\text{out}}v_{\text{out}}=\eta F_{\text{in}}v_{\text{in}}}
  
  Therefore,
  
  M A = F out F in = η v in v out {\displaystyle \mathrm {MA} ={F_{\text{out}} \over F_{\text{in}}}=\eta {v_{\text{in}} \over v_{\text{out}}}}
  
  So in non-ideal machines, the mechanical advantage is always less than the velocity ratio by the product with the efficiency η {\displaystyle \eta }. 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.