section_path: Ideal simple machine
section_name: Ideal simple machine
paragraph_text: Ideal simple machine
  
  If a simple machine does not dissipate energy through friction, wear or deformation, then energy is conserved and it is called an ideal simple machine. In this case, the power into the machine equals the power out, and the mechanical advantage can be calculated from its geometric dimensions.
  
  Although each machine works differently mechanically, the way they function is similar mathematically. In each machine, a force F in {\displaystyle F_{\text{in}}} is applied to the device at one point, and it does work moving a load F out {\displaystyle F_{\text{out}}} at another point. Although some machines only change the direction of the force, such as a stationary pulley, most machines multiply the magnitude of the force by a factor, the mechanical advantage
  
  M A = F out F in {\displaystyle \mathrm {MA} ={F_{\text{out}} \over F_{\text{in}}}}
  
  that can be calculated from the machine's geometry and friction.
  
  Simple machines do not contain a source of energy, so they cannot do more work than they receive from the input force. A simple machine with no friction or elasticity is called an ideal machine. Due to conservation of energy, in an ideal simple machine, the power output (rate of energy output) at any time P out {\displaystyle P_{\text{out}}} is equal to the power input P in {\displaystyle P_{\text{in}}}
  
  P out = P in {\displaystyle P_{\text{out}}=P_{\text{in}}\!}
  
  The power output equals the velocity of the load v out {\displaystyle v_{\text{out}}\,} multiplied by the load force P out = F out v out {\displaystyle P_{\text{out}}=F_{\text{out}}v_{\text{out}}\,}. Similarly the power input from the applied force is equal to the velocity of the input point v in {\displaystyle v_{\text{in}}\,} multiplied by the applied force P in = F in v in {\displaystyle P_{\text{in}}=F_{\text{in}}v_{\text{in}}\!}. Therefore,
  
  F out v out = F in v in {\displaystyle F_{\text{out}}v_{\text{out}}=F_{\text{in}}v_{\text{in}}\,}
  
  So the mechanical advantage of an ideal machine M A ideal {\displaystyle \mathrm {MA} _{\text{ideal}}\,} is equal to the velocity ratio, the ratio of input velocity to output velocity
  
  M A ideal = F out F in = v in v out {\displaystyle \mathrm {MA} _{\text{ideal}}={F_{\text{out}} \over F_{\text{in}}}={v_{\text{in}} \over v_{\text{out}}}\,}
  
  The velocity ratio is also equal to the ratio of the distances covered in any given period of time
  
  v out v in = d out d in {\displaystyle {v_{\text{out}} \over v_{\text{in}}}={d_{\text{out}} \over d_{\text{in}}}}
  
  Therefore, the mechanical advantage of an ideal machine is also equal to the distance ratio, the ratio of input distance moved to output distance moved
  
  M A ideal = F out F in = d in d out {\displaystyle \mathrm {MA} _{\text{ideal}}={F_{\text{out}} \over F_{\text{in}}}={d_{\text{in}} \over d_{\text{out}}}\,}
  
  This can be calculated from the geometry of the machine. For example, the mechanical advantage and distance ratio of the lever is equal to the ratio of its lever arms.
  
  The mechanical advantage can be greater or less than one:
  
  In the screw, which uses rotational motion, the input force should be replaced by the torque, and the velocity by the angular velocity the shaft is turned.