Editing Simple machine (section)

==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.<ref>This fundamental insight was the subject of Galileo Galilei's 1600 work {{lang|it|Le Meccaniche}} (''On Mechanics'').</ref> In each machine, a force <math>F_\text{in}</math> is applied to the device at one point, and it does [[Mechanical work|work]] moving a load <math>F_\text{out}</math> at another point.<ref name="Bhatnagar">{{cite book
  | last = Bhatnagar
  | first = V. P.
  | title = A Complete Course in Certificate Physics
  | publisher = Pitambar
  | year = 1996
  | location = India
  | pages = 28–30
  | url = https://books.google.com/books?id=pb45yhuNltEC&q=%22simple+machine%22+%22&pg=PA28
  | isbn = 978-81-209-0868-0}}</ref> 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]]

<math display="block">\mathrm{MA} = {F_\text{out} \over F_\text{in}}</math>

that can be calculated from the machine's geometry and friction.

Simple machines do not contain a source of [[energy]],<ref name="Simmons">{{cite book
  | last1 = Simmons
  | first1 = Ron
  | last2 = Cindy
  | first2 = Barden
   | title = Discover! Work & Machines
  | publisher = Milliken
  | year = 2008
  | location = US
  | pages = 29
  | url = https://books.google.com/books?id=geddKUGjI3cC&q=%22simple+machine%22+%22mechanical+advantage%22&pg=PA30
  | isbn = 978-1-4291-0947-5}}</ref> so they cannot do more [[Mechanical work|work]] than they receive from the input force.<ref name="Bhatnagar" /> A simple machine with no [[friction]] or [[Elasticity (physics)|elasticity]] is called an ''ideal machine''.<ref name="Gujral">{{cite book
  | last = Gujral
  | first = I. S.
  | title = Engineering Mechanics
  | publisher = Firewall Media
  | year = 2005
  | pages = 378–380
  | url = https://books.google.com/books?id=JM0OG-XUyu0C&q=%22simple+machine%22+self-locking&pg=PA382
  | isbn = 978-81-7008-636-9}}</ref><ref name="Uicker2003">{{Citation | first1=John J. Jr. | last1=Uicker |first2=Gordon R. |last2=Pennock |first3=Joseph E. |last3=Shigley |year=2003 |title=Theory of Machines and Mechanisms |edition=third |publisher=Oxford University Press |location=New York |isbn=978-0-19-515598-3 }}</ref><ref>{{cite book |first=Burton |last=Paul |year=1979 |title=Kinematics and Dynamics of Planar Machinery |publisher=Prentice Hall |isbn=978-0-13-516062-6 }}</ref> Due to [[conservation of energy]], in an ideal simple machine, the power output (rate of energy output) at any time <math>P_\text{out}</math> is equal to the power input <math>P_\text{in}</math>

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

The power output equals the velocity of the load <math>v_\text{out}\,</math> multiplied by the load force <math>P_\text{out} =  F_\text{out} v_\text{out}\,</math>. Similarly the power input from the applied force is equal to the velocity of the input point <math>v_\text{in}\,</math> multiplied by the applied force <math>P_\text{in} =  F_\text{in} v_\text{in}\!</math>. Therefore,

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

So the mechanical advantage of an ideal machine <math>\mathrm{MA}_\text{ideal}\,</math> is equal to the ''velocity ratio'', the ratio of input velocity to output velocity

<math display="block">\mathrm{MA}_\text{ideal} = {F_\text{out} \over F_\text{in}} = {v_\text{in} \over v_\text{out}}\,</math>

The ''velocity ratio'' is also equal to the ratio of the distances covered in any given period of time<ref name="Rao1">{{cite book
 | last1  = Rao
 | first1 = S.
 | last2  = Durgaiah
 | first2 = R.
 | title  = Engineering Mechanics
 | publisher = Universities Press
 | date   = 2005
 | pages  = 80
 | url    = https://books.google.com/books?id=vRR4FKAkJl4C&q=%22simple+machine%22+%22velocity+ratio%22+distance&pg=PA80
 | isbn   = 978-81-7371-543-3
 }}</ref><ref name="Goyal1">{{cite book
 | last1  = Goyal
 | first1 = M. C.
 | last2  = Raghuvanshee
 | first2 = G. S.
 | title  = Engineering Mechanics
 | publisher = PHI Learning
 | date   = 2011
 | page  = 212
 | url    = https://books.google.com/books?id=qNPE9RVkSTUC&q=%22simple+machine%22+%22velocity+ratio%22+distance&pg=PA212
 | isbn   = 978-81-203-4327-6
 }}</ref><ref name="Avison">{{cite book
 | last1  = Avison
 | first1 = John
 | title  = The World of Physics
 | publisher = Nelson Thornes
 | date   = 2014
 | page  = 110
 | url    = https://books.google.com/books?id=DojwZzKAvN8C&q=machine+%22velocity+ratio%22+%22distance+ratio%22&pg=PA110
 | isbn   = 978-0-17-438733-6
 }}</ref>

<math display="block">{v_\text{out} \over v_\text{in}} = {d_\text{out} \over d_\text{in}}</math>

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
{{Equation box 1
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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 arm]]s.

The mechanical advantage can be greater or less than one:
* If <math>\mathrm{MA} > 1\,</math>, the output force is greater than the input, the machine acts as a force amplifier, but the distance moved by the load <math>d_\text{out}</math> is less than the distance moved by the input force <math>d_\text{in}\,</math>.
* If <math>\mathrm{MA} < 1\,</math>, the output force is less than the input, but the distance moved by the load is greater than the distance moved by the input force.

In the [[screw (simple machine)|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.