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Levers	
  
h(ps://www.youtube.com/watch?
v=YlYEi0PgG1g	
  
	
  
Levers	
  
A	
  lever	
  is	
  a	
  rigid	
  rod	
  that	
  rotates	
  around	
  one	
  
point	
  to	
  move	
  a	
  load	
  by	
  applying	
  a	
  force	
  to	
  a	
  
third	
  point.	
  
Archimedes	
  worked	
  out	
  how	
  things	
  balance	
  
M	
  
M	
  M	
   M	
  
M	
   M	
  
M	
  
M	
   M	
  
Balance	
  occurs	
  when	
  moments	
  
are	
  equal	
  and	
  opposite.	
  
M1	
  
M2	
  
M1D1	
  =	
  M2D2	
  
D1	
   D2	
  
Law	
  of	
  the	
  Lever	
  
The	
  masses	
  are	
  applying	
  a	
  
downward	
  force	
  on	
  the	
  lever	
  
with	
  their	
  weight	
  –	
  which	
  is	
  a	
  
force.	
  So	
  the	
  simple	
  idea	
  of	
  
balancing	
  weights	
  on	
  a	
  pivot	
  
reveals	
  how	
  forces	
  act	
  on	
  a	
  
lever.	
  
F1	
  
F2	
  
F1D1	
  =	
  F2D2	
  
D1	
   D2	
  
Three
Classes of
Levers
“First Class Lever”
•  A first-class lever is a lever in
which the fulcrum is located
between the input effort and the
output load.
•  In operation, a force is applied
(by pulling or pushing) to a
section of the bar, which causes
the lever to swing about the
fulcrum, overcoming the
resistance force on the opposite
side.
Examples:
• Seesaw
• Scissors (double
lever)
Classes of Levers
 
	
  
Fulcrum	
  is	
  between	
  FE	
  (effort	
  force)	
  and	
  FL	
  (load	
  force)	
  
When	
  the	
  effort	
  moves	
  farther	
  than	
  load,	
  the	
  Mechanical	
  advantage	
  >1	
  
When	
  the	
  effort	
  moves	
  less	
  than	
  the	
  load,	
  the	
  Mechanical	
  Advantage	
  <	
  1	
  	
  
	
  
	
  
First Class LeverEffort	
  Force	
  
Load	
  Force	
  F	
  L	
  
F	
  E	
  
Lets	
  apply	
  the	
  Law	
  of	
  the	
  Lever	
  
Mechanical	
  Advantage	
  =	
  FL/FE	
  
	
  
What	
  is	
  the	
  Mechanical	
  Advantage	
  
of	
  this	
  lever?	
  
Load	
  
F1D1	
  =	
  F2D2	
  
D1	
   D2	
  
Effort	
  
Force	
  
10N	
  
D1	
  =	
  50cm	
   D2	
  =	
  10cm	
  
What	
  force	
  of	
  a	
  load	
  could	
  be	
  liXed?	
  
What	
  happens	
  if	
  the	
  effort	
  is	
  closer	
  to	
  
the	
  pivot	
  than	
  the	
  load?	
  
Mechanical	
  Advantage	
  =	
  FL/FE	
  
	
  
What	
  is	
  the	
  Mechanical	
  Advantage	
  
of	
  this	
  lever?	
  
Load	
  
F1D1	
  =	
  F2D2	
  
D1	
   D2	
  
Effort	
  
Force	
  
10N	
  
D1	
  =	
  10cm	
   D2	
  =	
  50cm	
  
What	
  force	
  of	
  a	
  load	
  could	
  be	
  liXed?	
  
The	
  mechanical	
  advantage	
  of	
  a	
  lever	
  is	
  the	
  raYo	
  
of	
  the	
  length	
  of	
  the	
  lever	
  on	
  the	
  applied	
  effort	
  
side	
  of	
  the	
  fulcrum	
  to	
  the	
  length	
  of	
  the	
  lever	
  on	
  
the	
  load	
  force	
  side	
  of	
  the	
  fulcrum.	
  
Load	
  	
  
DE	
   DL	
  
Effort	
  
Force	
  
MA	
  =	
  DE/DL	
  
Common examples
of first-class
levers include 
– crowbars, 
– scissors, 
– pliers, 
– tin snips 
– and seesaws. 

Examples	
  of	
  first	
  class	
  levers	
  
Load	
  is	
  between	
  fulcrum	
  and	
  Effort	
  	
  
Effort	
  moves	
  farther	
  than	
  Load.	
  	
  
MulYplies	
  Effort	
  Force,	
  but	
  does	
  not	
  change	
  its	
  direcYon	
  	
  
	
  The	
  mechanical	
  advantage	
  of	
  a	
  2nd	
  class	
  lever	
  is	
  always	
  greater	
  
than	
  1	
  
	
  
Second Class Lever
Load	
  
Effort	
  Force	
  
Explanation
•  Second	
  class	
  lever	
  
–  Load	
  is	
  located	
  between	
  the	
  effort	
  force	
  and	
  the	
  fulcrum.	
  	
  
–  Always	
  mulYplies	
  a	
  force	
  
–  Example:	
  Wheelbarrow	
  
L E
Always	
  mulYplies	
  a	
  force.	
  
•  Examples of
second-class
levers include:
•  nut crackers, 
•  wheel barrows, 
•  doors, 
•  and bottle
openers.	
Examples	
  of	
  second-­‐class	
  levers	
  
Evaluate	
  the	
  Lever	
  
Mechanical	
  Advantage	
  =	
  FL/FE	
  
	
  
Mechanical	
  Advantage	
  =	
  DE/DL	
  
	
  
What	
  is	
  the	
  Mechanical	
  Advantage	
  of	
  this	
  
lever?	
  
Load	
  
DE	
  
DL	
  
Effort	
  
Force	
  
10N	
  
DE	
  =	
  80cm	
   DL	
  =	
  20cm	
  
What	
  force	
  of	
  a	
  load	
  could	
  be	
  liXed?	
  
Effort	
  is	
  between	
  fulcrum	
  and	
  Load.	
  
Does	
  not	
  mulYply	
  force	
  	
  
Load	
  moves	
  farther	
  than	
  Effort.	
  	
  
MulYplies	
  the	
  distance	
  the	
  effort	
  force	
  travels	
  and	
  the	
  speed	
  at	
  which	
  
it	
  moves.	
  
	
  The	
  mechanical	
  advantage	
  of	
  a	
  3rd	
  class	
  lever	
  is	
  always	
  less	
  than	
  1.	
  
Third Class Lever
LE
•  For this class of levers, the input
effort is higher than the output
load, which is different from
second-class levers and some
first-class levers.
•  However, the distance moved by
the load is greater than the
distance moved by the effort.
•  In third class levers, effort is
applied between the output load
on one end and the fulcrum on
the opposite end.
“Third Class Lever”
Examples:
• Hockey Stick
• Tweezers
• Fishing Rod
Classes	
  of	
  Levers	
  
Explanation
•  Third	
  class	
  lever	
  
–  Effort	
  force	
  located	
  between	
  the	
  load	
  and	
  the	
  fulcrum.	
  	
  
–  Effort	
  arm	
  is	
  always	
  shorter	
  than	
  load	
  arm	
  
–  MA	
  is	
  always	
  less	
  than	
  one	
  
–  Example:	
  Broom	
  
LE
There	
  is	
  an	
  increase	
  distance	
  
moved	
  and	
  speed	
  at	
  the	
  other	
  end.	
  
Other	
  examples	
  are	
  baseball	
  bat	
  or	
  
hockey	
  sYck.	
  
Examples of Third Class Levers
•  Examples of
third-class
levers include:
–  tweezers, 
– arm hammers, 
– and shovels.
Third class lever in
human body.
Evaluate	
  the	
  Lever	
  
Mechanical	
  Advantage	
  =	
  FL/FE	
  
	
  
Mechanical	
  Advantage	
  =	
  DE/DL	
  
	
  
What	
  is	
  the	
  Mechanical	
  Advantage	
  of	
  this	
  
lever?	
  
Load	
  
DE	
  
DL	
  
Effort	
  
Force	
  
10N	
  
DE	
  =	
  20cm	
   DL	
  =	
  80cm	
  
What	
  force	
  of	
  a	
  load	
  could	
  be	
  liXed?	
  
Mechanical	
  Advantage	
  
•  Mechanical	
  Advantage	
  is	
  the	
  raYo	
  between	
  the	
  
load	
  and	
  effort.	
  	
  	
  
•  Mechanical	
  Advantage	
  	
  deals	
  only	
  with	
  forces.	
  
•  Mechanical	
  Advantage	
  	
  >	
  1	
  means	
  that	
  the	
  
output	
  force	
  will	
  be	
  greater	
  than	
  the	
  input	
  force.	
  	
  
–  (But	
  the	
  input	
  distance	
  will	
  need	
  to	
  be	
  greater	
  than	
  
the	
  output	
  distance.)	
  
• First and Second class levers have a positive mechanical
advantage.
• Third class levers have a mechanical disadvantage,
meaning you use more force that the force of the load you
lift.
Mechanical	
  Advantage	
  
Movement	
  Ra=o	
  
•  Movement	
  RaYo	
  deals	
  with	
  the	
  distance	
  
gained	
  or	
  lost	
  due	
  to	
  a	
  mechanical	
  advantage.	
  
•  Movement	
  RaYo	
  	
  >1	
  means	
  that	
  the	
  input	
  
distance	
  (or	
  effort)	
  to	
  move	
  a	
  load	
  will	
  be	
  
greater	
  than	
  the	
  output	
  distance	
  of	
  the	
  load.	
  	
  	
  
Mechanical Advantage: Example
Mechanical Advantage =
effort arm
resistance arm
Crazy Joe is moving bricks to build his cabin.
With the use of his simple machine, a lever, he moves
them easily.
The “effort arm” of his wheel barrow is 4ft., while the
resistance arm of his wheelbarrow is 1 ft.

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Levers notes

  • 2. Levers   A  lever  is  a  rigid  rod  that  rotates  around  one   point  to  move  a  load  by  applying  a  force  to  a   third  point.  
  • 3. Archimedes  worked  out  how  things  balance   M   M  M   M   M   M   M   M   M   Balance  occurs  when  moments   are  equal  and  opposite.   M1   M2   M1D1  =  M2D2   D1   D2  
  • 4. Law  of  the  Lever   The  masses  are  applying  a   downward  force  on  the  lever   with  their  weight  –  which  is  a   force.  So  the  simple  idea  of   balancing  weights  on  a  pivot   reveals  how  forces  act  on  a   lever.   F1   F2   F1D1  =  F2D2   D1   D2  
  • 6. “First Class Lever” •  A first-class lever is a lever in which the fulcrum is located between the input effort and the output load. •  In operation, a force is applied (by pulling or pushing) to a section of the bar, which causes the lever to swing about the fulcrum, overcoming the resistance force on the opposite side. Examples: • Seesaw • Scissors (double lever) Classes of Levers
  • 7.     Fulcrum  is  between  FE  (effort  force)  and  FL  (load  force)   When  the  effort  moves  farther  than  load,  the  Mechanical  advantage  >1   When  the  effort  moves  less  than  the  load,  the  Mechanical  Advantage  <  1         First Class LeverEffort  Force   Load  Force  F  L   F  E  
  • 8. Lets  apply  the  Law  of  the  Lever   Mechanical  Advantage  =  FL/FE     What  is  the  Mechanical  Advantage   of  this  lever?   Load   F1D1  =  F2D2   D1   D2   Effort   Force   10N   D1  =  50cm   D2  =  10cm   What  force  of  a  load  could  be  liXed?  
  • 9. What  happens  if  the  effort  is  closer  to   the  pivot  than  the  load?   Mechanical  Advantage  =  FL/FE     What  is  the  Mechanical  Advantage   of  this  lever?   Load   F1D1  =  F2D2   D1   D2   Effort   Force   10N   D1  =  10cm   D2  =  50cm   What  force  of  a  load  could  be  liXed?  
  • 10. The  mechanical  advantage  of  a  lever  is  the  raYo   of  the  length  of  the  lever  on  the  applied  effort   side  of  the  fulcrum  to  the  length  of  the  lever  on   the  load  force  side  of  the  fulcrum.   Load     DE   DL   Effort   Force   MA  =  DE/DL  
  • 11. Common examples of first-class levers include – crowbars, – scissors, – pliers, – tin snips – and seesaws. Examples  of  first  class  levers  
  • 12. Load  is  between  fulcrum  and  Effort     Effort  moves  farther  than  Load.     MulYplies  Effort  Force,  but  does  not  change  its  direcYon      The  mechanical  advantage  of  a  2nd  class  lever  is  always  greater   than  1     Second Class Lever Load   Effort  Force  
  • 13. Explanation •  Second  class  lever   –  Load  is  located  between  the  effort  force  and  the  fulcrum.     –  Always  mulYplies  a  force   –  Example:  Wheelbarrow   L E Always  mulYplies  a  force.  
  • 14. •  Examples of second-class levers include: •  nut crackers, •  wheel barrows, •  doors, •  and bottle openers. Examples  of  second-­‐class  levers  
  • 15. Evaluate  the  Lever   Mechanical  Advantage  =  FL/FE     Mechanical  Advantage  =  DE/DL     What  is  the  Mechanical  Advantage  of  this   lever?   Load   DE   DL   Effort   Force   10N   DE  =  80cm   DL  =  20cm   What  force  of  a  load  could  be  liXed?  
  • 16. Effort  is  between  fulcrum  and  Load.   Does  not  mulYply  force     Load  moves  farther  than  Effort.     MulYplies  the  distance  the  effort  force  travels  and  the  speed  at  which   it  moves.    The  mechanical  advantage  of  a  3rd  class  lever  is  always  less  than  1.   Third Class Lever LE
  • 17. •  For this class of levers, the input effort is higher than the output load, which is different from second-class levers and some first-class levers. •  However, the distance moved by the load is greater than the distance moved by the effort. •  In third class levers, effort is applied between the output load on one end and the fulcrum on the opposite end. “Third Class Lever” Examples: • Hockey Stick • Tweezers • Fishing Rod Classes  of  Levers  
  • 18. Explanation •  Third  class  lever   –  Effort  force  located  between  the  load  and  the  fulcrum.     –  Effort  arm  is  always  shorter  than  load  arm   –  MA  is  always  less  than  one   –  Example:  Broom   LE There  is  an  increase  distance   moved  and  speed  at  the  other  end.   Other  examples  are  baseball  bat  or   hockey  sYck.  
  • 19. Examples of Third Class Levers •  Examples of third-class levers include: –  tweezers, – arm hammers, – and shovels. Third class lever in human body.
  • 20. Evaluate  the  Lever   Mechanical  Advantage  =  FL/FE     Mechanical  Advantage  =  DE/DL     What  is  the  Mechanical  Advantage  of  this   lever?   Load   DE   DL   Effort   Force   10N   DE  =  20cm   DL  =  80cm   What  force  of  a  load  could  be  liXed?  
  • 21. Mechanical  Advantage   •  Mechanical  Advantage  is  the  raYo  between  the   load  and  effort.       •  Mechanical  Advantage    deals  only  with  forces.   •  Mechanical  Advantage    >  1  means  that  the   output  force  will  be  greater  than  the  input  force.     –  (But  the  input  distance  will  need  to  be  greater  than   the  output  distance.)  
  • 22. • First and Second class levers have a positive mechanical advantage. • Third class levers have a mechanical disadvantage, meaning you use more force that the force of the load you lift. Mechanical  Advantage  
  • 23. Movement  Ra=o   •  Movement  RaYo  deals  with  the  distance   gained  or  lost  due  to  a  mechanical  advantage.   •  Movement  RaYo    >1  means  that  the  input   distance  (or  effort)  to  move  a  load  will  be   greater  than  the  output  distance  of  the  load.      
  • 24. Mechanical Advantage: Example Mechanical Advantage = effort arm resistance arm Crazy Joe is moving bricks to build his cabin. With the use of his simple machine, a lever, he moves them easily. The “effort arm” of his wheel barrow is 4ft., while the resistance arm of his wheelbarrow is 1 ft.