Machines

1
Machines
2

• A simple machine is any device which will change
  the direction or magnitude of a FORCE.
• MACHINES ARE NOT ABLE TO REDUCE THE AMOUNT OF
  WORK THAT WILL BE REQUIRED TO DO SOMETHING. IN
  FACT, IF FRICTION IS CONSIDERED, A MACHINE WILL
  ALWAYS REQUIRE MORE WORK THAN THE SAME JOB DONE
  WITHOUT A MACHINE.

3

• Machines change the magnitude of a force by
  allowing a smaller force to act for a larger
  distance than would be possible without the
  machine.

4

• For example, consider an inclined plane 5 meters
  long that lifts a 10 N object 2 meters.
• Without friction work out work in Fd
  fD (10N)(2m)(f)(5m)
• With friction work out lt work in Fd lt
  fD (10N)(2m)lt(f)(5m)

5

• Mechanical Advantage is a non dimensional number
  which tells us by what factor the machine
  multiplies our input force.
• Ideally (in a situation without friction) we
  could calculate the mechanical advantage just by
  looking at the ratio of the distances found
  within a machine.

6

• There are many types of simple machines which
  make up mechanical systems
• Inclined planes (ramps, wedges, screws)
• pulleys
• levers
• gears
• wheels

7
Ramps (Inclined Planes)

• MA Fout / Fin
• MA din / dout
• MA length/ height

8
Ramps (Inclined Planes)

• Screws are actually incline planes, just rotating
• MA Fout / Fin
• MA din / dout
• MA length/ height

9
Pulleys

• MA of strings that support the bottom pulley

10
Levers

• First-Class Lever
• (pliers, see-saws, etc)
• Second-Class Lever
• (wheelbarrow, nutcracker, etc)
• Third-Class lever
• (biceps, tweezers, broom, fishing pole)

11
Levers

• MA Lin / Lout
• L lever arm (distance to fulcrum)
• MA Fout / Fin
• (load refers to out and effort refers to in)

12
Gears

• Instead of force and distance, gears affect
  torque and angular displacement

13
Gears

• Gear ratio output turns / input turns
• Gear ratio input torque / output torque

14
Gears

• MA 1 / gear ratio
• MA input turns/ of output turns
• MA teeth out / of teeth in

15
Wheels

• MA diameterwheel / diameteraxle
• MA circumfwheel / circumfaxle
• There is proportionally less friction on the axle
  then if the wheel slid along the ground

16
Efficiency

• Work in is the amount of work that is put into
  the machine by the energy source. This is often
  a person or a fuel.
• Work out is the amount of work that is done on
  some object by the machine.
• Efficiency tells us how much of the work which is
  put into a machine is actually applied to the
  object by the machine.

17
Efficiency

• With no friction, efficiency 100 meaning that
  all the work put in comes out on the object. With
  friction, efficiencylt 100 meaning that some of
  the work in is lost to friction.
• Efficiency work out / work in

18
Efficiency

• For example, with the above inclined plane
• ideal mechanical advantage din/dout
  5m/2m2.5
• This means that ideally we should get out 2.5
  times more force than we put in.

19
Efficiency

• Because of friction, the actual mechanical
  advantage will be less than if friction were
  absent, and has to be determined experimentally
  using the input and output forces.
• Using the early example of the ramp, the actual
  mechanical advantage Fout /Fin 10N/(gt4N)
  lt2.5
• This means that in actuality we will get out less
  than 2.5 times more force than we put in

20
Efficiency

• We can use the two mechanical advantages to find
  efficiency also.
• Efficiency (actual mech. advan.)/(ideal mech.
  advan.)
• Efficiency can also be defined by the ratio of
  Energy in to Energy out