Chapter 3 Mechanical Advantage

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Chapter 3 Mechanical Advantage Efficiency
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Simple Machinesat Work

• Simple machines are used to make a task easier
  via
• Changing the direction of the force

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• Magnifying the force by increasing the distance

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Mechanical Advantage

• States how many times the machine multiplies the
  force put into the machine
• Determined by a dimensionless ratio of
• work output to work input (AMA)
• the resistance force vs. the effort force (AMA)
• distance the effort is applied vs.
  distance the resistance is
  moved (IMA)
• distance of the effort arm vs.
  distance of the resistance arm
  (IMA)
• or for a pulley, the number of supporting strings
  (IMA)

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y
x
?y ?x
?x
x2
y2
y m(x)
m
?y
Students can now solve for any unknown x to get
the Effort Force needed
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y m(x)
1.95
2.93
3.92
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y m(x)
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y m(x)
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LEVER SYSTEMS Everyone Loves Their MA
Suppose that you need to move a large rock, but
it is too heavy for you to lift. You found a long
bar and a small rock. Use the objects below to
sketch a lever system that you might use to move
the large rock.
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A parent and a small child visit the playground.
They both get on a see-saw (teeter-totter) and
arrange it so that the see-saw balances
perfectly. Sketch how this might look. Explain
your thinking.
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• Where have you seen or experienced levers in
  action?
• Do you think all lever systems make a task easier?

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Preliminary Experiences

• Obtain your equipment and create as many lever
  systems as possible
• For each system you create, record a detailed
  diagram of your system and a qualitative
  description of the force needed to move the
  weight
• Pick one system and describe a real world
  application

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Part ALever I
Set up a lever system that looks something like
this. Collect data and find a function that seems
to fit your data.
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Part ALever II
Set up a lever system that looks something like
this. Collect data and find a function that seems
to fit your data.
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Part ALever III
Set up a lever system that looks something like
this. Collect data and find a function that seems
to fit your data.
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Part ALever IV
Set up a lever system that looks something like
this. Collect data and find a function that seems
to fit your data.
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Part B

• Compute MAs for the lever systems in part A
• Come up with a rule for how the location of the
  fulcrum is related to MA
• Come up with a rule for how MA relates to how
  much force you must exert to lift a heavy weight
  using levers
• Compare the MAs you computed

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Part C

• Calculate the efficiencies of the lever systems
  you worked with earlier

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• Determine the MA of the lever system using the
  distances indicated in the diagram. Review your
  earlier information if necessary. Show all your
  work.
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• Determine the MA of the lever system using the
  forces indicated in the table. Review your
  earlier information if necessary. Show all your
  work.
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• Calculate the efficiency of the lever system.
  Show all work.

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Solve each of the following problems at least two
different ways. Explain how you got each
answer. How much force would need to be applied
to this lever system in order to lift a weight
of 125N?     If you pull up with the force probe
a distance of 25 cm, how much will the weight be
lifted?
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• The human body is quite an efficient machine,
  and contains several examples of lever systems.
  Your forearm is a 3rd class lever. The elbow
  serves as a fulcrum, the hand supports the weight
  and the biceps muscle exerts the effort force.
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• How do you think the force exerted by your
  biceps muscle compares with the weight that you
  lift with your hand? Explain your reasoning.

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• Bend your elbow to raise
• and lower your forearm.
• Feel in front of your elbow
• to determine where the
• muscle attaches to the bone.
• Note the distance from the elbow.

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• Place a known weight in your hand, then bend
  your elbow to raise your forearm. Your task is to
  determine how much force your biceps muscle must
  exert to raise the weight. Take any measurements
  of your arm that you feel appropriate. Be sure to
  clearly explain your thinking and show all
  calculations. Feel free to add diagrams. Comment
  on what you notice regarding forces and
  distances.
• List any other examples of a 3rd class lever
  that you have seen.