Mechanical Advantage

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Mechanical Advantage Effeciency
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Objectives

• Explain how a machine makes work easier
• Describe and give examples of the force-distance
  trade-off that occurs when a machine is used
• Describe Calculate mechanical advantage
• Describe Calculate effeciency
• Explain why machines are not 100 efficient

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What is a machine?

• Machines make work easier by
• Changing the amount of force you exert
• Changing the distance over which you exert the
  force
• Changing the direction the force is exerted

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Which is easier?
Opening a paint can with your fingers?
Opening a paint can with a screwdriver?
OR
The force is multiplied and redirected.
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Which is easier?
Pushing a heavy box up a ramp into a truck?
Lifting a heavy box into a truck?
OR
The force is both multiplied and redirected.
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When using a machine to do work, two forces are
involved.

• Input Force (Fin)
• The force you apply to the machine in doing work
  (Win)
• Output Force (Fout)
• The force that the machine applies in doing work
  (Wout)

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Two types of work are involved.

• Work input is the amount of work done on a
  machine.
• Input force x input distance
• Work output is the amount of work done by a
  machine.
• Output force x output distance

• Ideally, without friction
• Win Wout
• (Fin) (din) (Fout) (dout)

How are the two related?
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Force-distance trade-off

• To decrease the force needed, increase the
  distance
• To increase the force needed, decrease the
  distance
• Examples wheelbarrow and hammer

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Force-Distance Trade-off (increases force)

• Wheel barrow
• Small force in a greater distance (lift handle
  of wheelbarrow)
• Large force applied a shorter distance (load in
  wheelbarrow lifted)

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Force-Distance Trade-off (decreases force)

• Hammer
• Large force applied over a short distance
• Small force applied over a long distance

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Measuring the benefits Mechanical Advantage

• Mechanical Advantage tells you how many times the
  machine multiples the force.
• a machine with a large mechanical advantage can
  make lifting a heavy load easier

Actual Mechanical Advantage (Reality) AMA
(Fout)/(Fin)
Ideal Mechanical Advantage (No Friction) IMA
(din)/(dout)
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Calculating Mechanical Advantage

1. What is the mechanical advantage of a machine
   that applies 200N to an object when you apply 50N
   to the machine?

Equation MA (Fout)/(Fin)
MA (200N)/(50N) MA 4
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Calculating Mechanical Advantage

• You apply 2000 N to a machine and the machine
  applies 200 N to an object. What is the
  mechanical advantage?

Equation MA (Fout)/(Fin)
MA (200N)/(2000N) MA 0.1
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Calculating Mechanical Advantage

• You apply 10 N to a machine and the machine
  applies 10 N to another object. What is the
  mechanical advantage.

Equation MA (Fout)/(Fin)
MA (10N)/(10N) MA 1
Can such a machine be useful?
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Mechanical AdvantageWhat does it mean?

• Mechanical Advantage 1
• There is no advantage to using the machine
• Mechanical Advantage gt 1
• The machine makes work easier
• Mechanical Advantage lt 1
• The machine makes work harder

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Efficiency

• We said that the input work equals the output
  work, or
• Win Wout
• However, some output work is lost due to
  friction.
• The comparison of work input to work output is
  called efficiency.
• No machine has 100 percent efficiency due to
  friction.
• What would improve the efficiency of a machine?
  (Hint What reduces friction?)

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Calculating Efficiency

• How efficient is a machine that takes 40 J of
  work and produces 30 J of work?

Equation Eff (Wout)/(Win) X 100
Eff (30J)/(40J) X 100 Eff 75
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Calculating Efficiency

• You do 250,000 J of work to cut a lawn with a
  hand mower. If the work done by the mower is
  200,000 J, what is the efficiency of the lawn
  mower?

Equation Eff (Wout)/(Win) X 100
Eff (200,000J)/(250,000J) X 100 Eff 80