10.2: Machines
And Mechanical Advantage
Machines make work easier
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Machines can change the direction of
force applied.
Machines can change the magnitude of
force applied.
The work you do ON a machine is called
work input, wi
The work done BY the machine is called
work output, wo
Doing work transfers energy.
Conservation of Energy
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Doing work with machines transfers energy
from one source to another.
Work output can NEVER be greater than
work input.
How helpful are machines?
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Effort force, Fe, is the force you exert ON a
machine.
Resistance force, Fr, is the force exerted BY
a machine.
Mechanical Advantage is a ratio comparing
resistance force to effort force. It has no
units.
MA
Fr
Fe
MA by the numbers
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When a machine has a mechanical
advantage >1, the machine increases the
force you apply. (Fe < Fr)
If a machine has a mechanical advantage
of 1, it changes the direction of your
force. (Effort force = Resistance force)
A machine can increase force or distance,
but it can NOT increase energy!
Breaking down work
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Recall work = force x distance.
Work input = Fe x de (dist your hand moves)
Work output = Fr x dr (weight of the object x
distance the object moves)
An IDEAL machine transfers ALL energy so
Wo = Wi or Frdr = Fede
By rewriting this equation as Fr/Fe = de/dr, ideal
MA = de/dr
We measure distances moved for IMA, but
forces exerted for Actual MA.
Efficiency
In real machines, not all work input comes out
as useful work output. Some energy is
converted into thermal energy or “lost” as
heat.
 This decreases the output of the machine.
 Efficiency is a ratio of work output to work
input OR Actual MA to Ideal MA.
Wo
MA
Efficiency (%)
x100 Efficiency(%)
x100
Wi
IMA
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Simple Machines
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The 6 simple machines include: lever, pulley,
inclined plane, wedge, wheel and axle, and
screw.
The IMA of all machines is the ratio of
distances moved.
For levers and wheel and axles, the IMA is the
ratio of effort distances (radius)/ resistance
distances (radius) or re/rr as both machines
have a “fixed” point or fulcrum.
Compound Machines
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A compound machine is a combination of
two or more simple machines linked
together.
The resistance force of one machine
becomes the effort force of the second.
In a bicycle, the pedal and front sprocket
(gear) are like a wheel and axle. Fe is the
force you exert on the pedal and Fr is the
force the front sprocket exerts on the chain.
The chain then exerts an Fe on the rear
wheel sprocket. The Fr is the wheel on the
road.
Compound Mechanical Advantages
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The mechanical advantage of a compound
machine is the product of the MAs of the
simple machines making it up.
MA = MAmachine1 x MAmachine2
For the bicycle:
MA
Fonchain Fonroad
x
Fonpedal Fbychain
Fonroad
Fonpedal
Example Problem
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Look at the bicycle wheel example
problem on page 237.
Fe
re
rr
Fr
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IMA = re/rr
Fr = MA (Fe)
de = IMA(dr)
Machines Applied
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When a cyclist is on a hill, they can
change the mechanical advantage needed
to manipulate the terrain, by choosing the
size of one or both sprockets.
Increasing the IMA increases the force the
wheel exerts on the road. This is good for
climbing a hill or accelerating.
On a level surface, less force is needed so
the rider decreases the IMA by reducing
the distance the pedals move each
revolution.
The “simple” body machine?
Principles of force and work can describe all motion
including our body.
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Lever systems in the body allow us to walk and run.
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Each lever has 4 parts:
1.
A rigid bar (bone)
2.
A source of force (muscle contractions)
3.
A fulcrum or pivot point (joints b/t bones)
4.
A resistance (weight of the body being moved)
These levers are not very efficient so exercise requires
energy.
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Your turn to Practice
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Do Ch 10 Rev p 242 #s 13, 14, 16
Do p 244 #s 48, 51, & 53