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UNIT D: MECHANICAL
SYSTEMSScience 8
Science 8 Unit D Section 2.0
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AN UNDERSTANDING OF MECHANICAL ADVANTAGE AND WORK HELPS IN
DETERMINING THE EFFICIENCY OF MACHINES.
Section 2.0
Science 8 Unit D Section 2.0
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MACHINES MAKE WORK EASIER
Topic 2.1
Science 8 Unit D Section 2.0
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WHAT WOULD BE EASIER:
DRIVING STRAIGHT UP A
MOUNTAIN?
DRIVING UP A MOUNTAIN
ON ROADS THAT BEND
BACK AND FORTH?
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MACHINES MAKE WORK EASIER
• A machine can make work easier by increasing the
amount of force that you exert on an object.
• A person alone could not exert enough force to lift a
heavy object, such as a car. But using a machine—the
lever—would make it possible. The scientific
explanation is that the lever provided mechanical
advantage.
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#1
MECHANICAL ADVANTAGE
• The mechanical advantage of a machine is the
amount by which a machine can multiply a force.
• The more a machine multiplies force, the greater its
mechanical advantage.
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MECHANICAL ADVANTAGE
• The force applied to the machine is called the input
force.
• The force the machine applies to the object is called
the output force.
• Input and output forces are measured in Newtons.
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CALCULATING MECHANICAL ADVANTAGE
• You can calculate the mechanical advantage of a
machine if you know the input and output forces.
Mechanical Advantage (MA) =𝐎𝐮𝐭𝐩𝐮𝐭 𝐟𝐨𝐫𝐜𝐞
𝐈𝐧𝐩𝐮𝐭 𝐟𝐨𝐫𝐜𝐞=
𝐅𝐨𝐮𝐭
𝐅𝐢𝐧
• The mechanical advantage is actually a ratio of forces
in the mechanical device. For this reason, mechanical
advantage is also called the force ratio of the machine.
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EXAMPLE
It takes 45 N to lift a 180 N
box with a pulley.
What is the mechanical
advantage of the pulley?
• Note: In order to actually
lift the box, you must put
in 45 N = the input force!
MA = Output force
Input force
MA = 180 N
45 N
MA = 4
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#4
SPEED RATIO
• Calculating the speed ratio is another way of analyzing
how machines work.
• Speed measures the distance an object travels in a
given amount of time. A measure of how the speed of
the object is affected by a machine is called the speed
ratio.
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CALCULATING SPEED RATIO
• The speed ratio is calculated by dividing the input
distance by the output distance.
Speed Ratio (SR) = 𝐈𝐧𝐩𝐮𝐭 𝐝𝐢𝐬𝐭𝐚𝐧𝐜𝐞
𝐎𝐮𝐭𝐩𝐮𝐭 𝐝𝐢𝐬𝐭𝐚𝐧𝐞=
𝒅𝐢𝐧
𝒅𝐨𝐮𝐭
• Where d = distance
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#5
EXAMPLE
You lift a weight by
1 m when you pull a
rope attached to a
pulley by 4 m.
What is the speed
ratio of the pulley?
• SR = Input distance
Output distance
• SR =4 m
1 m
• SR = 4
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SPEED RATIO EXPLAINED
The speed ratio of 4 means that the
part of the pulley where you apply
the input force moves four times
faster than the part where the output
force is—the load that you are lifting.
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PULLEYS: LESS FORCE BUT GREATER DISTANCE
• An advantage of pulleys is that they multiply the
force you exert.
• A disadvantage of pulleys is that you have to pull
much farther than the load actually moves.
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THE EFFECT OF FRICTION
• Friction is a force that opposes motion.
• It is caused by the surface roughness of materials.
• A rough surface creates more friction than a smooth
one.
• Friction opposes motion, so an extra force is needed
to overcome friction whenever you move an object.
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EFFICIENCY
• Friction does not affect the speed ratio, but it does
affect the mechanical advantage of a device, so it
also affects its efficiency.
• Efficiency is a measurement of how well a machine or
device uses energy.
Efficiency (%) = 𝐌𝐞𝐜𝐡𝐚𝐧𝐢𝐜𝐚𝐥 𝑨𝒅𝒗𝒂𝒏𝒕𝒂𝒈𝒆
𝐒𝐩𝐞𝐞𝐝 𝑹𝒂𝒕𝒊𝒐× 100
Efficiency (%) = 𝐌𝐀
𝐒𝐑× 100
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#9
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EXAMPLE: CALCULATING EFFICIENCY
A pulley has a speed ratio
of 3 and a mechanical
advantage of 2. Calculate
the % efficiency.
Round your answer to the
nearest hundredth.
• Efficiency (%) = MA
SR× 100
• Efficiency (%) = 2
3× 100
• Efficiency (%) = 66.67%
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#10
HOMEWORK!
• Check and Reflect
• Page 286
• # 2 – 5
• (Reference Book pg. 11)
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THE SCIENCE OF WORK
Topic 2.2
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THE MEANING OF WORK
• In the scientific sense, work is
done when a force acts on an
object to make the object move.
• It’s important to remember that
movement is needed before you
can say that work has been
done.
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HOW MUCH WORK IS BEING DONE?
• The amount of work done depends on two things:
• the amount of force exerted on the object
• the distance the object moved in the direction of
the applied force
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CALCULATING WORK
• The amount of work done can be calculated using the
following formula:
W = F × d
• Where:
• F = Force exerted on an object; measured in
Newtons (N)
• d = distance; measured in metres (m)
• W = Work; measured in Newton∙metre (N∙m), which
is also known as a joule (J).
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EXAMPLE: CALCULATING WORK
• You exert a force of 50 N to lift a
chair onto your desk which is
0.4 m high. How much work did
you do?
• W = F × d
• W = 50 N × 0.4 m
• W = 20 N·m or 20 J
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#13
ENERGY AND WORK
• Energy and work are closely related because without
energy, there would be no work.
• When you ride your bicycle, you exert a force on
the pedals. The force you apply to the pedals causes
the bicycle to move.
• In a car, the energy to drive the wheels comes from
gasoline.
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MACHINES: INPUT VS. OUTPUT
WORK INPUT
• The work input is the
work needed to use or
operate a machine.
Win = Fin × din
WORK OUTPUT
• The work output is the
work done by the
machine.
Wout = Fout × dout
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WORK AND FRICTION
• Recall that a machine’s mechanical advantage does
not equal to speed ratio in real situations. The
reason is friction.
• Friction is also the reason that work input does not
equal work output in real situations. It affects a
machine’s efficiency.
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CALCULATING EFFICIENCY
• Efficiency can also be calculated using work input and
work output.
Efficiency = 𝐖𝐨𝐫𝐤𝒐𝒖𝒕𝒑𝒖𝒕
𝐖𝐨𝐫𝐤𝒊𝒏𝒑𝒖𝒕× 𝟏𝟎𝟎
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#17
EXAMPLE: CALCULATING EFFICIENCY
• A pulley requires an input force of 10.4 N. You pull the
rope 2.0 m. The output force to move an object by 1.0 m
is 20.0 N. What is the efficiency of the pulley? Round to
the nearest percent. (Hint: Solve for Workout and Workin first.)
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#18
Wout = Fout × dout
Wout = (20.0 N) × (1.0 m)
Wout = 20.0 J
Win = Fin × din
Win = (10.4 N) × (2.0 m)
Win = 20.8 J
• Efficiency = Workout
Workin× 100
• Efficiency (%) = 20.0 J
20.8 J× 100 = 96%
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HOMEWORK!
• Check and Reflect
• Page 292
• # 1-4, 6-9
• (Reference Book pg. 13-14)
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THE BIG MOVERS -HYDRAULICS
Topic 2.3
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RECALL: HYDRAULIC SYSTEMS
• Most machines that move very large objects use a
hydraulic system that applies force to levers or gears.
• A hydraulic system uses a liquid under pressure to
move loads. A hydraulic system increases the
mechanical advantage of the levers in machines.
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RECALL: PRESSURE
• Recall that pressure is a measure of the amount of
force applied to a given area. It can be written as an
equation:
p = 𝐹
𝐴
• Where p is pressure, F is force, and A is area. The unit
of measurement for pressure is the pascal (Pa).
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THE WORLD’S GREATEST LAW…OKAY FINE, 2ND GREATEST LAW
(AFTER GRAVITY)
• Pascal discovered that pressure
applied to an enclosed fluid is
transmitted equally in all
directions throughout the fluid.
• This effect is known as Pascal’s
Law.
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EXAMPLE: A SIMPLE HYDRAULIC JACK WORKS BECAUSE OF
PASCAL’S LAW.
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So the pressure
on the output
piston equals
the pressure at
the input
piston.
The first piston
is the input
piston. This
piston is used to
apply the force
to the fluid,
which creates
pressure in the
fluid. The fluid transfers the pressure
equally in all directions.
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PISTONS AND PRESSURE
• In hydraulic systems, the pressure
is created using a piston.
• A piston is a disk that fits tightly
inside a cylinder.
• As the disk moves inside the
cylinder, it either pushes fluid out
or draws fluid into the cylinder.
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PISTONS AND PRESSURE
• The pressure in the fluid provides
the mechanical advantage that
makes hydraulic systems so
useful.
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CALCULATING MECHANICAL ADVANTAGE OF A HYDRAULIC JACK
• You can calculate the mechanical advantage of a
hydraulic jack if you know the input and output forces.
• Recall that the formula for calculating mechanical
advantage is:
MA =Output force
Input force
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EXAMPLE: CALCULATING MECHANICAL ADVANTAGE
• In a hydraulic jack, the
input force is 20 N and
the output force is 500 N.
Calculate the
mechanical advantage.
• MA =Output force
Input force
• MA =500 N
20 N
• MA = 25
• The jack’s mechanical
advantage is 25.
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PRESSURE AND MECHANICAL ADVANTAGE
• The reason for the large mechanical advantage in a
hydraulic system is the ability of the fluid to transmit
pressure equally.
• From Pascal’s law, we know that the pressure the small
piston creates is the same everywhere in the fluid.
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PRESSURE AND MECHANICAL ADVANTAGE
• So, psmall = plarge according to Pascal’s Law.
• But p = 𝐹
𝐴:
• psmall = plarge, so
𝐹𝑠𝑚𝑎𝑙𝑙
𝐴𝑠𝑚𝑎𝑙𝑙=
𝐹𝑙𝑎𝑟𝑔𝑒
𝐴𝑙𝑎𝑟𝑔𝑒
• We can use this ratio to solve for unknown values in
hydraulic systems.
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EXAMPLE: HYDRAULIC SYSTEM CALCULATIONS
• In a hydraulic system, a
small piston has an area
of 4 cm2. A large piston
has an area of 100 cm2.
You exert a force of 20 N
on the small piston. What
force is exerted on the
large piston?
•𝐹𝑠𝑚𝑎𝑙𝑙
𝐴𝑠𝑚𝑎𝑙𝑙=
𝐹𝑙𝑎𝑟𝑔𝑒
𝐴𝑙𝑎𝑟𝑔𝑒
•20 𝑁
4 𝑐𝑚2 = 𝑥
100 𝑐𝑚2
• Use cross-multiplication or
equivalent fractions to
solve.
• x = 500 N
• The force exerted on the
large piston is 500 N.
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A DISADVANTAGE
• The mechanical advantage of hydraulic systems has a
similar shortcoming to levers.
• To increase the force on the output piston, the input
piston has to move a greater distance.
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