Science 8 Unit D - Section 2 · PDF fileScience 8 Unit D Section 2.0 1 ... box with a pulley....

2016-12-06

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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


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MACHINES MAKE WORK EASIER

Topic 2.1


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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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#2

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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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#2

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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#8

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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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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#15

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!


• 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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#19

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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#21

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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#22

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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HOMEWORK!


• Page 300

• # 1-4

• Assess Your Learning

• Page 303

• # 1-3, 5

• (Reference Book pg. 15-16)


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Science 8 Unit D - Section 2 · PDF fileScience 8 Unit D Section 2.0 1 ... box with a pulley....

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