CHAPTER 3 LESSON 3 Work and Simple Machines

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What is a simple machine?Many machines are complex. A car, for example, has

thousands of parts. Some machines, however, have only a few parts. Simple machines do work using only one movement. There are six types of simple machines—the lever, wheel and axle, inclined plane, wedge, screw, and pulley.

LeversThe next time you open an aluminum beverage can,

watch how the finger tab works. The finger tab is a lever. A lever is a simple machine made up of a bar that pivots, or rotates, about a fixed point. The point about which a lever pivots is called a fulcrum. The fulcrum on a beverage can is where the finger tab attaches to the can.

The input force and output force act on opposite ends of the finger tab. The distance from the fulcrum to the input force on the tab is the input arm. The distance from the fulcrum to the end of the tab that pushes down on the lid is the output arm. The finger tab on a beverage can is a first-class lever.

There are three types of levers. Each type is illustrated and described on the next page. Notice that first-class, second-class, and third-class levers differ in the location of the input force and output force relative to the fulcrum.

What do you think? Read the statements below and decide whether you agree or disagree with them. Place an A in the Before column if you agree with the statement or a D if you disagree. After you’ve read this lesson, reread the statements to see if you have changed your mind.

Before Statement After

5. A doorknob is a simple machine.

6. A loading ramp makes it easier to lift a load.

Key Concepts • What is a simple machine?• How is the ideal mechanical

advantage of simple machines calculated?

• How are simple machines and compound machines different?

Organize Your Notes As you read this lesson, create a two-column table. List each type of simple machine and what you learn about it. Use your table to review the lesson.

Key Concept Check1. Identify Describe a simple machine.

Work and Simple Machines

Simple Machines

Read ing Check2. Name one way the types of levers differ from each other.

LESSON 3

CHAPTER 3

Reading Essentials Work and Simple Machines 49

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Visual Check3. Identify Give one example of each class of levers.

Mechanical Advantage of Levers See the figure above. If the output force is less than the

input force, the mechanical advantage of a lever will be less than 1. If the output force is greater than the input force, the mechanical advantage will be greater than 1. The mechanical advantage of a lever is equal to 1 when the input and output forces are the same.

The ideal mechanical advantage of a lever equals the length of the input arm divided by the length of the output arm. The formula for calculating the ideal mechanical advantage of a lever is shown below.

Ideal Mechanical Advantage of a Lever

ideal mechanical advantage = length of input arm (in meters)

____________________________ length of output arm (in meters)

IMA = Lin

____ Lout

First-Class Levers The figure at the top of the next page shows the possibilities for the mechanical advantage of a first-class, second-class, and third-class lever. Notice that the location of the fulcrum determines the mechanical advantage in the first-class lever. The mechanical advantage of the first-class lever is greater than 1 because the input arm is longer than the output arm. Thus, the output force is greater than the input force. When the mechanical advantage is equal to 1, the input and output arms and the input and output forces are equal. If the mechanical advantage is less than 1, the input arm is shorter than the output arm, and the output force is less than the input force.

Outputforce

Inputforce

Fulcrum

Third-Class Lever32 Second-Class LeverOutput

forceInputforce

Fulcrum

1 First-Class Lever

Outputforce

Inputforce

Fulcrum

Make a six-tab book. Use your book to summarize information about the six simple machines.

InclinedPlane

WheelandAxle

Lever

Wedge Screw Pulley

• The fulcrum is between the input force and the output force.

• The direction of the input force is always different from the direction of the output force.

• A hammer is a first-class lever when it is used to pull a nail out of wood.

• A finger tab on a beverage can is also a first-class lever.

• The output force is between the input force and the fulcrum.

• The output force and the input force act in the same direction.

• This lever makes the output force greater than the input force.

• A wheelbarrow, a nut cracker, and your foot are second-class levers.

• The input force is between the output force and the fulcrum.

• The output force is less than the input force.

• Both the input force and the output force act in the same direction.

• Tweezers, a rake, and a broom are all examples of third-class levers.

50 Work and Simple Machines Reading Essentials


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Second-Class Levers The center diagram above shows a second-class lever. In a second-class lever, the input arm is longer than the output arm. Thus, the mechanical advantage of a second-class lever is always greater than 1.

Third-Class Levers The right diagram above shows a third-class lever. The input arm of a third-class lever is always shorter than the output arm. Thus, the mechanical advantage of a third-class lever is always less than 1.

Levers in the Human BodyThe human body uses all three classes of levers. Muscles

provide the input force for the levers. Examples of levers in the neck, foot, and arm are shown below.

Key Concept Check5. Explain How is the ideal mechanical advantage of a lever calculated?

Visual Check 6. Compare your leg to the first-class lever. What acts as the fulcrum in your leg?

Visual Check4. Compare How does the input arm compare to the output arm in a second-class lever? In a third-class lever?

Mechanical Advantageof a Second-Class Lever

Mechanical Advantageof a Third-Class Lever

Inputforce

Outputforce

Outputarm Input

arm

Inputforce

Outputforce

Fulcrum

Outputarm

Inputarm

Fulcrum

Inputforce

Outputforce

Fulcrum

Outputarm

Inputarm

Mechanical Advantageof a First-Class Lever

First-Class Lever

Output

force

Output

force

Input force

Input

force

Output

force

Input

force

Second-Class Lever

Third-Class Lever



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The Neck Your neck acts as a first-class lever. The fulcrum is the joint that connects the skull to the spine. The neck muscles provide the input force. The output force is applied to the head and helps support your head’s weight.

The Foot When you stand on your toes, the foot acts as a second-class lever. The ball of your foot is the fulcrum. The muscles on the back of the lower leg provide the input force.

The Arm Your forearm works like a third-class lever. The elbow is the fulcrum, and the input force comes from muscles near the elbow.

Wheel and AxleA wheel and axle is an axle attached to the center of a wheel and

both rotate together. Note that axle is another word for a shaft. The handle on a water faucet is a wheel and axle. The handle is the wheel because it has a larger diameter. The axle is the shaft attached to the handle. The handle and the shaft both rotate when the handle turns. The figure below will help you understand the input force and output force of a wheel and axle.

Mechanical Advantage of a Wheel and AxleThe length of the input arm is the radius of the wheel.

The length of the output arm is the radius of the axle. You use these lengths to calculate the ideal mechanical advantage, as shown by the following equation.

Ideal Mechanical Advantage of Wheel and Axle

ideal mechanical advantage =radius of wheel (in meters)_______________________radius of axle (in meters)

IMA =

rwheel_____raxle

Visual Check8. Explain In the faucet handle shown in the figure, why is the output force greater than the input force?

7. Identify Your hand acts as a third-class lever when you throw a ball. If the input force comes from the muscles near your wrist, and the output force propels the ball off your fingers, what acts as the fulcrum?

Wheel

Axle

Output force

Input

force



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Mechanical Advantage of Inclined PlanesThe ideal mechanical advantage of an inclined plane

equals its length divided by its height. The longer an inclined plane is, the less force is needed to move an object on it.

Ideal Mechanical Advantage of an Inclined Plane

ideal mechanical advantage = length of inclined plane (in meters)

_______________________________ height of inclined plane (in meters)

IMA = l __ h

As the figure above shows, using the ramp requires only a 300-N force to move the 1,500-N box. However, because of friction, no ramp operates at its ideal mechanical advantage.

Using a Wheel and AxleAs you know, a screwdriver makes it easier to turn a screw.

But how does a screwdriver work? Think of the mechanical advantage of the screwdriver to understand how it works. When you turn a screwdriver, you apply an input force to the handle (the wheel). The output force is applied to the screw by the screwdriver’s shaft (the axle). Because the wheel is larger than the axle, the mechanical advantage is greater than 1. This makes the screw easier to turn.

Inclined Planes Ramps are often used to move heavy objects. The ancient

Egyptians, for example, used ramps to move the huge stone blocks used to build the pyramids. A ramp is an inclined plane—a flat, sloped surface. As shown in the figure below, it takes less force to move an object upward along an inclined plane than it does to lift the object straight up.

Weight =

1,500 N

Force = 300 N

Force = 1,500 N 5 m1 m

Visual Check 9. Distinguish What does the figure show about the force needed to move the box up a ramp?



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WedgesA sloped surface that moves is called a wedge. A wedge is

a type of inclined plane with one or two sloping sides. A doorstop is a wedge that has one sloped side. An axe is a wedge with two sloped sides. The shape of the wedge gives the output forces a different direction from the input force.

Your front teeth also are wedges. As you bite down on food, the downward input force is changed by your teeth to a sideways force that pushes the food apart.

ScrewsA screw is an inclined plane wrapped around a cylinder. When

you turn a screw, the screw threads change the input force to an output force. The output force pulls the screw inward into the material.

PulleysAnother kind of simple machine is the pulley—a grooved

wheel with a rope or a cable wrapped around it. Large cranes at construction sites use pulleys to lift heavy loads. Types of pulleys are shown in the figure below.

Fixed Pulleys Have you ever pulled down on a cord to raise a window blind? The cord passes through a fixed pulley. A fixed pulley changes only the direction of the force.

Movable Pulleys and Pulley Systems A pulley can also be attached to the object being lifted, as shown in the middle diagram below. This is called a movable pulley. Movable pulleys decrease the force needed to lift an object. The distance over which the force acts increases. A pulley system is a combination of fixed and movable pulleys that work together.

Visual Check11. Identify Circle the diagram that shows both a fixed and a movable pulley working together.

Reading Check10. Describe How are a wedge and a ramp different?

Fixed Pulley Movable Pulley Pulley System

100 N

100 N

100 N 100 N 100 N

50 N

50 N 50 N

50 N

Mechanical advantage = 1 Mechanical advantage = 1 Mechanical advantage = 2

50 N


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Mechanical Advantage of Pulleys Pulley systems change the size and direction of an input force. The ideal mechanical advantage of a pulley or pulley system is equal to the number of sections of rope pulling up on the object.

What is a compound machine?A compound machine is formed when two or more

simple machines work together. A can opener is a compound machine. It uses a second-class lever to move the handle. A wheel and axle turn the blade. A wedge punctures the lid of the can.

GearsA gear is a wheel and axle with teeth around the wheel.

Two or more gears working together form a compound machine. When the teeth of the two gears interlock, the turning of one gear causes the other gear to turn. The direction of motion changes from one gear to the next.

Different-sized gears turn at different speeds. Small gears turn faster than large gears. The amount of force sent through a set of gears is also affected by the size of the gears. The input force applied by a large gear is reduced when it is applied to a smaller gear.

Efficiency of Compound MachinesHow can you determine the efficiency of a compound

machine? First, you find the efficiency of each simple machine. Then, you multiply the efficiencies of the simple machines to calculate the efficiency of the compound machine.

Consider the can opener. It is made up of three simple machines. Suppose the efficiencies are as follows:

• efficiency of lever = 95%

• efficiency of wheel and axle = 90%

• efficiency of wedge = 80%

The efficiency of the can opener is equal to the product of these efficiencies.

efficiency of the can opener = 95% × 90% × 80% = 68%

Each simple machine decreases the overall efficiency of the compound machine.

Key Concept Check 12. Describe How are simple machines and compound machines different?

13. Calculate the efficiency of a compound machine made up of a simple machine that is 90% efficient and another simple machine that is 85% efficient.



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Mini Glossary

Reread the statements at the beginning of the lesson. Fill in the After column with an A if you agree with the statement or a D if you disagree. Did you change your mind?

What do you think

END OF LESSON

Log on to ConnectED.mcgraw-hill.com and access your textbook to find this lesson’s resources.

ConnectED

fulcrum: the point about which a lever pivots

inclined plane: a ramp or a flat, sloped surface

lever: a simple machine made up of a bar that pivots, or

rotates, about a fixed point

pulley: a simple machine that is a grooved wheel with a rope or

cable wrapped around it

screw: an inclined plane wrapped around a cylinder

simple machine: a machine that does work using only one

movement

wedge: a sloped surface that moves

wheel and axle: an axle attached to the center of a wheel

and both rotate together

1. Review the terms and their definitions in the Mini Glossary. Write one or two sentences that describe how a wheel and axle work together as a machine.

2. Match each simple machine in Column 1 with the correct item in Column 2. Write the correct letter on the blank line.

Column 1 Column 2

1. tooth a. inclined plane

2. doorknob b. wheel and axle

3. threads of a lightbulb c. wedge

4. wheelbarrow d. screw

5. ramp e. pulley

6. flagpole f. lever



CHAPTER 3 LESSON 3 Work and Simple Machines

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