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Work and EnergyIntroduction to Chapter 4

Engineering is the process of applying science to solve problems. Technology is theword we use to describe machines and inventions that result from engineeringefforts. The development of the technology that created computers, cars, and thespace shuttle began with the invention of simple machines. In this chapter, you willdiscover the principles upon which simple machines operate. You will study severalsimple machines closely and learn how machines can multiply and alter forces.

Investigations for Chapter 4

Machines can make us much stronger than we normally are. In this Investigation,you will design and build several block and tackle machines from ropes and pulleys.Your machines will produce up to six times as much force as you apply. As part ofthe Investigation, you will identify the input and output forces and measure themechanical advantage.

Archimedes said “Give me a lever and fulcrum and I shall move the Earth.” Whilethe lever you study in this Investigation will not be strong enough to move a planet,you will learn how to design and build levers than can multiply force. You will alsofind the rule that predicts how much mechanical advantage a lever will have.

4.1 Forces in Machines How do simple machines work?

4.2 The Lever How does a lever work?

Chapter 4Machines

andMechanical

Systems

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Chapter 4: Machines and Mechanical Systems

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Learning Goals

In this chapter, you will:

Describe and explain a simple machine.

Apply the concepts of input force and output force to various machines.

Determine the mechanical advantage of a machine.

Construct and analyze a block and tackle machine.

Describe the difference between science and engineering.

Understand and apply the engineering cycle to the development of an invention or product.

Describe the purpose and construction of a prototype.

Design and analyze a lever.

Calculate the mechanical advantage of a lever.

Recognize the three classes of levers.

Vocabulary

engineering input machine output armengineering cycle input arm mechanical advantage output forceengineers input force mechanical systems prototypeforce lever output simple machinefulcrum

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4.1 Forces in Machines

Figure 4.1: A bicycle is a good example of a machine. A bicycle efficiently converts forces from your muscles into motion.

Figure 4.2: Applying the ideas of input and output to a bicycle.

4.1 Forces in MachinesHow do you move something that is too heavy to carry? How do humans move mountains? How areskyscrapers built? The answer to these questions has to do with the use of simple machines. In thissection, you will learn how simple machines manipulate forces to accomplish many tasks.

Mechanical systems and machines

The world withoutmachines

Ten thousand years ago, people lived in a very different world. Their interactionswere limited by what they could pick up and carry, how fast they could run, whatthey could eat (or what could eat them), and where they could find shelter. Itwould be quite a problem for someone to bring large building materials back homewithout today’s cars and trucks.

What technologyallows us to do

Today’s technology allows us to do incredible things. Moving huge steel beams,digging tunnels that connect two islands, and building 1,000-foot skyscrapers areexamples. What makes these accomplishments possible? Have we developedsuper powers since the days of our ancestors?

What is amachine?

In a way we have developed super powers. Our powers came from our cleverinvention of machines and mechanical systems. A machine is a device withmoving parts that work together to accomplish a task. A bicycle is a good exampleof a mechanical system that is made of several machines. All the parts of a bicyclework together to transform forces from your muscles into speed and motion. Infact, a bicycle is one of the most efficient machines ever invented.

The concepts ofinput and output

Machines are designed to do something useful. You can think of a machine ashaving an input and an output. The input includes everything you do to make themachine work, like pushing on the pedals. The output is what the machine does foryou, like going fast.

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Simple machines

The beginning oftechnology

The development of the technology that created computers, cars, and the spaceshuttle begins with the invention of simple machines. A simple machine is amechanical device that does not have a source of power and accomplishes a taskwith only one movement (such as a lever). A lever allows you to move a rock thatweighs 10 times as much as you do (or more). Some other important simplemachines are the wheel and axle, the block and tackle, the gear, and the ramp.

Input force andoutput force

Simple machines work by manipulating forces. It is useful to think in terms of aninput force and an output force. The input force of a lever is the force you exert tomove it. The output force is the force the lever applies to the thing you are tryingto move. Figure 4.3 shows an example of using a lever to move a heavy load.

Ropes and pulleys The block and tackle is another simple machine that uses a rope and pulleys tomultiply forces. The input force is the force you apply to the rope. The outputforce is the force that gets applied to the load you are trying to lift. One personcould easily lift an elephant with a properly designed block and tackle! Figure 4.5shows an example of using a block and tackle machine.

Machines withinmachines

Most of the machines we use today are made up of combinations of different typesof simple machines. For example, the bicycle uses wheels and axles, levers (thepedals and a kickstand), and gears. If you take apart a VCR, a clock, or a carengine, you will also find simple machines adapted to fit very specific purposes.

Figure 4.3: With a properly designed lever, a person can move many times his own weight.

Figure 4.4: A block and tackle machine made with a rope and pulleys allows one person to lift tremendous loads.

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4.1 Forces in Machines

Figure 4.5: A block and tackle with a mechanical advantage of two. The output force is two times stronger than the input force.

Mechanical advantage

Definition offorce

Simple machines work by changing force and motion. Remember that a forceis an action that has the ability to change motion, like a push or a pull. Forcesdo not always result in a change in motion. For example, pushing on a solidwall does not make it move (at least not much). But, if the wall is not wellbuilt, pushing could make it move. Many things can create force: wind,muscles, springs, motion, gravity, and more. The action of a force is the same,regardless of its source.

Units of force Recall from earlier chapters that there are two units we use to measure force:the newton and the pound. The newton is a smaller unit than the pound. Thereare 4.48 newtons in 1 pound. A person weighing 100 pounds would weigh 448newtons.

Simple machinesand force

Simple machines are best understood through the concepts of input and outputforces. The input force is the force applied to the machine. The output force isthe force the machine applies to accomplish a task.

Mechanicaladvantage

Mechanical advantage is the ratio of output force to input force. If themechanical advantage is bigger than one, the output force is bigger than theinput force (figure 4.5). A mechanical advantage smaller than one means theoutput force is smaller than the input force.

Mechanicalengineers

Today, we call the people who design machines mechanical engineers. Manyof the machines they design involve the multiplication of forces to lift heavyloads; that is, the machines must have a greater output force than input forcein order to accomplish the job.

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How ropes and pulleys work

The forces inropes and strings

Ropes and strings carry tension forces along their length.A tension force is a pulling force that always acts alongthe direction of the rope. Ropes or strings do not carrypushing forces. This would be obvious if you ever tried topush something with a rope. In your Investigations, youwill use strings which behave just like ropes used in largermachines.

Every part of arope has the same

tension

If friction is very small, then the force in a rope is the sameeverywhere. This means that if you were to cut the ropeand insert a force scale, the scale would measure the sametension force at any point.

The forces inropes and pulleys

Figure 4.6 shows three different configurations of a ropeand pulleys. Notice that each case uses a different numberof pulleys. Each time the rope is threaded around a pulley,another vertical section of the rope is added to helpsupport the load. As you pull on the rope, your input forceis felt at every point along the rope. As a result, in case (A)the load feels two upward forces equal to your pull. In case(B) the load feels three times your pulling force, and incase (C) the load feels four times your pull.

Mechanicaladvantage

If there are four loops of rope directly supporting the load,each newton of force you apply produces 4 newtons ofoutput force. Configuration (C) has a mechanicaladvantage of 4. The output force is four times bigger thanthe input force.

Multiplying forcewith ropes and

pulleys

Because the mechanical advantage is 4, the input force formachine (C) is one-fourth the output force. If you need anoutput force of 20 N, you only need an input force of 5 N!A machine made with a rope and pulleys is extremelyuseful because it multiplies force so effectively.

Figure 4.6: The block and tackle machine is a compact arrangement of one rope and multiple pulleys that can be configured in different ways. Note: Pulleys sometimes come in sets. The picture above shows two sets, each containing three pulleys.

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Science and engineering

Inventions solveproblems

You are surrounded by inventions, from the toothbrush you use to clean your teethto the computer you use to do your school projects. Where did the inventionscome from? Most of them came from practical applications of science principles.

What istechnology

The application of science to solve problems is called engineering or technology.From the invention of the plow to the microcomputer, all technologies arise fromsomeone’s perception of a need for things to be done better. Although technologycomes in many forms, there are some general principles that apply to all forms oftechnological design or innovation. People who design technology to solveproblems are called engineers.

Science andtechnology

Scientists study the world to learn the basic principles behind how things work.Engineers use scientific knowledge to create or improve inventions that solveproblems.

A sampleengineering

problem

Suppose you are given a box of toothpicks and some glue, and are assigned tobuild a bridge that will hold a brick without breaking. After doing research, youcome up with an idea for how to make the bridge. Your idea is to make the bridgefrom four structures connected together. Your idea is called a conceptual design.

The importance ofa prototype

You need to test your idea to see if it works. If you could figure out how muchforce it takes to break one structure, you would know if four structures will holdthe brick. Your next step is to build a prototype and test it. Your prototype shouldbe close enough to the real bridge so that what you learn from testing can beapplied to the final bridge. For example, if your final bridge is to be made withround toothpicks, your prototype also has to be made with round toothpicks.

� Leonardo da Vinci

The Italian inventor andpainter Leonardo da Vinci(1452-1519) was one of thegreatest engineers ever. Hisinventions are remarkable fortheir creativity, imagination,and technical detail. He oftendescribed technologies thatmost people of his timethought were impossible.

Da Vinci always thoughtabout new ways to do things.In particular, he developeddesigns for several kinds ofmachines that he hopedwould allow people to fly. DaVinci’s ideas were so farahead of his time that hisflying machines could not bebuilt. Many look like ourmodern flying machines. Thefirst helicopter and the hangglider look like da Vinci’sdesigns from 500 years ago.

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Testing theprototype

You test the prototype by applying more and more force until it breaks. You learnthat your structure breaks at a force of 5 newtons. The brick weighs 25 newtons.Four structures are not going to be enough. You have two choices now. You canmake each structure stronger, by using thread to tie the joints. Or, you could useseven structures in your bridge instead of four. The evaluation of test results is anecessary part of any successful design. Testing identifies potential problems inthe design in time to correct them.

Changing thedesign and testing

again

If you decide to build a stronger structure, you will need to make anotherprototype and test it again. Good engineers often build many prototypes and keeptesting them until they are successful under a wide range of conditions. Theprocess of design, prototype, test, and evaluate is the engineering cycle. The bestinventions go through the cycle many times, being improved each cycle until allthe problems are worked out.

Good design takestime

Discipline, patience, and persistence are necessary in engineering design. Youwould not want to drive over a bridge that had been designed and built too fast.You want to know that the engineers who designed the bridge thoroughly testedtheir design to make it safe.

Even the bestdesigns are always

being improved

It is very rare that an invention works perfectly the first time. In fact, machines gothrough a long history of being designed, built, tested, analyzed, redesigned,rebuilt, and retested. Most practical machines such as the automobile are nevertruly completed. There are always improvements that can be added as technologygets more sophisticated (figure 4.8). The first cars had to be cranked by hand tostart! Today’s cars start with the turn of a key or the touch of a remote-start button.

Figure 4.7: The engineering cycle is how we get an idea for an invention from concept to reality.

Figure 4.8: Many inventions are continually being redesigned and improved.

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4.2 The Lever

4.2 The LeverThe lever is another example of a simple machine. In this section, you will learn about the relationshipsbetween force and motion that explain how a lever works. After reading this section and doing theInvestigation, you should be able to design a lever to move almost anything!

What is a lever?

Levers are usedeverywhere

The principle of the lever has been used since before humans had writtenlanguage. Levers still form the operating principle behind many commonmachines. Examples of levers include: pliers, a wheelbarrow, and the humanbiceps and forearm (figure 4.9).

Your muscles andskeleton use levers

You may have heard the human body described as a machine. In fact, it is: Yourbones and muscles work as levers to perform everything from chewing tothrowing a ball.

Parts of the lever A lever includes a stiff structure (the lever) that rotates around a fixed point calledthe fulcrum. The side of the lever where the input force is applied is called theinput arm. The output arm is the end of the lever that moves the rock or lifts theheavy weight. Levers are useful because we can arrange the fulcrum and thelengths of the input and output arms to make almost any mechanical advantage weneed.

How it works If the fulcrum is placed in the middle of the lever, the input and output forces arethe same. An input force of 100 pounds makes an output force of 100 pounds.

Figure 4.9: Examples of three kinds of levers. The pair of pliers is a first class lever because the fulcrum is between the forces. The wheelbarrow is a second class lever because the output force is between the fulcrum and input force. Human arms and legs are all examples of third class levers because the input forces (muscles) are always between the fulcrum (a joint) and the output force (what you accomplish with your feet or hands).

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The mechanical advantage of a lever

Input and outputforces for a lever

The input and output forces are related by thelengths on either side of the fulcrum. Whenthe input arm is longer, the output force islarger than the input force. If the input arm is10 times longer than the output arm, then theoutput force will be 10 times bigger than theinput force (figure 4.10).

The mechanicaladvantage of a

lever

Another way to say this is that the mechanicaladvantage of a lever is the ratio of lengthsbetween the input arm and the output arm. Ifthe input arm is 5 meters and the output arm is1 meter, then the mechanical advantage willbe 5. The output force will be five times aslarge as the input force.

The output forcecan be less thanthe input force

You can also make a lever where the outputforce is less than the input force. You wouldbe right if you guessed that the input arm isshorter than the output arm on this kind oflever. You might design a lever this way if youneeded the motion on the output side to belarger than the motion on the input side.

The three types oflevers

There are three types of levers, as shown infigure 4.11. They are classified by the locationof the input and output forces relative to thefulcrum. All three types are used in manymachines and follow the same basic rules. Themechanical advantage is always the ratio ofthe lengths of the input arm over the outputarm.

Figure 4.10: The mechanical advantage of a lever is the ratio of the length of the input arm over the length of the output arm.

Figure 4.11: The three classes of levers. For the third class, the input force is larger than the output force.

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Chapter 4 Review

Chapter 4 Review

Vocabulary review

Match the following terms with the correct definition. There is one extra definition in the list that will not match any of the terms.

Set One Set Two1. input force a. The force applied by a machine to accomplish

a task after an input force has been applied1. engineering cycle a. A working model of a design

2. machine b. A device that multiplies force 2. engineering b. A scientific field devoted to imagining what machines will be used in the future

3. mechanical system c. An unpowered mechanical device, such as a lever, that has an input and output force

3. prototype c. Output force divided by input force

4. output force d. The force applied to a machine 4. mechanical advantage d. The process used by engineers to develop new technology

5. simple machine e. A measurement used to describe changes in events, motion, or position

e. The application of science to solve problems

f. An object with interrelated parts that work together to accomplish a task

Set Three1. fulcrum a. The force applied to a machine to produce a

useful output force

2. input arm b. The pivot point of a lever

3. lever c. The distance from the fulcrum to the point of output force

4. output arm d. The distance from the fulcrum to the point of input force

e. A simple machine that pivots around a fulcrum

Chapter 4 Review

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Concept review

1. Why is a car a good example of a mechanical system? Write ashort paragraph to explain your answer.

2. What does the phrase multiply forces mean? Include the termsmachine, input force, and output force in your answer.

3. Compare and contrast the scientific method and theengineering cycle.

4. You are an inventor who wants to devise a new style oftoothbrush. Describe what you would do at each phase of theengineering cycle to invent this new toothbrush.

5. Describe a problem that would have to be solved by anengineer. Try to think of example problems you see in yourschool, home, city, or state.

6. Describe an example of a new technology that you have seenrecently advertised or sold in stores.

7. How would you set up a lever so that it has a mechanicaladvantage greater than 1? Include the terms input arm, outputarm, and fulcrum in your answer.

8. Draw diagrams that show a seesaw at equilibrium and atnonequilibrium. Include captions that describe each of yourdiagrams. Be sure to discuss forces and motion in yourcaptions.

9. Why are levers considered to be simple machines?

10. Which configuration is the best lever for lifting the rock?

11. The lever in the picture will:

a. stay balanced.

b. rotate clockwise.

c. rotate counterclockwise.

12. The lever has a mass of 3kilograms at 30 centimeters onthe left, and a mass of 2kilograms at 30 centimeters onthe right. What mass should behung at 10 centimeters (on theright) for the lever to be inbalance?

13. How are force and distance related to how a lever works?

14. Would you rather use a machine that has a mechanicaladvantage of 1 or a machine that has a mechanical advantageof more than 1? Explain your reasoning in your answer.

a. 1 kg

b. 2 kg

c. 2.5 kg

d. 3 kg

e. 10 kg

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Chapter 4 Review

Problems

1. Above is a data table with sample data for lifting (input) forcevs. the number of supporting strings in a block and tacklemachine. Use the data to answer the following questions.

a. Describe the relationship between the lifting (input) forceand the number of supporting loops of string.

b. Make a graph that shows the relationship between lifting(input) force and number of supporting loops of string.Which variable is dependent and which is independent?

c. Calculate the mechanical advantage for each number ofsupporting loops of string.

2. If you were going to use a pulley to lift a box that weighs 100newtons, how much force would you need to use if the pulleyhad:

a. 1 supporting loop of rope?

b. 2 supporting loops of rope?

c. 5 supporting loops of rope?

d. 10 supporting loops of rope?

3. Use the input and output forces listed in the table below tocalculate the mechanical advantage.

4. One of the examples in the table in problem 3 has a very lowmechanical advantage. Identify this example and explain whyyou might or might not want to use this machine to liftsomething that weighs 200 newtons.

5. Does mechanical advantage have units? Explain your answer.

6. If you lift a 200-newton box with a block and tackle machineand you apply 20 newtons to lift this box, what would be themechanical advantage of the machine?

7. If a lever has an input arm that is 15 feet long and an output armthat is 25 feet long, does the lever have mechanical advantagegreater than one? Why or why not?

8. Betsy wants to use her own weight to lift a 350-pound box. Sheweighs 120 pounds. Suggest input and output arm lengths thatwould allow Betsy to lift the box with a lever. Draw a lever andlabel the input and output arms with the lengths and forces.

Input Force Output Force Mechanical Advantage

10 newtons 100 newtons

30 N 30 N

500 N 1,350 N

625 N 200 N

Chapter 4 Review

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�Applying your knowledge

1. Why is a ramp a simple machine? Describe how a ramp worksto multiply forces using your knowledge of simple machines.

2. You need awheelbarrow totransport some soilfor your garden. Theone you have givesyou a mechanicaladvantage of 3.5. Ifyou use 65 newtonsof force to lift thewheelbarrow so that you can roll it, how much soil can youcarry with this wheelbarrow? Give the weight of the soil innewtons and be sure to show your work.

3. The block and tacklemachine on a sailboat canhelp a sailor raise hermainsail. Without a machine,she needs 500 newtons offorce to raise the sail. If theblock and tackle gives her amechanical advantage of 5,how much input force mustbe applied to raise the sail?Be sure to show your work.

Your jaw works as a lever when you bite an apple. Your armalso works as a lever, as do many other bones in your body.Using the diagrams above, answer the following questions byanalyzing the changes in force and distance.

4. Using the distances shown, calculate and compare themechanical advantage of the jaw and arm. Which is larger?

5. Suppose the jaw and biceps muscles produce equal input forcesof 800N (178 lbs.). Calculate and compare the output forces inbiting (jaw) and lifting (arm). Which is larger?

6. Suppose you need an output force of 500N (112 lbs). Calculateand compare the input forces of the jaw and biceps musclesrequired to produce 500 N of output force. Explain how yourcalculation relates to the relative size of the two muscles.