Overview

Lesson Procedure

60-65 minutes of class time across 5 phases.

1. Warm-Up5 minutes
2. Direct Instruction15-20 minutes
3. Guided Practice15 minutes
4. Independent Practice20 minutes
5. Closure5 minutes

1. Warm-Up5 minutes

   Ask students to rub their palms together hard for ten seconds, then answer the prompt on paper.

   Warm-Up Prompt

   Write one sentence that uses the words force, friction and energy and says how they are connected in what you just did. Then circle the word or phrase in your sentence that does the connecting.

   Take three or four sentences. Students usually connect the terms with words such as "causes," "turns into" or "because." Point out that those connecting words are what this standard is about: a science text is a web of concepts, and the reader's job is to see how each concept is tied to the others, whether as cause and effect, as a pair, as a proportion or as one thing turning into another.

2. Direct Instruction15-20 minutes

   Part 1: Kinds of relationships and their signals. Keep this table up for the whole lesson. Science writers rarely say "here is a relationship"; they show it with small words and with the order of their sentences.

   Relationships among concepts in science texts, and the words that signal them

   Relationship	Signal words	Where to find one today
   Cause and effect	so, because, the consequence is, produces	"the consequence is that the available out-come of the machine is more or less diminished" (T1, paragraph 1)
   Condition	if ... then, unless, provided	"unless we are able to see clearly what part friction really plays" (T1, paragraph 1)
   Conversion or transfer	converts into, turns into, goes into	"the converter of it into some less apparent" form (T1, paragraph 1)
   Pair or equality	equal and opposite, of the same size, in its turn	"a force of the same size: this second force is the reaction force" (T2, paragraph 3)
   Proportion or dependence	depends on, doubled, the ratio of	"When the normal force doubled, the kinetic friction about doubled" (T2, paragraph 6)
   Contrast or category	not ... but, while, static and kinetic	"Static friction acts while the block is still at rest; kinetic friction acts while it slides" (T2, paragraph 2)

   Part 2: Model with Stewart (T1). Balfour Stewart was a Scottish physicist, and his book explained the new law of the conservation of energy to general readers. In this excerpt he asks where energy goes when friction seems to destroy it. Read it aloud once. On the second reading, mark each move in his argument in the margin (problem, possible answers, question, cases, answer), then compare with Diagram 1.

   1What Friction does. 46. The two examples now given are quite sufficient to enable our readers to see the true function of a machine, and they are now doubtless disposed to acknowledge that no machine will give back more energy than is spent upon it. It is not, however, equally clear that it will not give back less; indeed, it is a well-known fact that it constantly does so. For we have supposed our machine to be without friction--but no machine is without friction--and the consequence is that the available out-come of the machine is more or less diminished by this drawback. Now, unless we are able to see clearly what part friction really plays, we cannot prove the conservation of energy. We see clearly enough that energy cannot be created, but we are not equally sure that it cannot be destroyed; indeed, we may say we have apparent grounds for believing that it is destroyed--that is our present position. Now, if the theory of the conservation of energy be true--that is to say, if energy is in any sense indestructible--friction will prove itself to be, not the destroyer of energy, but merely the converter of it into some less apparent and perhaps less useful form.

   247. We must, therefore, prepare ourselves to study what friction really does, and also to recognize energy in a form remote from that possessed by a body in visible motion, or by a head of water. To friction we may add percussion, as a process by which energy is apparently destroyed; and as we have (Art. 39) considered the case of a kilogramme shot vertically upwards, demonstrating that it will ultimately reach the ground with an energy equal to that with which it was shot upwards, we may pursue the experiment one step further, and ask what becomes of its energy after it has struck the ground and come to rest? We may vary the question by asking what becomes of the energy of the smith’s blow after his hammer has struck the anvil, or what of the energy of the cannon ball after it has struck the target, or what of that of the railway train after it has been stopped by friction at the break-wheel? All these are cases in which percussion or friction appears at first sight to have destroyed visible energy; but before pronouncing upon this seeming destruction, it clearly behoves us to ask if anything else makes its appearance at the moment when the visible energy is apparently destroyed. [...]

   3When Motion is destroyed, Heat appears. 48. Now, in reply to the question we have put, it may be confidently asserted that whenever visible energy is apparently destroyed by percussion or friction, something else makes its appearance, and that something is heat. Thus, a piece of lead placed upon an anvil may be greatly heated by successive blows of a blacksmith’s hammer. The collision of flint and steel will produce heat, and a rapidly-moving cannon ball, when striking against an iron target, may even be heated to redness. Again, with regard to friction, we know that on a dark night sparks are seen to issue from the break-wheel which is stopping a railway train, and we know, also, that the axles of railway carriages get alarmingly hot, if they are not well supplied with grease.

   • The frame of an argument: problem, two readings and a condition (T1, paragraph 1)

     What problem does paragraph 1 set up, and how does its last sentence connect friction to the conservation of energy?

     Result: The problem: machines give back less energy than is spent on them, because "no machine is without friction." Stewart then offers two readings: energy may be destroyed, or it may be changed into a less visible form. The last sentence joins them with a condition: "if energy is in any sense indestructible--friction will prove itself to be, not the destroyer of energy, but merely the converter of it." So friction and energy are tied together by an if-then link, and the rest of the excerpt tests which reading is true. The "not ... but" contrast names the two possible roles of friction.

   • Cause and effect across a list of cases: visible energy and heat (T1, paragraphs 2-3)

     Paragraph 2 lists a hammer and an anvil, a cannon ball and a railway train. How do these cases lead to the answer in paragraph 3?

     Result: Paragraph 2 turns the problem into a question ("what becomes of its energy after it has struck the ground and come to rest?") and varies it across cases in which "percussion or friction appears at first sight to have destroyed visible energy." Paragraph 3 gives one answer that covers all of them: "whenever visible energy is apparently destroyed by percussion or friction, something else makes its appearance, and that something is heat." The relationship is cause and effect: friction or percussion is the process, loss of visible energy and the appearance of heat are its results. Each example in paragraph 3 matches a case in paragraph 2, such as the train stopped at the break-wheel and the sparks from it.

   Close the model by naming the structure: Stewart does not define friction and energy separately. He relates them through an argument, and the relationship (friction converts visible energy into heat) is the conclusion the whole passage is built to reach.

3. Guided Practice15 minutes

   Pairs read the lab handout (T2) and draw a line between every two key terms that the handout connects, writing the connecting words on the line. Then check as a class and work the three examples together. Diagram 2 shows the forces from paragraphs 2-3, drawn to scale.

   1Purpose. This lab measures the friction force on a wooden block sliding across a level wooden board, and asks how that force depends on how hard the two surfaces press together. All data in this handout are invented for teaching.

   2Forces. A force is a push or a pull that one object exerts on another, measured in newtons (N). The weight of the block is the pull of Earth on it; with g = 9.8 N/kg, one 0.250 kg block weighs 2.45 N. The normal force is the push of the board on the block, at right angles to the board's surface. On a level board, with no one pressing down on the block or lifting it, the normal force equals the weight. Friction is the force the board exerts on the block along the surface, opposite to the direction in which the block slides or is about to slide. Static friction acts while the block is still at rest; kinetic friction acts while it slides.

   3Force pairs. Every force is one half of a pair. When the board pushes up on the block, the block pushes down on the board with a force of the same size: this second force is the reaction force. In the same way, when friction from the board drags the block backward, the block drags the board forward. The two forces of a pair act on different objects, so they never cancel each other. The normal force and the weight both act on the block, so they are not a pair, even though they are equal here; the reaction to the block's weight is the block's pull on Earth.

   4Procedure. Hook a spring scale to the block and pull horizontally. Increase the pull slowly and record the largest reading just before the block starts to move: this is the peak static friction. Then pull so that the block slides at a slow, steady speed and record the reading: this is the kinetic friction. At steady speed the pull and the kinetic friction are equal, because the forces on the block balance. Repeat with two and then three identical blocks stacked, three trials each, and average the trials.

   5Results. One block (normal force 2.45 N): peak static friction 1.10 N, kinetic friction 0.71 N. Two blocks (normal force 4.90 N): 2.02 N and 1.52 N. Three blocks (normal force 7.35 N): 3.16 N and 2.18 N.

   6Interpretation. In every stack, kinetic friction was smaller than peak static friction, so it takes more force to start the block than to keep it sliding. When the normal force doubled, the kinetic friction about doubled; the ratio of kinetic friction to normal force, called the coefficient of kinetic friction, stayed close to 0.30 for all three stacks.

   7Energy. While the block slides 0.80 m at steady speed, the pull does work on it: work = force × distance. The block's kinetic energy, its energy of motion, does not change, because its speed does not change. The energy goes instead into thermal energy, as the rubbing surfaces warm slightly. After one slide the warming is far too small to feel; rubbing your palms together hard does the same thing faster.

   • Paired and unpaired forces: weight, normal force and reaction force (T2, paragraph 3)

     The normal force and the weight on the block are equal and opposite. Why does paragraph 3 say they are not an action-reaction pair?

     Result: Paragraph 3 gives the test: "The two forces of a pair act on different objects." The normal force (board on block) and the weight (Earth on block) both act on the block, so they fail the test; they are equal only because the board is level and nothing else pushes. The reaction to the normal force is the block pushing down on the board, and "the reaction to the block's weight is the block's pull on Earth." The text relates the key terms in two different ways: as a pair across two objects (action and reaction force) and as a balance on one object (normal force and weight).

   • A proportional relationship: friction and normal force (T2, paragraphs 5-6)

     Paragraph 6 says the ratio of kinetic friction to normal force "stayed close to 0.30." Check this with the results in paragraph 5, and say what relationship the ratio expresses.

     Result: 0.71 ÷ 2.45 ≈ 0.290, 1.52 ÷ 4.90 ≈ 0.310 and 2.18 ÷ 7.35 ≈ 0.297, so all three are close to 0.30 (mean ≈ 0.299). A nearly constant ratio means kinetic friction is proportional to the normal force: the harder the surfaces press together, the larger the friction, in the same proportion. The coefficient of kinetic friction is the name the text gives to that ratio. The peak static values give a larger ratio, about 0.43 (1.10 ÷ 2.45 ≈ 0.449, 2.02 ÷ 4.90 ≈ 0.412, 3.16 ÷ 7.35 ≈ 0.430), which fits paragraph 6's point that starting takes more force than sliding.

   • Force, distance and energy: where the work goes (T2, paragraph 7)

     Use paragraph 7 to find the work done by the pull when the three-block stack slides 0.80 m at steady speed, and explain where that energy goes.

     Result: At steady speed the pull equals the kinetic friction, 2.18 N (paragraphs 4 and 5). Work = force × distance = 2.18 N × 0.80 m ≈ 1.74 J. The kinetic energy does not change, "because its speed does not change," so the 1.74 J cannot have gone into motion; the text says it goes "into thermal energy, as the rubbing surfaces warm slightly." Friction is the link between the force the student applies and the energy that ends up as warmth, the same role Stewart gives it in T1.

   Debrief with one question: Which paragraph of T2 would you need to reread if you forgot why the normal force and the weight do not cancel as a pair? (Paragraph 3.) Students should see that a technical text often puts its definitions first (paragraph 2), then the relationships between the defined terms (paragraph 3), then the evidence (paragraphs 5-6).

4. Independent Practice20 minutes

   Students read the second Stewart excerpt below on their own and answer quiz questions 1-20 with the text open. The [...] paragraph marks two articles left out, in which Stewart applies the same law to a rifle's recoil. Remind students to name the relationship a question asks about (pair, contrast, cause, proportion) before choosing, and to cite paragraphs in short answers.

   1Action and Reaction, Equal and Opposite. 12. But while an impenetrable veil is drawn over the individual in this warfare of clashing atoms, yet we are not left in profound ignorance of the laws which determine the ultimate result of all these motions, taken together as a whole.

   2In a Vessel of Goldfish. Let us suppose, for instance, that we have a glass globe containing numerous goldfish standing on the table, and delicately poised on wheels, so that the slightest push, the one way or the other, would make it move. These goldfish are in active and irregular motion, and he would be a very bold man who should venture to predict the movements of an individual fish. But of one thing we may be quite certain: we may rest assured that, notwithstanding all the irregular motions of its living inhabitants, the globe containing the goldfish will remain at rest upon its wheels.

   3Even if the table were a lake of ice, and the wheels were extremely delicate, we should find that the globe would remain at rest. Indeed, we should be exceedingly surprised if we found the globe going away of its own accord from the one side of the table to the other, or from the one side of a sheet of ice to the other, in consequence of the internal motions of its inhabitants. Whatever be the motions of these individual units, yet we feel sure that the globe cannot move itself as a whole. In such a system, therefore, and, indeed, in every system left to itself, there may be strong internal forces acting between the various parts, but these actions and reactions are equal and opposite, so that while the small parts, whether visible or invisible, are in violent commotion among themselves, yet the system as a whole will remain at rest.

   [...]

   4In a Falling Stone. 15. We may even extend the law to cases in which we do not perceive the recoil or reaction at all. Thus, if I drop a stone from the top of a precipice to the earth, the motion seems all to be in one direction, while at the same time it is in truth the result of a mutual attraction between the earth and the stone. Does not the earth move also? We cannot see it move, but we are entitled to assert that it does in reality move upwards to meet the stone, although quite to an imperceptible extent, and that the law of action and reaction holds here as truly as in a rifle, the only difference being that in the one case the two objects are rushing together, while in the other they are rushing apart. Inasmuch, however, as the mass of the earth is very great compared with that of the stone, it follows that its velocity must be extremely small, in order that the mass of the earth, multiplied into its velocity upwards, shall equal the mass of the stone, multiplied into its velocity downwards.

   516. We have thus, in spite of our ignorance of the ultimate atoms and molecules of matter, arrived at a general law which regulates the action of internal forces. We see that these forces are always mutually exerted, and that if A attracts or repels B, B in its turn attracts or repels A. We have here, in fact, a very good instance of that kind of generalization, which we may arrive at, even in spite of our ignorance of individuals.

5. Closure5 minutes

   Exit ticket: "Choose two key terms from today's texts. Write one sentence that states how the text relates them, name the kind of relationship, and quote the words in the text that signal it." Sort the tickets into "relationship, type and signal," "relationship only" and "terms defined separately" to plan the next lesson.

   Teacher note on Stewart's language. Stewart wrote in 1873, and some of his terms differ from today's. His "visible energy" is the kinetic and potential energy of whole objects; "percussion" means a hard impact; "break-wheel" is his spelling of brake wheel. He calls heat "a species of motion" of molecules, which is close to the modern idea of thermal energy. In T3, his statement that the goldfish globe "will remain at rest" is true of the system's center of mass: the globe may rock slightly as the fish move, but internal forces cannot carry it across the table. Students should read his terms by his definitions, then translate them.

   Homework passage. The homework uses the design note below. It relates friction, reaction forces, kinetic energy and potential energy in a modern technical setting.

   1Purpose. This note explains why escape ramps are built beside long mountain downgrades and how a ramp stops a truck whose brakes have failed. The truck and its numbers are invented for teaching; the resistance values are typical ones used in ramp design.

   2Why brakes fail on a long downgrade. A truck's service brakes work by friction: brake linings press against drums or discs that turn with the wheels. The friction between them slows the wheels and turns the truck's kinetic energy into thermal energy in the brakes. On a grade several kilometers long, gravity keeps speeding the truck up, so the brakes must keep turning the energy the truck gains as it loses height into heat. If the driver brakes too hard for too long, the drums or discs overheat, the friction between them and the linings drops, and the brakes lose much of their stopping force. This loss is called brake fade.

   3The ramp. An escape ramp is a lane that leaves the highway and runs into an arrester bed, a trough about a meter deep filled with loose, rounded gravel. Many ramps also slope uphill. As the tires sink into the bed, they shove gravel ahead of them and to the sides; the gravel pushes back on the tires with forces of the same size in the opposite direction, and these backward pushes on the truck slow it down. The shoving and grinding of the stones turns the truck's kinetic energy into thermal energy and into the motion of the stones.

   4Measuring the resistance. Designers describe how strongly a surface resists a rolling truck by its rolling resistance, written as a fraction of the truck's weight. Smooth pavement is about 0.01; loose pea gravel is about 0.25. On an uphill ramp, gravity also pulls back along the slope, adding about the grade written as a decimal: 0.05 for a 5 percent grade. The total retarding force is the sum of these fractions times the truck's weight.

   5An example truck. A loaded truck of mass 30,000 kg enters a ramp at 25 m/s (90 km/h). Its kinetic energy is ½mv², and its weight is mg, with g = 9.8 N/kg. The truck stops when the retarding force, acting over the stopping distance, has removed all of its kinetic energy: force × distance = kinetic energy. On an uphill ramp, part of the kinetic energy is not turned into heat but stored as gravitational potential energy, the energy of the truck's higher position. A truck stopped on an uphill ramp could roll back down, so the deep gravel also holds it in place.

Differentiation Strategies

Assessment Guidance

1. Question 1 of 20 · Multiple Choice

   Paragraph 1 is one sentence after the heading "Action and Reaction, Equal and Opposite." What job does that sentence do in the structure of the passage?

   AIt gives the first example of the law, the globe of goldfish BIt says the laws for all the atoms' motions, taken as a whole, can be known CIt defines action and reaction as two forces that act on the same body DIt concludes that the law of action and reaction can never be tested on single atoms

2. Question 2 of 20 · Multiple Choice

   Why does Stewart set the globe "delicately poised on wheels" (paragraph 2) and then imagine the table as "a lake of ice" (paragraph 3)?

   ATo show that the fish swim faster and more freely once the globe itself can move BTo show that friction from the table is what keeps the globe still CTo show that the cold of the ice weakens the forces between the fish and the water DTo remove friction from outside, so that only internal forces could move the globe

3. Question 3 of 20 · Multiple Choice

   According to paragraph 3, how are the internal forces in the globe related to the motion of the globe as a whole?

   AThey are equal and opposite actions and reactions, so the whole stays at rest BThey are too weak to matter, so the system as a whole stays at rest on its wheels CThey add together, so the globe slowly drifts the way most of the fish swim DThey are balanced by the friction of the delicate wheels

4. Question 4 of 20 · Multiple Choice

   In paragraph 3, what does Stewart treat as "the system" that cannot move itself as a whole?

   AThe fish alone, apart from the glass globe that holds them BThe table and the delicate wheels under the globe CThe globe and the fish inside it, taken as one whole DEach single fish, taken one at a time

5. Question 5 of 20 · Multiple Choice

   In paragraph 4, which two forces make up the action-reaction pair?

   AThe pull of the earth on the stone and the push of the air on the stone BThe pull of the earth on the stone and the pull of the stone on the earth CThe weight of the stone and the push of the ground on it when it lands DThe stone's downward velocity and the earth's upward velocity

6. Question 6 of 20 · Multiple Choice

   Paragraph 4 explains why no one sees the earth move up toward a falling stone. Which relationship does the explanation rest on?

   AThe earth moves only after the stone has landed and come to rest BThe earth's pull on the stone is much weaker than the stone's pull on the earth CA larger mass needs a smaller velocity to give the same mass times velocity DThe earth is held in place by the pull of the sun and the other planets

7. Question 7 of 20 · Multiple Choice

   Which formula states the relationship in the last sentence of paragraph 4? Use M and V for the earth's mass and velocity, and m and v for the stone's.

   AMV² = mv² BM ÷ V = m ÷ v CV = v DMV = mv

8. Question 8 of 20 · Multiple Choice

   Paragraph 4 begins, "We may even extend the law to cases in which we do not perceive the recoil or reaction at all." What does this sentence show about how the cases are ordered?

   AThe cases go from ones where the law is easy to see to one where it must be inferred BThe cases are arranged in the order in which they were discovered, oldest first CThe falling stone is offered as an exception, a case where the law does not hold DThe falling stone is the case that first proved the law

9. Question 9 of 20 · Multiple Choice

   In paragraph 5, what do the letters A and B stand for?

   ATwo particular atoms named earlier in the chapter BThe action and the reaction CThe stone and the earth, and nothing else DAny two bodies or parts that act on each other

10. Question 10 of 20 · Multiple Choice

    Which outline best matches the structure of the whole passage?

    AA law stated as a question, then one experiment, then a list of exceptions BA claim about the whole, then the goldfish, then the falling stone, then a general law CA definition of force, then the history of the law, then modern measurements DThe falling-stone case, then the goldfish case, then a claim that the whole can be known

11. Question 11 of 20 · Multiple Choice

    A goldfish pushes water backward with its tail. By the law in paragraph 5, what else must be happening?

    AThe water pushes the fish forward with a force of the same size BThe water pushes the fish backward, so the fish slows down CNothing else, because water is not a solid body DThe glass of the globe pushes the fish forward with a larger force

12. Question 12 of 20 · Multiple Choice

    Paragraph 3 ends: "while the small parts ... are in violent commotion among themselves, yet the system as a whole will remain at rest." What relationship does "while ... yet" set up?

    ACause and effect: the commotion of the parts causes the whole to rest BA contrast between the motion of the parts and that of the whole CA time sequence: first the commotion, later the rest DA definition of the word commotion

13. Question 13 of 20 · Multiple Choice

    Use the rule at the end of paragraph 4. A 2.0 kg stone falls toward the earth, whose mass is 6.0 × 10²⁴ kg. At the moment the stone's speed is 10 m/s, how fast is the earth moving up toward it?

    A1.7 × 10⁻²⁴ m/s B3.0 × 10²³ m/s C3.3 × 10⁻²⁴ m/s D5.8 × 10⁻¹² m/s

14. Question 14 of 20 · Multiple Choice

    Paragraph 2 says it would take "a very bold man" to predict the movements of one fish. How does this sentence connect to paragraph 5?

    AIt prepares paragraph 5's point that a law can be found without knowing individuals BIt shows that Stewart thought the law of action and reaction fails for living things CIt shows that fish obey a different law from the atoms described in paragraph 1 DIt is a joke that adds color to the passage but plays no part in the argument

15. Question 15 of 20 · Short Answer

    Paragraph 1 speaks of "the ultimate result of all these motions, taken together as a whole," and paragraph 5 of "a general law which regulates the action of internal forces." Explain how these two sentences frame the passage, and how the cases between them connect the concepts of internal force, system and motion of the whole. Cite paragraphs.

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16. Question 16 of 20 · Short Answer

    Use the numbers from question 13 (a 2.0 kg stone at 10 m/s, and the earth's velocity you found). Find the kinetic energy, ½mv², of the stone and of the earth at that moment. What does the comparison show about how a pair of equal and opposite forces relates to the energy each body gains?

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17. Question 17 of 20 · Short Answer

    When you walk, your shoe pushes backward on the floor through friction. Use paragraphs 4 and 5 to explain what pushes you forward, how friction and the reaction force are related here, and why the floor and the earth do not visibly move.

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18. Question 18 of 20 · Short Answer

    In paragraph 3, equal and opposite actions and reactions leave the goldfish globe at rest. In paragraph 4, an equal and opposite pair of pulls sets both the stone and the earth moving. A classmate says these two cases contradict each other. Use the passage to explain why they do not.

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19. Question 19 of 20 · Short Answer

    Draw or describe a concept map of paragraphs 3-5 that uses at least five of these terms: internal force, action, reaction, system, parts, mass, velocity, general law. Label each link with a verb phrase and give the paragraph.

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20. Question 20 of 20 · Short Answer

    Compare the structure of T1 (friction and heat) with the structure of T3 (action and reaction). Give one way the two structures are alike and one way they differ, and explain how each structure helps a reader connect its key terms.

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These standards connect to RST.9-10.5: prerequisites to review first, parallel standards at the same level, and next steps that build on it.

Standard text: Common Core State Standards for English Language Arts & Literacy. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.