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Work Physics course exercises Liceo Scientifico Isaax Newton - Roma Work in accordo con il Ministero dellIstruzione, Università, Ricerca e sulla base delle Politiche Linguistiche della Commissione Europea percorso formativo a carattere tematico-linguistico-didattico- metodologico scuola secondaria di secondo grado a cura di Serenella Iacino

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Work Indice modulo clil Strategies – Before Prerequisites Linking to Previous Knowledge and Predicting Glossary Italian / English Strategies – During Video Keywords riferite al video attraverso esercitazioni mirate Conceptual Map Strategies – After Exercises: - Multiple Choice - Matching - True / False - Cloze or Completion - Flow Chart - Think and Discuss Summary and Summary Questions Web References di approfondimento come input interattivi per test orali e scritti e per esercitazioni basate sul Problem Solving Answer sheets

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Work work Physics first theorem for right-angle triangles of trigonometry concept of vector dot product of two vector trigonometric functions Maths 1 the prerequisites are concept of force Newtons second law Newtons third law the free-body diagram concept of displacement Strategies Before Prerequisities

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Work Strategies Before Linking to Previous Knowledge and Predicting 1.Do you know the dot product of two vectors? 2.Do you know Newtons second law? 3.Do you know Hookes law? 4.Are you able to draw the free–body diagram? 5.Do you know the first theorem of trigonometry for right– angle triangles? 6.Do you know the laws of uniformly accelerated motion? 2

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Work Strategies Before Glossary Italian / English altezza – height angolo acuto – acute angle angolo ottuso – obtuse angle attrito – friction base – base coefficiente angolare – gradient energia – energy energia cinetica - kinetic energy forza – force forza di gravità – gravity forza elastica – elastic force forza normale – normal grandezza scalare – scalar quantity intensità – magnitude legge di Hooke – Hookes law 3

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Work Strategies Before Glossary Italian / English lunghezza – length modulo – modulus molla allungata – stretched spring molla compressa – compressed spring moto uniformemente accelerato – uniformly accelerated motion peso – weight prodotto scalare – dot product retta – straight-line risultante delle forze – resultant of forces schema del corpo libero – free-body diagram seconda legge di Newton – Newtons second law spostamento – displacement teorema dellenergia cinetica – work-energy theorem unità di misura – unit of measure vettore – vector velocità – velocity

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Work Circle the odd one out Strategies During Keywords magnitude, right-angle triangle, obtuse, displacement, gravity, friction, elastic force, free-body diagram, integral, spring, axis, constant force, sin function, energy of motion, straight line, velocity, direction, uniform motion, area, uniformly accelerated motion, kinetic energy, unit of measure, variable force, length, component, Hookes law, height, vector quantity. 4

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Work work constant force dot product one force more forces force integral of force non constant force Work-energy theorem free-body diagramkinetic energy displacement Strategies During Complete the Conceptual Map 5

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Work What is the unit of measure of work ? The same as Kinetic energy The same as force N / s N s 6 Strategies After Multiple Choice

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Work Strategies After Multiple Choice This graph represents a force as a function of displacement. What is the work done by the force between 2 m and 8 m? 170 N 170 J 180 J 180 N s (m) F (N) o 2468 10 30 20 40

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Work Strategies After Multiple Choice A basket is stationary on a floor without friction; a girl pushes it with her foot, applying a constant force parallel to the displacement, the magnitude of which is 20 N. If the work done by the force is 100 j, what is the displacement of the basket? 5 m 5 5 10 m 50 cm None of these 3

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Work Strategies After Multiple Choice A spring is compressed by amount x=4 cm; if the work done by the elastic force is equal to 6 j, what is the spring constant? 300 m N3000 m N 6000 m N 7500 m N

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Work Strategies After Multiple Choice A lift, having mass m=1500 kg, goes up with constant velocity for 25 m. What is the work done by the tension on the cables? 9.9 9.9 10 j 2 8.1 8.1 10 j 3 1.4 1.4 10 j 4 3.7 3.7 10 j 5

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Work Strategies After Matching Match the graphs with the correct values of the work: 1 a 180 b 170 c 190 2 F (N) s (m) 248 10 30 20 40 6 2486 10 30 20 40 3 F (N) s (m) 2486 10 30 20 40 7

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Work Strategies After Matching Match the sentences and the definitions of work: 1 A woman pushes a shopping trolley 2 An electric train moves in a uniform circular motion 3 A spring stretched Negative work Positive work Zero work abc

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Work Strategies After True/False The work done by a force upon an object is zero if the force and the displacement are perpendicular. If an object falls from a height h, the work done by the force of gravity is proportional to the height. T T F F The work done by friction is positive because friction opposes displacement. TF 8

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Work Strategies After True/False Work is a vector quantity. The work done by a force is the dot-product of the force and the vector displacement. The work done by the elastic force on a compressed spring is proportional to the square of the spring constant. TF T T F F

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Work Strategies After Completion Exercise Complete these sentences: The work done by a constant force upon an object is ……………………………………………………………………………………………………………… ……………………………………………………………………………………………………………… If the force and the vector displacement are parallel and have the same direction, then the work is ……………………………………………………………………………………………………………… ……………………………………………………………………………………………………………….. Work is a …………….quantity and its unit of measure is…………………………………………………………………………………………………………… …………………………………………………………………………………………………………...... 9

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Work Complete these sentences: If the force is constant, parallel to the displacement s and has the same direction, then the work done by the force is represented by ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… If the force changes over time and is represented by the function f(x), then the work is given by…………………………............................................................................................................................................................ Strategies After Completion Exercise

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Work Strategies After Flow Chart Complete the flow chart in order to determine the total work done upon a box by a man that pushes it on a floor, applying a horizontal force F, knowing that the floor develops a friction force. start end the work done by gravity is zero as is that done by normal draw the free-body diagram so that the total work is given by the work of friction and by force F 10

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Work Strategies After Think and Discuss The following activity can be performed in a written or oral form. The teacher will choose the modality, depending on the ability (writing or speaking ) that needs to be developed. The context in which the task will be presented to the students is: A)A student is writing an article about the change of mechanical work into the heat through the Joules Whirlpool. The student should: 1)Write an article; 2)Prepare the article or the debate, outlining the main points of the argument, on the basis of what has been studied; 3)If the written activity is the modality chosen by the teacher, the student should provide a written article, indicating the target of readers to whom the article is addressed and the type of magazine / newspaper / school magazine where the article will be published; 4)If the oral activity is the modality chosen by the teacher, the student should present his point of view on the topics to the whole class and a debate could start at the end of his presentation. 11

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Work Strategies After Summary In Physics work is always done by forces, in fact a force acting upon an object does work when the initial point of application of the force is displaced. So if F is the magnitude of a constant force acting upon an object, θ is the angle between F and the displacement s, then the mechanical work is the dot product of the force F and the displacement s. Its unit of measure is Joule and is a scalar quantity. According to the measure of the angle ( θ >90°, θ <90°or θ =90°), the work can be positive, negative or equal to zero. When many forces act upon an object, we can calculate the work done by each force and then we add them to obtain the sum of work. Graphically, on a Cartesian plane, the work of a constant force, that is parallel to the displacement and has the same direction, is represented by the area of the rectangle having base s and height F. 12

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Work But if the force F changes over time and is represented by the function f(x), then the work is given by the integral of f(x). The force of gravity is a constant force while the elastic force is a variable force. Energy is the ability to perform work. If we apply a force F to an object of mass m, this force changes its velocity and the object moves in an uniformly accelerated motion; applying the laws of this motion, we can demonstrate a relationship called The Work-Energy Theorem which affirms the work done by this force is energy of motion and is called Kinetic Energy or just K. We can observe that if the work is positive, then the kinetic energy increases; if the work is negative, then the kinetic energy decreases, while if the work is zero, the kinetic energy doesnt change, so the velocity is constant. 1.Answer to the following questions. The questions could be answered in a written or oral form, depending on the teachers objectives. Strategies After

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Work How do you define the work done by a constant force upon an object? When is work equal to zero? When do you need the free–body diagram to calculate work? How do you calculate the work done by a force that changes over time? What is the work done by a compressed spring? How do you define kinetic energy? When does kinetic energy dicreases? What is the unit of measure of work? Is gravity a constant force? Strategies After 2. Write a short abstract of the summary (max 150 words) highlighting the main points of the video.

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Work http://www.physics.org/aboutus.asp physics.org is brought to you by the Physics in Society team at the Institute of Physics. Our aim is to inspire people of all ages about physics. Let us be your guide and show you the best physics places on the web. http://www.aahperd.org NASPE's mission is to enhance knowledge, improve professional practice, and increase support for high quality physical education, sport, and physical activity programs. http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html This site was honored because of its comprehensive coverage of most of physics, the creative use of multimedia and linking, and the impact it has had on students worldwide. Online tutorials cover a wide range of physics topics, including modern physics and astronomy. Material is organized through extensive concept maps." Web References

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Work Activities based on Problem Solving Solve the following problems on work: A waitress pushes on a floor a tea–trolley of mass m=10 Kg, for 5 metres, applying a horizontal force, the magnitude of which is 40 N. If at the end of the displacement the velocity is 2 m/s, what is the friction coefficient? 1) 2)During a football match, a ball of mass m=0.500 Kg is kicked by a footballer, reaching the velocity of 129.6 Km/h. What is the work done on the ball by the footballer? 13

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Work Activities based on Problem Solving Solve the following problems on work: A baby–sitter pushes a pram for 10 metres along the avenue of a park, applying a constant force having the same direction of the displacement and a magnitude of 50 N. Ignoring friction, what is the work done by the baby–sitter? 3) 4)A boy goes down to the swimming–pool through a water slide, leaving from a height h. What is the quotient between the kinetic energy at middle height and at the end of the slide?

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Work Activities based on Problem Solving Solve the following problems on work: A box of mass m=3.4 Kg goes down a plane inclined at 30 degrees to the ground. Ignoring friction, if the height of the plane is 3 m, what is the total work done on the box? 5) A boy pulls a sled of mass m=10 Kg for 10 metres, applying a force inclined at 45 degrees to the horizontal, the magnitude of which is 50 N. If the ground develops a friction force, the coefficient of which is 0.4, what is the sum of work done on the sled? What is the velocity of the sled? 6)

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Work Solve the following problem on work: A skier, having mass m=55 Kg, goes down along a track that has a slope of 30° to the horizontal. His initial velocity is equal to 3.6 m/s. During the descent, his motion is impeded by a friction force the magnitude of which is 70 N. Ignoring air resistance, what is his velocity at the moment in which the skier has travelled 49 m from the point of departure? 7) Activities based on Problem Solving

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Work Answer Sheets Multiple Choice : The same as kinetic energy; 170 J; 5 m; 7500 N / m; 3.7 10 J. Matching : 2a; 3b; 1c. b1; c2; a3. True / false : T; T; F; F; F; T. Completion exercise : the dot product of the force F and the displacement vector s; positive; scalar Joule; the area of the rectangle having base s and height the force F; the integral. Problem solving : 1) 0.37; 2) 324 J; 3) 500 J; 4) 0.5; 5) 100 J; 6) 103 J and 4.5 m / s; 7) 19 m / s. Keywords Vector quantity, sin function, uniform motion. 5 Conceptual Map Pag.31

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Work WORK constant force dot product one force more forces displacement constant force free-body diagram non constant force integral of force kinetic energy Work-energy theorem Answer Sheets Conceptual Map

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Work Answer Sheets Flow Chart Solution Complete the flow chart in order to determine the total work done upon a box by a man that pushes it on a floor, applying an horizontal force F, knowing that the floor develops a friction force. start end draw the free-body diagram the work done by gravity is zero as is that done by normal so that the total work is given by the work of friction and by force F

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