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**Physics course exercises**

Liceo Scientifico Isaac Newton - Roma Potential energy and mechanical energy conservation in accordo con il Ministero dell’Istruzione, 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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**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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**Strategies Before Prerequisities**

1 Strategies Before Prerequisities Physics Maths the prerequisites are the prerequisites are the free-body diagram newton’s second law concept of mechanical work work done by gravity work done by elastic force kinetic energy work-energy theorem dot product of two vector funzioni goniometriche first theorem for right-angle triangles of trigonometry Energy conservation

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**Linking to Previous Knowledge and Predicting**

Strategies Before Linking to Previous Knowledge and Predicting Do you know the dot product of two vectors? Are you able to draw the free-body diagram? How do you define the work done by a force on an object? What is the work done by gravity and by elastic force? How do you define kinetic energy? Do you know the work–energy theorem? 2

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**Strategies Before 3 Glossary Italian / English altezza – height**

angolo acuto – acute angle angolo ottuso – obtuse angle attrito – friction conservazione dell’energia – energy conservation energia – energy energia cinetica – kinetic energy energia potenziale – potential energy energia potenziale elastica – elastic potential energy energia potenziale gravitazionale – gravitational potential energy energia sonora – sound energy energia termica – thermal energy forza – force forza conservativa – conservative force

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**Strategies Before Glossary Italian / English**

forza di gravità - gravity forza elastica – elastic force forza non conservativa – non conservative force forza normale – normal lunghezza – length molla allungata – stretched spring molla compressa – compressed spring moto – motion perpendicolare – perpendicular spostamento – displacement teorema dell’energia cinetica – work-energy theorem unità di misura – unit of measure velocità – velocity verticale – vertical vettore - vector

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**Strategies During Keywords**

4 Strategies During Keywords Circle the odd one out Velocity, gravitational potential energy, conservative, friction, closed route, kinetic energy, height, length, breadth, change of mechanical energy, normal force, electric potential energy, elastic potential energy, energy conservation, compressed spring, gravity, sound energy, displacement, thermal energy.

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**Complete the Conceptual Map**

5 Strategies During Complete the Conceptual Map mechanical energy gravitational potential energy elastic potential energy work done by conservative forces and non conservative forces work done by conservative forces variation of mechanical energy energy conservation kinetic energy potential energy

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**Strategies After 6 Multiple Choice**

A helicopter drops a case of humanitarian aid from a height of 25 m. What is the velocity of the case when it reaches the ground? 5.0 m / s 8.0 m / s 12 m / s 22 m / s

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**Strategies After Multiple Choice 0.39 m 0.41 m 1 m**

A bar of soap falls onto a shower tray with an initial velocity v = 1 m/s ; if it reaches the tray at 3 m/s, what is the height from which it falls? None of these 0.39 m 0.41 m 1 m

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**Strategies After Multiple Choice 2.66 10 J 2.27 10 J 3.91 10 J**

An airplane of mass m = 1250 Kg flies with a constant velocity v = 25.0 m/s at a height of 185 m. What is its total mechanical energy? J J J J 6 5

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**Strategies After Multiple Choice 4 v 2 v v / 2 8 v**

In Sherwood forest, Robin Hood shoots an arrow vertically upward with a velocity v. In the point of maximum height, the arrow reaches a potential energy U. If its potential energy is 4U, what is its initial velocity? 4 v 2 v v / 2 8 v

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**Strategies After 7 Matching**

Match the graphs with the kinetic energy in function of the velocity v, the elastic potential energy in function of the stretching x and the gravitational potential energy in function of the height h. 1 2 3 U h K v U x

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**Strategies After Matching -47 J -104 J -66 J**

Match the graphs with the correct values of the work done by friction force on a box of mass m=3.7 kg, that moves on a floor from one point A to another point B, if the coefficient of friction is 0.26. 4.0 m 1.0 m 4.0 m 1.0 m 1.0 m 1.0 m B B 1 B 2 3 2.0 m A 3.0 m A A 2.0 m 1.0 m 3.0 m -47 J -104 J -66 J

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**Strategies After True/False T F T F**

8 Strategies After True/False Ignoring the resistance of the air, if a bullet is fired vertically upward, at the point of maximum height, its potential energy is greatest. T F A conservative force always does work equal to zero. T F

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**Strategies After True/False T F T F**

The work done by friction through a closed route is zero. T F The work done by a non conservative force is equal to the change of mechanical energy. T F

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**Strategies After True/False T F T F**

If the forces are conservative or non conservative, the change of kinetic energy is equal to the work done by them. T F Elastic potential energy is the work done by elastic force to return the spring to its initial position T F

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**Strategies After 9 Completion Exercise Complete these sentences:**

Gravitational potential energy is the work and depends only on Elastic potential energy is the energy of a A force is called conservative if

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**Strategies After Completion Exercise Complete these sentences:**

Friction is a non in fact friction always opposes and does work that is transformed Mechanical energy is conserved only in the system in which are involved. The work done by a non conservative force is equal to

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**Strategies After 10 Flow Chart**

start Complete the flow chart in order to determine the final velocity of a wagon of the Roller Coaster that goes down, without friction, from an initial position A, having height h to the ground, to a final position B, having height h to the ground. A B then the initial potential energy so apply the Energy Conservation end determine the initial kinetic energy and also the final mechanical energy

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**Strategies After 11 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 contexts in which the task will be presented to the students are: A student is writing an article about energy and chemical transformations A student is preparing for an interview on a local TV about the transformation of the gravitational potential energy into heat. The student should: Write an article or prepare an interview; Prepare the article or the debate, outlining the main points of the argument, on the basis of what has been studied; 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; 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.

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**Strategies After 12 Summary**

Under specific conditions, a stationary object can have energy. General forms of energy, stored in an object, are called potential energies, and according to the force to which they are linked, we have gravitational potential energy, which is the work done by gravity on an object, and elastic potential energy, which is the work done by elastic force on a stretched or compressed spring to return it to its initial position. The forces that do work, are divided into conservative and non conservative forces. A conservative force does work which is independent of the route taken and only depends on the initial position and final position. Gravity and elastic force are conservative forces. So, the work done by a conservative force through a closed route is always zero. A force is called non conservative if its work depends on the chosen route, between the initial position and the final position.

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Strategies After Friction is a non conservative force: it always opposes motion and does negative work that is not stored as potential energy but is transformed into sound or thermal energy. In physics mechanical energy of an object is the sum of its potential and kinetic energies. It is conserved only in the systems where conservative forces are involved: in fact, kinetic energy is transformed into potential energy, just as potential energy is transformed into kinetic energy. In a system with no conservative forces, the mechanical energy can change, as in the case of friction where mechanical work is transformed into sound or thermal energy. In this cases the Law of energy conservation is no longer valid. Answer to the following questions. The questions could be answered in a written or oral form, depending on the teacher’s objectives.

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Strategies After In addition to kinetic energy, which other forms of energy do you know? How do you define gravitational potential energy and elastic potential energy? When is a force called conservative? Is the work done by a force always equal to zero? Which are the features of a non conservative force? What kind of force is friction? When is mechanical energy conserved? Is a roller coaster an example of energy conservation? What is the work done by non conservative force equal to? 2. Write a short abstract of the summary (max 150 words) highlighting the main points of the video.

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**Web References 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. NASPE's mission is to enhance knowledge, improve professional practice, and increase support for high quality physical education, sport, and physical activity programs. 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.”

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**Activities Based on Problem Solving**

13 Activities Based on Problem Solving Solve the following problems : A pendulum of mass m=80 gr and length l=120 cm swings at an angle of 25° to the position of equilibrium. What is the potential energy of the pendulum in this position? 1) 2) At the circus, during a show, a trapeze artist of mass m=50 Kg, falls down to the safety net from a height of 4.5 m with initial velocity equals to 4.0 m/s. Ignoring air resistance, what is her velocity when she lands on the net? 3) An apple falls down vertically and lands on the ground with velocity v=40.0 Km/h. Ignoring air resistance, what is the height h from which it falls?

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**Activities based on Problem Solving**

Solve the following problems : 4) A child is on a swing; when the swing is at its lowest point, its velocity is equal to 2.02 m/s. Ignoring air resistance, what is the maximum height that the child will reach? An object of mass m = 1.80 Kg moves on a rough surface with velocity v=2.00 m/s and, before stopping it compresses a spring of 11.0 cm. If the coefficient of friction is equal to 0.560, what is the spring constant? 5)

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**Answer Sheets Keywords Breadth, electric potential energy.**

Conceptual Map Pag 29 Multiple Choice: 22 m/s; 0.41 m; J; 2 v. Matching: 1 K v; 2 U x; 3 U h. A (-104 J); B (-47 J); C (-66 J). True / false: T; F; F; T; T; T. Completion exercise: Work done by gravity on a object and depends only on the height h; stretched or compressed spring and is the work done by elastic force to return the spring to its initial position; it does work which is independent of the route taken and it depends on the initial and final positions; conservative force – motion – negative – into sound or thermal energy; conservative forces; The change of mechanical energy. Problem solving: 1) J; 2) 10 m / s; 3) 6.3 m; 4) m; 5) 415 N/m. 6 -2

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**work done by conservative**

Answer Sheets Conceptual Map mechanical energy potential energy kinetic energy gravitational potential energy elastic potential energy work done by conservative forces and non conservative forces work done by conservative forces variation of mechanical energy energy conservation

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**Answer Sheets Flow Chart Solution**

start Complete the flow chart in order to determine the final velocity of a wagon of the Roller Coaster that goes down, without friction, from an initial position A, having height h to the ground, to a final position B, having height h to the ground. determine the initial kinetic energy then the initial potential energy and also the final mechanical energy A so apply the Energy Conservation B end

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