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Physics course exercises

Liceo Scientifico Isaax Newton - Roma

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in accordo con il Ministero dell’Istruzione, Università, Ricercae 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 clilStrategies – 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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Physics

•first theorem for right-angletriangles of trigonometry

•concept of vector •dot product of two vector •trigonometric functions

Maths

1

the prerequisites are the prerequisites are

•concept of force •Newton’s second law •Newton’s third law •the free-body diagram •concept of displacement

Strategies BeforePrerequisities

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Strategies BeforeLinking to Previous Knowledge and Predicting

1. Do you know the dot product of two vectors?

2. Do you know Newton’s second law?

3. Do you know Hooke’s 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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Strategies Before

Glossary Italian / English

altezza – height

angolo acuto – acute angle

angolo ottuso – obtuse angle

attrito – friction

base – basecoefficiente angolare – gradientenergia – energyenergia cinetica - kinetic energyforza – forceforza di gravità – gravityforza elastica – elastic forceforza normale – normalgrandezza scalare – scalar quantityintensità – magnitudelegge di Hooke – Hooke’s law

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Strategies Before

Glossary Italian / English

lunghezza – length

modulo – modulus

molla allungata – stretched springmolla compressa – compressed springmoto uniformemente accelerato – uniformly accelerated motionpeso – weight

prodotto scalare – dot productretta – straight-linerisultante delle forze – resultant of forcesschema del corpo libero – free-body diagramseconda legge di Newton – Newton’s second lawspostamento – displacement

teorema dell’energia cinetica – work-energy theoremunità di misura – unit of measurevettore – vectorvelocità – velocity

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Circle the odd one out

Strategies DuringKeywords

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, Hooke’s law, height,

vector quantity.

4

Work

work

constant force

dot product

one force

more forces

force

integral of force

non constant force

Work-energy theorem

free-body diagram kinetic energy displacement

Strategies During

Complete the Conceptual Map

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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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Strategies AfterMultiple 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 N170 N

170 J170 J

180 J180 J

180 N180 Ns (m)

F (N)

o 2 4 6 8

10

30

20

40

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Strategies AfterMultiple 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 m5 m5 5 ∙ 10 m 50 cm50 cmNone of None of thesethese

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Strategies AfterMultiple 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?

300300m

N

30003000m

N

60006000m

N

75007500m

N

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Strategies AfterMultiple 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 j2

8.1 8.1 ∙ 10 j3

1.4 1.4 ∙ 10 j4

3.7 3.7 ∙ 10 j5

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Strategies AfterMatching

Match the graphs with the correct values of the work:

1

a 180180 b 170170 c 190190

2

F (N)F (N)

s (m) s (m)2 4 8

10

30

20

40

6 2 4 86

10

30

20

40

3

F (N)

s (m)2 4 86

10

30

20

40

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Strategies AfterMatching

Match the sentences and the definitions of work:

1 A woman pushes a shopping trolleyA woman pushes a shopping trolley

2 An electric train moves in a uniform circular motionAn electric train moves in a uniform circular motion

3 A spring stretchedA spring stretched

Negativework

Positivework

Zerowork

a b c

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Strategies AfterTrue/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.

T F

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Strategies AfterTrue/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.

T F

T

T F

F

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Strategies AfterCompletion 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……………………………………………………………………………………………………………

…………………………………………………………………………………………………………......

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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 AfterCompletion Exercise

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Strategies AfterFlow 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

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Strategies AfterThink 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 Joule’s 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.

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Strategies AfterSummary

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.

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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 doesn’t 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 teacher’s objectives.

Strategies After

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• 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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http://www.physics.org/aboutus.aspphysics.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.orgNASPE'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.htmlThis 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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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?

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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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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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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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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.

KeywordsVector quantity, sin function, uniform motion.

5

Conceptual MapPag.31

Work

WORK

constant force

dot product

one force

more forces

displacementconstant force

free-body diagram

non constant force

integral of force

kinetic energy

Work-energy theorem

Answer SheetsConceptual Map

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Answer SheetsFlow 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