Potential energy and mechanical energy conservation 1 Physics course exercises Liceo Scientifico Isaac Newton - Roma Potential energy and mechanical energy

potential energy and mechanical energy conservation

1

Physics course exercises

Liceo Scientifico Isaac Newton - Roma

Potential energy and mechanical energy conservation

in accordo con il Ministero dell’Istruzione, Università, Ricercae sulla base delle

Politiche Linguistiche della Commissione Europea

percorso formativo a carattere tematico-linguistico-didattico-metodologicoscuola secondaria di secondo grado

a cura di Serenella Iacino


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


Strategies BeforePrerequisities

Energy conservation

Physics

•dot product of two vector •funzioni goniometriche •first theorem for right-angletriangles of trigonometry

Maths

1

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


Strategies BeforeLinking to Previous Knowledge and Predicting

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

2. Are you able to draw the free-body diagram?

3. How do you define the work done by a force on an object?

4. What is the work done by gravity and by elastic force?

5. How do you define kinetic energy?

6. Do you know the work–energy theorem?

2


Strategies Before

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 – forceforza conservativa – conservative force

3


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


Keywords Strategies During

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.

4


8

mechanical energy

Complete the Conceptual Map

energy conservation

elastic potential energy

gravitational potential energy

work done by conservativeforces and non

conservative forces

variation of mechanical energy

potential energy kinetic energy

work done by conservative forces

5Strategies During


Strategies After

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?

Multiple Choice

12 m / s12 m / s8.08.0 m / s 5.0 m / s5.0 m / s 22 m / s22 m / s

6


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?

1 m1 m0.410.41 m 0.39 m0.39 m None of None of thesethese

Strategies AfterMultiple Choice


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?

2.66 10 J2.66 10 J2.27 10 J2.27 10 J3.91 10 J3.91 10 J 6.18 10 J6.18 10 J66 6 5

Strategies After

Multiple Choice


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?

v / 2v / 22 v2 v4 v4 v 8 v8 v

Strategies After

Multiple Choice


1 2 3

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.

K vU h U x

7

Strategies After

Matching


1 2 3

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.

-47 J -66 J

A A

BB

A

B

4.0 m

4.0 m

1.0 m1.0 m

1.0 m 1.0 m

1.0 m2.0 m

2.0 m

3.0 m

3.0 m

-104 J

Strategies After

Matching


• 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

T F

• A conservative force always does work equal to zero.

8

Strategies AfterTrue/False


• 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



• Elastic potential energy is the work done by elastic force to return the

spring to its initial position

• If the forces are conservative or non conservative, the change of

kinetic energy is equal to the work done by them.

T F

T F



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 ...................................................

.................................................................................................

9 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

............................................................................................

Strategies After

Completion Exercise


Strategies AfterFlow Chart

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.

start

end determine the initial kinetic energy

A

B

then the initial potential energy

and also the final mechanical energy

so apply the Energy Conservation

10


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)A student is writing an article about energy and chemical transformations B)A student is preparing for an interview on a local TV about the transformation of the gravitational potential energy into heat.

The student should:

1)Write an article or prepare an interview;

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 Strategies After

Think and Discuss


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.

12

Strategies After

Summary


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.

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


• 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.

Strategies After


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


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?

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?

3)

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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)

Activities based on Problem Solving


Answer Sheets

Multiple Choice:22 m/s; 0.41 m; 2.66 10 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) 8.8 10 J; 2) 10 m / s; 3) 6.3 m; 4) 0.208 m; 5) 415 N/m.

Keywords

Breadth, electric potential energy.

6

-2

Conceptual MapPag 29


mechanical energy

Conceptual Map

energy conservation

elastic potential

energy

gravitational potential

energy

work done by conservativeforces and non

conservative forces

variation of mechanical energy

potential energy

kinetic energy

work done by conservative forces

Answer Sheets


Answer SheetsFlow Chart Solution

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

start

end

determine the initial kinetic energy

then the initial potential energy

and also the final mechanical energy

so apply the Energy Conservation

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Potential energy and mechanical energy conservation 1 Physics course exercises Liceo Scientifico Isaac Newton - Roma Potential energy and mechanical energy