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potential energy and mechanical energy conservation
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
1
potential energy and mechanical energy conservation
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
potential energy and mechanical energy conservation
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
potential energy and mechanical energy conservation
2
Strategies Before
Linking 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?
potential energy and mechanical energy conservation
3
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 – force
forza conservativa – conservative force
potential energy and mechanical energy conservation
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
potential energy and mechanical energy conservation
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.
potential energy and mechanical energy conservation
5
Strategies During
Complete the Conceptual Map
mechanical energy
gravitational
potential
energy
work done by conservative
forces and non
conservative forces
work done by
conservative forces
variation of
mechanical energy
energy conservation
kinetic energy
8
potential energy
elastic
potential
energy
potential energy and mechanical energy conservation
6
Strategies After
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
potential energy and mechanical energy conservation
Strategies After
Multiple Choice
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?
0.39 m
0.41 m
1m
None of
these
potential energy and mechanical energy conservation
Strategies After
Multiple 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?
6
3.91 10 J
6
2.27 10 J
6
2.66 10 J
5
6.18 10 J
potential energy and mechanical energy conservation
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?
4v
2v
v/2
8v
potential energy and mechanical energy conservation
7
Strategies After
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.
3
2
1
U
h
K
v
U
x
potential energy and mechanical energy conservation
Strategies After
Matching
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
4.0 m
1.0 m
1.0 m
1.0 m
1
1.0 m
B
2
B
2.0 m
A
A
2.0 m
B
3
A
3.0 m
1.0 m
3.0 m
-47 J
-104 J
-66 J
potential energy and mechanical energy conservation
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
potential energy and mechanical energy conservation
Strategies After
True/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
potential energy and mechanical energy conservation
Strategies After
True/False
•
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
potential energy and mechanical energy conservation
9
Strategies After
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 ...................................................
.................................................................................................
potential energy and mechanical energy conservation
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
............................................................................................
potential energy and mechanical energy conservation
10
Strategies After
Flow 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 A to the
ground, to a final position B, having
height hB to the ground.
start
then the initial potential energy
so apply the Energy Conservation
determine the initial kinetic energy
and also the final mechanical energy
end
potential energy and mechanical energy conservation
11
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 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.
potential energy and mechanical energy conservation
12
Strategies After
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.
potential energy and mechanical energy conservation
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.
1. Answer to the following questions. The questions could be answered in a
written or oral form, depending on the teacher’s objectives.
potential energy and mechanical energy conservation
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.
potential energy and mechanical energy conservation
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.
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.”
potential energy and mechanical energy conservation
13
Activities Based on Problem Solving
Solve the following problems :
1) 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?
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?
potential energy and mechanical energy conservation
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?
5) 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?
potential energy and mechanical energy conservation
Answer Sheets
Keywords
Breadth, electric potential energy.
Conceptual Map
Pag 29
Multiple Choice:
22 m/s; 0.41 m; 2.66 106 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:
-2
1) 8.8 10 J; 2) 10 m / s; 3) 6.3 m; 4) 0.208 m; 5) 415 N/m.
potential energy and mechanical energy conservation
Answer Sheets
Conceptual Map
mechanical energy
potential energy
kinetic energy
gravitational
potential
energy
work done by conservative
forces and non
conservative forces
variation of
mechanical energy
work done by
conservative forces
energy conservation
elastic
potential
energy
potential energy and mechanical energy conservation
Answer Sheets
Flow 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 hA to the ground, to a
final position B, having height
hB to the ground.
start
determine the initial kinetic energy
then the initial potential energy
and also the final mechanical energy
so apply the Energy Conservation
end