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Physics course exercises
Liceo Scientifico Isaax Newton - Roma
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in accordo con il Ministero dell’Istruzione, Università,
Ricerca
e sulla base delle
Politiche Linguistiche della Commissione Europea
percorso formativo a carattere tematico-linguistico-didatticometodologico
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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1
Strategies Before
Prerequisities
Physics
Maths
the prerequisites are
the prerequisites are
•first theorem for right-angle
triangles of trigonometry
•concept of vector
•dot product of two vector
•trigonometric functions
•concept of force
•Newton’s second law
•Newton’s third law
•the free-body diagram
•concept of displacement
work
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Strategies Before
Linking 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?
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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 – Hooke’s law
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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 – Newton’s second law
spostamento – displacement
teorema dell’energia cinetica – work-energy theorem
unità di misura – unit of measure
vettore – vector
velocità – velocity
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Strategies During
Keywords
Circle the odd one out
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.
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Strategies During
Complete the Conceptual Map
work
more forces
constant
force
non constant
force
one force
Work-energy
theorem
dot product
force
integral of force
free-body diagram
kinetic energy
displacement
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Strategies After
Multiple Choice
What is the unit of measure of work?
The same as force
The same as Kinetic energy
N∙s
N/s
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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?
F (N)
170 N
40
180 J
30
20
170 J
10
o
2
4
6
8
s (m)
180 N
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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?
50 cm
3
5 ∙ 10 m
5m
None of
these
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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
N
m
3000
N
m
6000
7500
N
m
N
m
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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?
2
9.9 ∙ 10 j
3
8.1 ∙ 10 j
4
1.4 ∙ 10 j
5
3.7 ∙ 10 j
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Strategies After
Matching
Match the graphs with the correct values of the work:
F (N)
F (N)
F (N)
40
40
40
30
30
30
20
20
20
10
10
10
1
2
4
6
8
a 180
s (m)
2
2
4
6
8
b 170
s (m)
3
2
4
6
8
c 190
s (m)
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Strategies After
Matching
Match the sentences and the definitions of work:
Negative
work
Positive
work
Zero
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a
b
c
1 A woman pushes a shopping trolley
2 An electric train moves in a uniform circular motion
3 A spring stretched
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Strategies After
True/False
•
The work done by a force upon an object is zero if the force and the
displacement are perpendicular.
T
•
If an object falls from a height h, the work done by the force of
gravity is proportional to the height.
T
•
F
F
The work done by friction is positive because friction opposes
displacement.
T
F
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Strategies After
True/False
•
Work is a vector quantity.
T
•
F
The work done by the elastic force on a compressed spring is
proportional to the square of the spring constant.
T
•
F
The work done by a force is the dot-product of the force and the
vector displacement.
T
F
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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……………………………………………………………………………………………………………
…………………………………………………………………………………………………………......
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Strategies After
Completion Exercise
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………………………….................................................................
...........................................................................................
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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
as is that done by normal
so that the total work is given by
the work done by gravity is zero
the work of friction and by force F
draw the free-body diagram
end
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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 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 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.
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Strategies After
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.
Work
Strategies After
•
•
•
•
•
•
•
•
•
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?
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.
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."
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Activities based on Problem Solving
Solve the following problems on work:
1) 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?
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:
3) 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?
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:
5) 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?
6) 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?
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Activities based on Problem Solving
Solve the following problem on work:
7) 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?
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Answer Sheets
Keywords
Vector quantity, sin function, uniform motion.
Conceptual Map
Pag.31
Multiple Choice:
5
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.
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Answer Sheets
Conceptual Map
free-body
diagram
kinetic energy
WORK
more forces
constant
force
non constant
force
one force
Work-energy
theorem
dot product
integral of force
constant force
displacement
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
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
end