Download Printable Activities

Science 10th grade
LEARNING UNIT
How do world components
change?
S/K
LEARNING OBJECT
Why is heat said to be dissipative?
Skill 1: Calculate mechanical work based on a graph of
distance vs. force and as the result of a dot product between
vectors.
Skill 2: Determine the total mechanical energy in physical
systems.
Skill 3: Establish relationships among total mechanical energy
and kinematic equations.
Skill 4: Illustrate and explain everyday life situations in which
mechanical energy is preserved or situations in which it is not.
Skill 5: Establish relationships between work, energy and
power.
Language
Socio cultural context of
the LO
Curricular axis
Standard competencies
Background Knowledge
English Review topic
Vocabulary box
Skill 6: Practice the use of passive voice as a tool to review
the studied contents.
English
Colombia
Physical environment
Establish relationships between different forces which act on
bodies at rest or in uniform linear motion and establish
conditions to preserve mechanical energy.
Knowledge on SI, unit conversion, properties of matter,
physical phenomena.
Passive voice
ü Electrical goods (n): items that are made to be sold
and which use electricity to operate.
ü Coal (n): a hard, black substance that is found in the
ground and burned as fuel
ü Marble (n): a small hard ball of glass used in children’s
games
ü Slide (n): a large object that children climb and slide
down as a game.
ü Spring (n): a piece of metal that curves round and
round
Definitions
retrieved
on
June
1st,
2016
from
http://dictionary.cambridge.org/
NAME: _________________________________________________
GRADE: ________________________________________________
Introduction
What do you consider necessary for people surrounding us and for
ourselves to move?
Human beings need energy to live, move, breath, keep our heart
beating, maintain blood circulating, and even think.
The energy the sun provides to the earth is crucial for food production.
Foods are our source of energy, so that we can carry out all vital and
daily life activities. The food we eat contains stored chemical energy,
which transforms in kinetic chemical energy when our bodies move, and
at the same time, turns into heat’.
In addition, human beings require energy for the operation of machines:
cars, electric plants, electrical goods, industrial plants etc. To meet
those needs, human beings have used as a source: oil, coal, natural
gas, which are non-renewable sources. At the same time, human beings
use the water of a waterfall (hydraulic energy), the wind (wind power),
sunlight (solar energy) etc. those originate from natural phenomena, so
they are renewable sources of energy.
Objectives
ü
ü
ü
ü
To explain the law of energy conservation in macroscopic systems.
To relate mechanical energy with energy conservation.
To establish the importance of energy when doing some work.
To identify the importance of power in the speed at which an
activity is performed.
ACTIVITY 1
Skill 2: Determine the total mechanical energy in physical
systems.
Skill 3: Establish relationships among total mechanical energy
and kinematic equations.
Skill 4: Illustrate and explain everyday life situations in which
mechanical energy is preserved or situations in which it is not.
ENERGY
Energy is the property or capacity bodies and substances have to cause
transformations around them, because of interactions between the parts
of a system or systems.
Pedro climbs the slide to slip down through it. The higher it is, the
funnier it gets, since he can go faster when falling down. What Pedro
does not know is that when sliding down, two forces act: gravitational
potential energy and kinetic energy.
Figure 1. Example of potential and kinetic energy.
When Pedro is at the highest point of the slide, he has gravitational
potential energy before sliding, which depends on the height. The higher
Pedro goes, the more potential energy is accumulated. Potential energy
is directly proportional to the mass of an object.
Potential Energy
We define it as the energy associated with an object at a determined
height regarding a reference point.
The equation of Gravitational potential energy is:
Epg = m · g · h
Where m: mass measured in Kg, g: gravity, h: average height in
meters. It is expressed in Joules.
Let’s see the following example:
What is the potential energy that an 800 Kg elevator, located 380 m
over the ground has?
It is a very simple case; we only have to apply the data given in the
formula:
Ep = (800 Kg) x (9.8 m/s2) x (380 m) = 2.979.200 J
Figure 2. Elevator. Potential energy example.
Remember that…
The weight of a body is equal to its mass. That is why a person with
more weight has more potential energy.
Potential elastic energy is another kind of energy, which a system
can feature. This is the kind of energy released when a spring is
compressed and you let it go. The energy it has will depend on the
compression applied to it; more compression means more energy. This
energy is transformed in kinetic energy or in energy available to perform
a job, for example propel a ball.
The equation for potential energy is:
Epe= 1/2kx2
K is an elastic constant of the spring measured in N/m, and “x” is the
length acquired by the spring when compressed and stretched measured
in meters. We express it in Joules.
The example shows a force of 540 N, which stretches a spring at a
distance of 0.150 m. What potential energy does the spring have when
a mass of 60 Kg hangs vertically from it?
Figure 3. Potential energy. Spring to which a force and mass are
applied.
To determine the potential elastic energy stored in the spring, we must
know the constant force of the spring and the deformation caused by
the weight of the 60kg mass.
A force of 540 N stretches the spring up to 0.150m. The constant force
is:
k = Fe/x= 540N/0.150m = 3600 N/m.
So, the x deformation of the spring caused by the weight of the mass is:
X= Fe/k= (m.g)/k
X= (60Kg Ÿ 9.8m/s^2)/(3600N/m) = 0.163m
The potential elastic energy stored in the spring is:
Epe= 1/2(3600N/m · 0.1632) = 47.82 J
Pedro slips over the slide, so he generates movement in his mass; this
movement is generated by kinetic energy. Kinetic energy is defined as
the energy associated to an object at a moving state.
The equation for kinetic energy is:
Ec = 1/2· m·v2
Where m: mass, v: velocity.
Let’s check the following example:
What is the kinetic energy of an 860 Kg car, which moves at 50 km/h?
Figure 4. Kinetic Energy. Car with constant speed and weight.
We convert the speed units, 50 Km/h to m/s.
50Km/h· 1000m/1km· 1h/3600s=13,9m/s
Ec = 1/2·860Kg· 13,92m⁄s = 83.000Jules
In the following link, you will be able to revise complementary
information https://www.youtube.com/watch?v=ASZv3tIK56k
Did you know that…?
When we go to ride our bicycles or simply to run, we are producing
kinetic energy.
The total mechanical energy in a system is the addition of kinetic and
potential energy and it is represented by the equation:
Em = Ep + Ec
The law of energy conservation states that energy cannot be created or
destroyed, only transformed. On a system, there’s nothing capable of
creating or destroying energy. If the quantity of energy varies, this is
due to the interaction with another object or the surrounding
environment.
The law of energy conservation of mechanical energy states that a
system final energy is equal to a system final energy.
Figure 6 shows how energy transforms into a system and initial energy
is equal to final energy. We push a block of mass m against the spring
and it is compressed to X distance. The potential elastic energy is stored
in the system spring-block. When the block is released from the resting
state, the potential elastic energy is transformed into kinetic energy of
that block.
Figure 5. Energy preservation, where U is potential elastic energy and K
kinetic energy.
For more information, check the following video
https://www.youtube.com/watch?v=IqV5L66EP2E
Now we calculate the mechanical energy produced by Pedro at the
moment of slipping down the slide. Figure 6 presents the data to take
into account to determine the mechanical energy.
Figure 6. Mechanical energy example. (Figure retrieved from URL
http://previews.123rf.com/images/3drenderings/3drenderings1203/3dre
nderings120306635/12969401-3d-rinden-de-personaje-de-dibujosanimados-con-tobog-n-Foto-de-archivo.jpg)
We have a speed of 10 m/s, a mass of 50 kg and a height of 2 meters
Em = Ep + Ec
Em = m · g · h + 1/2· m·v2
Em = 50Kg · 9.8m/s2 · 2m + 1/2· 50kg·(10m/s2)2
Em = 3480 J
Did you know that…?
“La Chorrera” Waterfall located in the municipality of Choachí is the
highest waterfall in Colombia. It is 590 meters and falls from the top of
outstanding cliffs in the Colombian Andes. This height makes water fall
with a huge potential gravitational and kinetic energy, as a consequence
with a high mechanical energy.
Mechanical energy preservation
Conservative forces are forces where work is performed separately
from the path followed by the object. For example, weight and gravity
are conservative forces. Additionally, the work done by a conservative
force on a mobile particle through any closed path is equal to zero.
The work done (Wc) on an object by a conservative force, which is
constituent of a system, while the object moves from one position to
another is equal to the initial value of the system’s potential energy
minus the final value:
Wc = Epi – Epf = ΔEp
A non-conservative force is defined as the sum of the kinetic and
potential energies on a system, as the mechanical energy of the system:
where the work done on a path or trajectory is different from zero and
depends on the object’s trajectory. It is stated they are forces extracting
energy from a mechanical system.
The most common example is friction. Whenever there is a kind of
friction between two objects, heat is released over a surface: for
example, when we rub our hands, they heat up. When there is friction,
more work needs to be done to keep an object moving. This indicates
that the work will never be equal to zero.
Wnc = ΔEm
Figure 7. Non-conservative energy. Muscular strength. (Figure retrieved
from URL
http://images.clipartlogo.com/files/ss/original/366/36660289/muscularman-pumping-iron.jpg)
Learning Activity
Activity 1
1. Determine the mechanical energy of a waterfall, which is 100m high,
falls at a speed of 120km/h and has a mass of 800Kg.
Figure 8. Waterfall. (Figure retrieved from URL
http://st.depositphotos.com/2527057/3036/v/950/depositphotos_30363
629-Illustration-of-cartoon-waterfall.jpg)
2. Determine the speed of a 3Kg ball rolling down a hill. The hill is 12m
high.
Activity 2
Skill 1: Calculate mechanical work based on a graph of distance vs.
force and as the result of a dot product between vectors.
Skill 5: Establish relationships between work, energy and power.
MECHANICAL WORK
Work is a physical magnitude, which is expressed as the product of the
amount of force used to move an object, multiplied by the distance the
object covered.
It is important to keep in mind that the direction of force is not
necessarily going in the same direction as the object. When those
directions are opposite, we obtain the angle called cosine α. This angle is
added to the preceding equation, like this:
W = F x d x cos α
When we apply a net force on an object making it move, meaning there
is movement, we can say that such force produced mechanical work,
which can be positive if the system gains energy or negative if it loses
energy (determined by the value of the angle). Specifically, work is the
point product between force and displacement.
Figure 9. Kinds of work
When work is positive
Positive work is produced when the vector direction has an angle of 0°
to 89°. That means, the maximum value of work is achieved when work
and displacement have the same direction (cos 0°=1).
When work is negative
Negative work is produced when the direction of force is opposed to the
direction of displacement, meaning that this force features an angle
between 91° and 180° (cos 180°=-1).
Figure
10.
Kinds
of
work
(Figure
retrieved
from
URL
http://www.fisic.ch/cursos/segundo-medio/trabajo-mec%C3%A1nico-i/)
When work is null
Work is null when the direction of force has a 90° angle, that is to say, it
is completely perpendicular to the direction of displacement (cos
90°=0).
When work is net
Usually, there is more than one force intervening on a mechanical
system. For this reason, we must calculate the work done by each force
and then we add up those values to obtain the net value.
Wnet = WP + WN + WFR + WF
Units to measure work
When distance is measured in meters (M) and force in newton (N), work
is measured in joules (J)
Let’s see the following example:
A book with 2.0 Kg mass slides over a table. When we apply a 20N
force, which is parallel to the horizontal, it moves 5.0m.
Determine the box acceleration, the speed at 4s, assuming the book
was at rest, the kinetic energy and work done.
Book acceleration,
F=m·a
a= F/m a=20N·2.0Kg = 80m/s2
Book speed at 4s,
V= Vi + a·t
V = 0 + 80m/s · 4s = 320m/s
Work done,
W = F·d
W = 20N · 50m = 1000J
Kinetic energy,
Wnet= Ec – Ec0
1000J = Ec
Very important…
Net work is expressed as: Wnet = Ec -Eco. The relationship between work
and kinetic energy is known as the work- energy theorem, this means,
the difference between final and initial kinetic energy.
For instance, a girl applies a force F that has a 60°angle regarding the
horizontal. The force she applies has two components, one on Y (force
applied to lift) and another on X (force applied to push). In this case,
only the component on X, which is parallel to the direction of
displacement, executes work on the wheelbarrow, this is considered a
positive work.
Figure 10. Work applied to a wheelbarrow by a girl.
In this example, the force applied is 300N with a 30° angle, producing a
2M displacement. To obtain the work:
Figure 11. Force applied to an object. (Figure retrieved from URL
www.e-class.8m.net)
W = 300 N x 2 M x cos 30°
W = 300 N x 2 M x 0.86602540378
W = 519, 61 J
A 6.0 kg block, initially at rest, is pulled to the right, along a horizontal
surface with no friction using a 12N constant horizontal force. Find the
block speed after it has moved 3.0 m.
Figure 12. Work applied to an object. Block pulled to the right with a
force of 12N. Figure retrieved from: Física para ciencias e ingeniería.
2008. PDF.
W = F·Δx = 12N · 3.0m = 36J
W = Ec -Eco
W = 1/2· m·v2
v= √(2W/m) = √((2·36J)/ (6.0 Kg)) = 3.5m/s
Think about this…
By borrowing Galileo’s inertia principle, Newton formulated his first law,
which states that bodies neither move nor change speed unless a force
intervenes.
To know more about energy, force and work watch the following video:
https://www.youtube.com/watch?v=WSY4HzWZIlo
Power P is the rate of change in work done regarding time. It can be
stated that power is the measure of rapidity in which work is done.
Power is expressed as:
P = W/Δt
where, W is the work done and Δt is the time taken. The unit of power
in SI is J/s, and is known as watt (W).
Let’s see the following example:
We have two motors: motor 1 applies a 5000N force and pulls up the
object 2m along a ramp in 5s; motor 2 applies the same force and pulls
up the object at the same distance along the ramp in 10s. Both motors
perform a 10000 J work.
Motor 1: P = 1000J/5s = 2000 W
Motor 2: P = 1000J/10s = 1000 W
We can state that motor 1 performs the work faster, then, it has more
power
When we do any work on an object, we transfer energy to it. Therefore,
its energy increases.
The system doing work develops power; this explains energy
consumption at the moment of transferring it. Power is developed by a
system, which does work and is expressed as:
P = E/t
Where E is transferred energy and t is the time taken at the moment of
doing the work.
For example: a crane used on a construction pulls up a 200Kg load from
the ground to a 10m height, at a constant speed, in 30s. What is the
potential energy increase of that body, the work on the load and the
power developed by the crane?
Potential energy increase,
Ep= m·g·h = 200Kg·9,8m/s2·10m= 19.600J
Work done by the load is,
F = m·g = 200Kg·9,8m/s2 = 1960J,
Work is equal to,
W = F · d = 1960J·10m = 19.600J
Power developed by the crane is
P = 19600J/(30 s) 653 W
Activity 2
Learning Activity
1. A 2.5 Kg block is pushed on a table by a 15N force at a 25° angle,
over the horizontal, generating a 2,2M displacement. Find the work done
by:
a. Force applied;
b. Normal forced applied by the table;
c. Gravity force;
d. Net force applied on the block.
Figure 13. Force applied to an object. (Figure retrieved from URL
http://es.slideshare.net/hebervela5/problemas-resueltos-trabajomecnico)
2. Calculate the energy consumed at home.
A washing machine keeps running during 25 minutes, if the power
consumed is 2000W and the power transmission company charges 295$
for the energy, determine:
a) The energy consumed by the washing machine in KW-h;
b) The cost of keeping the washing machine running during those 25
minutes.
Socialize your answers with a classmate.
Try to do the same exercise with different electrical goods at home
Abstract
Below you will find a summary of the formulas regarding the contents
studied in the unit.
!
Kinetic energy: Energy associated to a moving object. Ec = · % · &2
"
Potential energy: Energy associated to an object at a determined
height. Epg = m · g · h
Mechanical energy: Addition of kinetic and potential energies. Em = Ep
+ Ec
Conservative energy: It is equal to the initial value of potential energy
on the system minus the final value. Wc = Epi – Epf = Δep
Non-conservative energy: Addition of system´s kinetic and potential
energy or mechanical energy of the system. Wnc = Δem
Force: Physical capacity to do a work or a movement. F=m·a
Work: Product of the force used to move an object at x distance. W = F
x d x cos α
Power: It is the rate of work change developed regarding time. P
=
'
()
Power and energy: Energy used to do work in x time. P =
*
+
Homework
This homework is aimed at relating the knowledge acquired in the LO
1. Concerning the questions:
Why is heat dissipative? And what is the connection it has with
mechanical energy?
In groups of maximum 4 students, prepare a presentation and present
drawings and posters or Power Point presentations to exemplify the
answers to the preceding questions.
2. In the following practical exercise look for the student who is able to
determine the influence of mechanical energy on an everyday situation.
It is key for the teacher to present clear reasons about the importance
mechanical energy has. Teachers should also relate the activity to the
contents studied in the learning unit.
Work in groups of maximum 4 students to do the activity.
Materials:
ü
ü
ü
ü
ü
ü
Cardboard
Book or magazines
Two marbles of different sizes
A 50 cm ruler
Liquid silicone
A plastic cup
Procedure:
ü With the cardboard, make a canal where you can place the ruler.
ü Using silicone, paste the ruler to the base of the cardboard canal
to give it shape and strengthen it.
ü Put a canal end on the end of a book, which is not over 5 cm high.
ü Put the paper cup on the other canal end.
ü Release each marble over the canal from the tilted end.
What happens to each different-sized marble when they reach the
plastic cup? Does the marble move the cup? If so, which marble moves
it more?
∗
Increase the height of the canal by using more books, so that it is
15 cm high. Throw the marbles again through the canal.
What happens to the cup when the marbles reach it? Do they move it?
Which marble moves it more? Why do they move it more at this height?
Which marble moves faster and why?
Students must record their answers on the printable materials. In class,
they will debate the answer obtained by each one.
Evaluation
The evaluation allows us to check on the knowledge acquired regarding
mechanical energy, work and energy preservation.
1. Identify the following statements as true (T) or false (F):
a) Potential energy is defined as the energy associated to an object
at a determined height, regarding a reference point.
b) The equation for potential energy is: Ep = m·g·t.
c) The mechanical energy of a system is equal to the kinetic energy.
d) The law of energy conservation states that energy can neither be
created nor destroyed, it can only be transformed.
e) We call conservative forces to those whose work done depends on
the path followed by the object.
f) Gravity and weight are conservative forces.
g) The vectors used to calculate mechanical work are: energy,
distance and displacement distance.
h) An object does null work when force and displacement have the
same direction.
i) Force is measured in joules and work in Newton.
j) Power measures the speed at which work is done.
2. Use the words in the box to complete the following sentences.
Mechanicalenergy–Mass–Mechanicalwork–Speed–Kineticenergy–Force–
Potentialenergy–Distance
a)
The total_______________________ in a system is the sum of
_____________________ and ______________________.
b)
_______________________ can be defined as the result of
____________ multiplied by _____________ squared.
c)
_______________________ is defined as the energy associated
to an object at a determined height regarding a reference point.
d)
_______________________ can be defined as the product of
_______________ applied to an object by the ________________
covered by the object, as well as, the angle formed by the direction of
force regarding the horizontal.
3.
Questions 3 through 5 are multiple-choice ones with only one possible
answer. With these questions, we would like to check on students’
correct interpretation of the knowledge acquired at a mathematical level
about mechanical energy.
A sphere of 0.20Kg mass is shot out of the inferior edge on a ramp at a
5.0 ms speed and at 1.20 m height over the ground.
Determine:
Figure 14. Guideline for questions 3, 4, 5. (Figure retrieved from
Hipertexto Santilla. 2011. Pág. 196)
3. Mechanical energy at point A.
•
4.9 J
•
5J
•
2.5J
4. Kinetic energy, when height regarding the ground is 0.60m.
•
4.1J
•
4.5J
•
3.5J
5. The speed of the sphere, when its height from the ground is 0.60m is.
•
6.1m/s
•
6.9m/s
•
5.5 m/s
Bibliography
Serway,R. A. (2008). Física para ciencias e ingenierías. México, D.F.:
Editorial Thomson.
Ballen, M. B. (2011). Hipertexto Física 1. Bogotá: Editorial Santillana.
Parker, S. (1990). Diccionario de Química. México, D.F.: Editorial Mc
Graw Hill. Pág. 105, 251.
Colombiaaprende.com (2016).
www.colombiaaprende.com/catalogodecontenidos [Retrieved on May
13, 2016].
areaciencias.com
(2016).
¿Qué
es
la
energía?
http://www.areaciencias.com/fisica/energia-cinetica-y-potencial.html
[Retrieved on May 12, 2016].
fisicalab.com
(1994).
Energía
conservativa.
https://www.fisicalab.com/apartado/fuerzas-conservativas#contenidos
[ Retrieved on May 14, 2016].
fismec.com
(2014).
Energía
mecánica.
http://www.fismec.com/energia_energia_mecanica [Retrieved on May
13, 2016].
Youtube.com
(2016).
Energía
cinética
https://www.youtube.com/watch?v=ASZv3tIK56k
[Retrieved on May 14, 2016].
y
potencial.
aprendemostecnologia.org (2009). Energía potencial y cinética.
https://aprendemostecnologia.org/tag/energia-potencial/ [Retrieved on
May 13, 2016].
fisic.ch (2013). Tipos de trabajo. http://www.fisic.ch/cursos/segundomedio/trabajo-mec%C3%A1nico-i/ [Retrieved on May 14, 2016].
Figura
15.
Fuerza
aplicada.
http://es.slideshare.net/hebervela5/problemas-resueltos-trabajomecnico
Glossary
Force: physical capacity to do work or a movement.
Speed: It is the space travelled by a body in the time unit.