Download Conservation of energy

LABUAN MATRICULATION COLLEGE
SCIENCE INFORMATIC
WS011
CONSERVATION OF ENERGY
GROUP MEMBER:
1. ADRIAN HO IK LIANG (MS0915542624)
2. MOHD. TARHAMIZI BIN ABD HAMID ( MS0915515816)
3. ZURINAH BINTI PAKEE ( MS0915517005)
4. DESMOND ANAK BONNIK (MS0915514779)
5. ELMA LIM ( MS0915514865)
LECTURER'S NAME: MR. SYED NASIR BIN SYED AHMAD
Content
Title
Page
INTRODUCTION
1
POTENTIAL ENERGY
2
GRAVITATIONAL POTENTIAL ENERGY
3
ELASTIC POTENTIAL ENERGY
4
KINETIC ENERGY
5
PRINCIPLE OF CONSERVATION ENERGY
8
WORK-ENERGY THEROM
13
CONCLUSION
15
BIBLIOGRAPHY
16
Introduction Conservation of Energy
Energy is a very difficult concept to define. It is like trying to define money. We all know
what to do with money, but we simply cannot define it without referring to what we do with
it. The same is true of energy,although we have not generally developed money in our
daily day or everdays lives. But we also think that energy as the currency of mother nature.
Just as transfers and store of money are necessary for process to occur Financial World,
transfer and store of energy are nessary for process to occur in our natural world.
Besides that, energy is one of the most important concept in science field. But we cannot
give a simple general definition of energy in only a fews fews words. In this conservation of
energy, we can define translation of potential and kinetic energy. Later, we will know or
examine others types of energy, such as that related to heat. The crucial aspect of all the
types of energy is that the sum of all types and the total of energy is remain the same after
any process occurs as it was before: that is the quantity “ energy “ can be difined so that it
is a conserved quantity.
Moreover, Conservation laws are the cornerstones of physics, both theoretically and
practically. Most scientisc would probably name the conservation of energy as the most
profound and far-reaching of these important laws to people. When we say something is
conserved, it mean constant, or has a constant value. Because so many things continually
change in physical processes, conserved quantities are extremely helpful in our attempts
to understand and describe the universe. Keep in mine, though, that quantities are
generally conserved only under special conditions.
One of the important of the conservation laws is that concerning conservation of energy. A
familiar statement is that the total energy of the universe is conserved. This is true
because the whole universe is taken to be a system. A system is defined as a definite
quantity of matter enclosed by boundaries, either real or imaginary. In effect, the universe
is the largest possible closed, or isolated , system we can image. Within a closed system,
particles can interact with each other but have absolutely no intreraction with anything
outside.In generally then,the amounts of energy remain constant when on from the
system.(including thermal enegy and radiation)
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In another hand, energy is perhaps the concept most important to the science field or
stream. The combination of the energy and matter made up the universe. Matter is
substances and energy is the mover of the substances. Matter are things that we can see,
smell, touch, taste or fel it. Matter is mass and occupied the space. Energy, on the other
hand, it abstract. We cannot see, feel, taste, smell or touch of the most energy.
Supprisingly, the idea of energy was unknown to Issac Newton, and its existence was still
being debated in 1850s. Although energy is familiar to us now days,it still diffiuclt to define
it because energy is not only “things” but both a thing and a process-as if it were both a
noun and verbs.
Persons, places, and things all have energy but we usually observe energy only when it
undergoes change. Put another ways, energy is nature's way to keeping score. We sence
energy only when the score change or either when there is a transformation from one form
of energy to another(as an example: when radian from the sun changes to thermal energy
when it vibrates cells in our skin) or when there is a transfer of energy from another point
to other point. Interestingly, just as water is composed of tiny lump( H2O molecules)
energy changes also occurs in tiny lump or known as quanta.
Within such a system energy may be converted, but the total among of all form of energy
is constant or unchange.Totals of energy can never be create or destroy.
Potential energy
Potential energy can be thought as energy stored within a physical system. Potential
Enrgy is called because it has the potential to be change into other forms of energy, such
as kinetic energy, and to do work in the process. The standard (SI) unit of measure for
potential energy is the joule, the same as for work or energy in general.
The term "potential energy" was coined by the 19th century Scottish engineer and
physicist William Rankine.
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Gravitational Potential Energy
As we know, there are two type of potential energy. One of the potential energy is
gravitational potential energy. The gravitational potential energy is difened as the potential
energy of a body due to the elevated position. For your information, the gravitational
potential energy of an object is depands on its height from the grounds. Besides that, the
object's weight also influence the gravitational potential energy.
Therefore, if the height of an object form ground is higher, then the gravitational potential
energy also become higher. As an example, when you lift an object upwards, its meants
that you increase the gravitationalm potential energy of the object. Other than that, if the
object is heaiver, then the gravitational potential energy will be greater when lifting it
upwards. This is due to the energy transferred in lifting the object upwards.
There are a few factors that affect the gravitational potential energy are its height relative
to some referring point, its mass and the strength of the gravitational potential energy field
in its.Thus, a book lying on a table has less gravitational potential energy than the same
book on top of a taller cupboard, and less gravitational potential energy than a heavier
book lying on the same table.
It was important to notice that "height" is the common sense of the term that cannot be
used for gravitational potential energy calculations when gravity is not assumed to be a
constant.
In calculation, the formula that we must used to determine the gravitational potential
energy is:
change in gravitational potential energy = weight x change in height
or
change in gravitational potential energy = mgh
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** example calculation that involved gravitational potential energy
An althele of mass 50kg runs up a hill. The foots of the hills is 400m above the sea levels.
The summit is 1200m above the sea level. By how much does the alhlete's gravitational
potential energy increase?
[ acceleration due to the gravity g = ms-2]
step 1:
calculate the increase in height
step 2:
write down the equation for gravitational potential energy, then subtitute value and solve it.
Change in gravitational energy = weight x change in height
= mgh
= 50kg x 10 ms¯² x 800m
= 400000
so, the athelete gravitational potential energy increses by 400000 J.
Elastic Potential Energy
Elastic Potentitial energy can be difined as the energy stored in in elastic materials as the
result of their stretching or compressing.
Any spring that has been stretched or compressed had stored elastic potential energy.
This mean that the spring is able to do work on another object by exerting a force over
some distance as the spring resumes its original length. The energy stored in a spring is
also called strain energy. The work done by a constant force,F is given by W=Fs, but this
rule cannot be used to find work done by spring, because the forces that acts is not
constant. The forces becomes larger as the extension increase. In this event, the area
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under a force-displacement (F-s) graph is the work done on an object or the energy
change that has occurred, we can use this approach to find the work done by a spring.
Fs
W = area under the Fs − x graph
F
W =
0
1
Fx1
2
x
x1
W =
1
(kx1 ) x1
2
W =
1 2
kx1 = U s
2
Kinetic Potential Energy
The kinetic energy of a body can be defined as the amount of work it can do in coming to
rest, or what amounts to the same thing,the amount of work that must have been done on
it to increase it's velocity from zero to it's highest velocity.Kinetic energy also often called
as the energy of motion.It is directly proportional to the square of the instantaneous speed
of a moving object. A body of mass m, is moving with velocity, v:
Kinetic Energy = 1/2 mv²
kinetic energy is a positive, scalar quantity
To Show That Kinetic Energy = 1\2 mv² (variable force)
Under the action of a force F, a body of mass m, suppose to be moves a small distances
ðs.Though the force may be varying ðs is so small, the force can be considered constant
over the distance ðs.The work done ðw is given equation as:
ðw = Fðs
If the force increases the velocity of the body from zero to v,the total work done W, is given
by equation by:
5
W = ∫Fds
using Newton`s second law
F = m dv/dt
where dv\dt is the acceleration of the body.Then
W = ∫m dv/dt ds
remember that v = ds/dt
W = ∫ mv dv
and therefore,
W = [½mv²]
The kinetic energy of a body depends only on it's mass and it's velocity. The kinetic energy
is independent of the way in which the body needed this velocity. Hence, the result that
has just been derived could have been obtained more simply by specifying that the body
was accelerated by a constant force.
To Show That Kinetic Energy = ½mv² (constant force)
If a body of mass m, moves a distance s, under the action of a constant force F, the work
done W, by the force is given by the equation:
W = Fs
If the acceleration is a, then from Newton`s second law F = ma, so
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W = mas
if the body has been accelerated from rest to some velocity v,
then
v² = u² + 2as
as = v²/2
then W = ½mv²
therefore, kinetic energy = ½mv²
** example solve problem in kinetic energy.
A stationary object of mass 3.0 kg is pulled upwards by a constant force of magnitude 50
N. Determine the speed of the object when it is travelled upwards through 4.0 m.

F

s

F

mg

mg
(Given g = 9.81 m s-2)
Solution: m=30.0kg ; F= 50 N; s = 4.0m and u=0
The nett forces acting on the object is given by:
Fnett = F – mg
= 50 – (30)(9.81)
= 20.6 N
By appling the work-kinetic energy therom, thus
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Wnett = Kf + Ki
Fnett s= ½ mv2 – 0
(20.6)(4.0) = ½ (3.0) v2
v = 7.41 ms-1
Principle of Conservation Of Energy
Principle of conservation state that in any energy transformation, the total amount of
energy before and after the transformation is constant. Energy cannot be created or
destroyed. Energy only can be converted from one form to another or be transformed from
one object to one object or place to place.
Σ Ei= Σ Ef
Ki + Ui = Kf + Uf
In generally, the amount of energy remains constant when no mechanical work is done on
or by the system and no energy is transmitted to or from the system including thermal
energy and radiation. Principle of conservation of mechanical energy states that total
amount of mechanical energy( kinetic energy + potential energy) which the bodies posses
in an isolated system is constant. It applies only to frictionless motion, for example, to
conservative systems.
E=K+U
total mechanical energy = potential energy + kinetic energy
The total mechanical energy is constant in a conservative system
Ei = Ef
Ki + Ui = Kf + Uf
½ mivi2 + mighi = ½ mfvf2 + mfghf
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In system with non-conservative force, the total mechanical energy is changed. The work
done by the non-conservative forces acting on an object is equal to the total change in
kinetic and potential energy.
WNL =
Since the change in kinetic energy can be the result of many types of forces, it is
conservent to separate
 KE into three part:
1. The change in kinetic energy due to the internal conservatite forces,
2. The change in kinetic energy due to internal conservatite force,
 Kinf −c
 Kinf −nc
3. The change in kinetic energy due to external forces ( conservative or nonconservatite servative),
 Kexf
 K = Kint−c Kint −nc Kext
or
 Kfui Kint−nc K ext= KU  f
Conservatite forces are forces for which the work done does not depand on the path taken
but only on the initial and final positions. Non-conservatite forces are forces for which the
work done depands on the path taken.
Example of conservatite forces:
I. Gravitational forces
II. The spring forces
III. Electric
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Example of non-conservatite forces:
I. Friction
II. Air resistance
III. Tension in cord
IV. Motor or rocket propulsion
V. Bush or pull by a person
From a universal point of view, the total energy of the universe is constant. If the part of the
universe gains energy in some forms, another part must lose an equal amount of energy.
No violtion of this principle has been found. The total energy is always conserved as long
as all forms of energy are accounred.
**Example of energy that energy transferred to kinetic energy.
Demonstration
When a pendulum is displaced, it
gains gravitational potential energy
due to its increased height. When
subsequently released, this energy
becomes transferred to kinetic energy.
This data logging experiment explores the relationship between these changes of energy.
Apparatus and materials:
Light gate, interface and computer
Pendulum
Stand, clamp and boss
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Ruler in clamp
Micrometer
Electronic balance
Technical notes
1.Set up the apparatus so that the stationary pendulum bob hangs exactly in front of the
light
sensor,
interrupting
the
light
beam.
2.Connect the light gate via an interface to a computer running data-logging software. The
program should be configured to obtain measurements of kinetic energy. These are
derived from the interruption of the light beam by the pendulum bob - this moves a
distance
equal
to
its
diameter
during
the
interruption
time.
3.The internal calculation within the program requires the mass and diameter of the bob to
be entered into the software, so that the velocity of the bob and kinetic energy are
calculated. Measure the diameter using a micrometer. Measure the mass using an
electronic balance with a sensitivity of 0.01 g. Accumulate the series of results in a table.
This should also include a column for the manual entry of displacement height
measurements, taken from the ruler.
Safety
Read our standard health & safety guidance
Procedure
Data collection
a . Displace the bob so that it is raised 1.0 cm above its rest height as shown above. Hold
the bob against the ruler. Note the reading for the point of contact which is on a level with
the centre of the bob. Release carefully and allow it to perform ONE swing to and fro. This
should produce two lines of data in the table, corresponding to the forward and back parts
of the swing. Repeat this five times. The table shows ten values.
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b. Enter 1.0 cm in the 'height fallen' column.
c. Repeat this procedure for heights of 2, 3, 4 and 5 cm.
Analysis
Depending upon the software, the results may be displayed on a bar chart as the
experiment proceeds. Note the increase in values of kinetic energy as the height fallen is
increased.
Investigate the relationship between kinetic energy and height fallen more precisely by
plotting a XY graph of these two quantities. (Y axis: kinetic energy; X axis: height fallen)
This usually gives a straight line indicating proportionality. Use a curve- matching tool to
identify
the
algebraic
form
of
the
relationship.
The gravitational potential energy lost depends in direct proportion upon height fallen.
Therefore the straight line graph indicates that kinetic energy gained is proportional to
potential energy lost.
Teaching notes:
1.Students can add a further column to the table, to calculate the potential energy lost from
the height fallen, using m g Δh. Care is needed with units. In view of the small values of
energy, it may be useful to calculate energy values in millijoules. Calculation of potential
energy should yield values numerically the same as the corresponding kinetic energy. This
would support the Law of Conservation of Energy.
2. If the results are less than convincing, discuss the potential sources of error. Prime
suspects must be the measurements performed using the ruler, micrometer and scales.
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* Notes: this experiment was submitted by Laurence Rogers, Senior Lecturer in Eduction
at Leicester University.
This experiment was checked in May 2006.
Work Energy Theorem
Work energy theorem is difined as that work done by an object is the same as the change
of the object's kinetic energy. The equation derived:
Wtotal =
K
= ½ mvf2 - ½ mvi2
Altough this equation for a force that is constant in direction and magnitude, it also valid for
any forces, thus making the work-energy therom is generally. The work in the work energy
theorem equation also defined as the net work or work based on the net force. For
instance if we push a box.
W = Fs
is equal to Fnets = ½mvf² – ½mvi²
However, only partial of the total work responsible for the change of the objects kinetic
energy while the rest is lost in form of heat energy.
Work-energy theorem is created by the relationship between concept of work with
resultant force and the change in kinetic energy. By moving a body of mass m, along the xaxis with the constant resultant force F, directed along the axis, the body`s acceleration is
constant and given by Newton`s Second Law of motion with the body`s gain velocity over
time thus changing the body`s kinetic energy and will undergoes displacement,s.
13
Replace the v and u with vf and vi respectively
v² = u² + 2as
vf² = vi² + 2as
where a = vf² – vi²
2s
we multiply both side with m
ma = m(vf² – vi²)
2s
where F = ma
F = mvf² – mvi²
2s
and Fs = ½mvf² – ½mvi²
where Fs = work done = W
½mv² = kinetic energy = kE
W = kEf – kEi
W = ∆kE
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Conclusion
In conclusion, energy is needed to some work. Besides that, energy also are important to
the science field. As we know that energy divide two part that is potential energy and
kinetic energy. Potential energy can be difined as the energy stored in a body or system
because of its position, shape or state. Potential energy also divided into two part of
energy which is gravitational energy and elastic potential energy. Gravitational potential
energy can be difined as the energy stored in a body or system because of its position.
Besides that, elastic potential energy also difined as the energy stored in elastic materials
as the result of their streching or compressing. Example of materials that applies elastic
potential energy is spring and rubber band. Kinetic energy can be defined as the energy of
a body due its motion. Example of kinetic energy is roller coaster.
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