UNIT 1 - ENERGY & MOTION
Lesson 1.2 CONSERVATION OF ENERGY
Overview
This lesson deals with the conversion of energy from one
form to another and the law of conservation of energy. On
completion of the lesson, you should be able to discuss
various different forms of energy including molecular
potential energy, internal energy and chemical potential
energy. You should also be able to explain how energy is
conserved when work is done.
ToDo
Watch the video presentation.
Carry out the activities.
Read through the lesson notes and do the exercises.
Refer to the solutions and check your answers.
At
home: Prepare for
Lab 1.2 by reading the instructions and collecting the necessary
materials and equipment.
Prepare for the two activities in Lesson 1.3.
Lesson 1.2 Activities
- Roller
Coaster: Roller Coaster - Energy or Momentum?
- Oscillating
Spring: Use a weight oscillating up and down
at the end of a spring to show how energy is
converted from gravitational potential energy to
kinetic energy to elastic potential energy and
then back again as it moves up and down.
Activity
1.2.1 ROLLER COASTER
What this illustrates
Roller coasters convert gravitational potential
energy to kinetic energy and then back to gravitational
potential eregy etc. If a roller coaster goes ito a loop
without sufficient kinetic energy, it will drop out of
the loop - or roll backwards.
In this activity, you can experiment with different
starting points and determine the minimum height at which
a marble or steel ball must start to roll in order for it
to complete a loop in the roller coaster track.
You can also make a U-shaped track and illustrate the
loss in energy due to friction as the ball travels from
one side of the U to the other.
What you will need:
- ~8ft of flexible foam
pipe insulation.
- Small metal ball or
glass marble
- Duct tape
Caution: The ball or marble may
leave the track at a relatively high speed. Take
precautions to avoid any damage which could be caused by
the flying ball. Persons observing the movement of the
ball withing 3 ft of the apparatus should wear eye
protection.
Procedure:
- Using a sharp knife
or blade, split the pipe insulation along its
length to create two u-shaped channels that can
be used to guide the ball along a specific path.
Use the duct tape to join the pieces to make one
long channel.
- Mount the channel on
a suitable support structure or frame to make a
"roller coaster" track for the marble
or metal ball.
- Set up a track that
will allow the ball to loop-the-loop.
- Determine the lowest
starting point at which the ball will complete a
loop without falling from the track.
- Modify the track to
allow for multiple loops.
- Determine the lowest
starting point at which the ball will complete 2
or 3 loops.
What to measure
1) Measure the height at which the ball must start to
roll (in relation to the height of the loop) for it to
complete a loop without leaving the track.
2) Using a U-shaped track, measure the height at which
the ball starts to roll and then the height that it
reaches at the other end of the U. The difference in
height represents the loss in gravitational potential
energy due to friction.
Repeat this 2 or 3 times starting at different heights.
What to calculate
You can estimate the energy loss due to friction in the U-shaped
track. The energy loss due to friction is equivalent to
the loss in gravitational potential energy when the ball
moves from one side of the U to the other.
If M1 is the mass of the ball or marble in kilograms,
H1 is the height at which it starts to roll (in meters)
and H2 is the height that it reaches on the other side of
the U,
The loss in energy = M1 x (H1 - H2) x 9.81 Joules.
For
example
When the flexible foam channel is mounted in the shape of
a "U", a steel ball with a mass of 20 grams
starts rolling 1 meter above the lowest point in the U.
After passing the bottom of the U, it only climbs to a
height of 85 centimeters above the lowest point. How much
energy does the ball lose due to friction as it moves
along the track from one leg of the U to its highest
point on the other side of the U?
Solution
The mass of the ball in kilograms is 20/1000 = 0.02 kg.
When the ball starts to roll, it has a GPE relative to
the lowest point equal to 0.02 x 9.81 x 1 = 0.1962 Joules.
When it reaches its highest point on the other side of
the U, it has
a GPE = 0.02 x 9.81 x 0.85 = 0.1668 Joules. The loss due
to friction is therefore: 0.1962 - 0.1668 = 0.0294 Joules.
Additional
Exercise
It would also be interesting to design a u-shaped track
that will keep a ball moving backwards and forwards for
the longest possible time.
Use different shaped U tracks. Allow the ball to start
rolling from a fixed height and count the number of times
the ball cycles backward and forward before it comes to
rest.
Give possible reasons why
a track that is too steep or not steep enough does not
perform as well as the track that allows the ball to move
backwards and forwards for the longest time or the most
cycles.
Discussion
Kinetic energy is the energy that an object has as a
result of its speed. Momentum is not a form of energy -
it is a combination of the velocity of an object in a
particular direction and its mass. A roller coaster may
gather momentum as it accelerates down a steep track but
it loses that momentum when it changes direction.
Momentum is calculated by multiplying the mass and the
velocity of an object in a particular direction.
The Kinetic Energy of the
roller coaster is calculated by multiplying its mass by
the square of its speed. Speed does not depend on
direction and so the kinetic energy of the roller coaster
will be maintained if its speed is maintained even if its
direction changes
A roller coaster loses
energy slowly as a result of friction with the air and
friction with the tracks but constantly coverts the bulk
of its energy between gravitational potential energy and
kinetic energy.
In order to do a loo-the-loop,
the ball will have to start at a height slightly higher
than the highest point of the loop. It will need
additional energy to keep it moving when it reaches the
highest point of the loop and it will also need
additional energy to make up for energy lost due to
friction with the track and the air.
Activity
1.2.3 Marble Coaster
The purpose of this activity is to design a marble
coaster track (chute) that has as many loops, twists and
turns as possible.
Overall Objective
Build the "wildest" marble coaster that still
delivers the marble to the end of the chute.
Conclusion
This activity has helped us to understand how energy is
converted between gravitational potential energy and
kinetic energy when a marble or ball travels in a chute.
(The energy loss due to friction appears to be relatively
small.)
When we study projectiles
later in this unit, we’ll use a smaller version of
this chute to launch a marble horizontally from the top
of a table and estimate it’s launch speed from the
distance it travels before hitting the floor.
We’ll also use
marbles and chutes to study the conservation of momentum
when collisions occur.
Conservation of energy
The law of conservation of energy states that energy
cannot be created or destroyed. Einstein showed that
energy could be converted to matter and visa versa but
apart from nuclear reactions, we can regard energy as
indestructible.
Internal Energy
Internal energy (sometimes called thermal energy) is the
sum of the kinetic energy and molecular potential energy
of each molecule or particle of an object. If the
temperature of an object increases, so does its internal
energy.
Chemical Energy
Energy stored in substances during chemical reactions or
as a result of their ability to release energy during
chemical reactions. Chemical energy is absorbed or
released when the electromagnetic potential energies of
the atoms and molecules that make up the material change.
Magnetic Potential
Energy
An object that is influenced by a magnetic fiels can have
magnetic potential energy.
Elastic Potential
Energy
Energy that is stored by distorting the shape of an
object.
Pressure Energy
Pressure is the force acting on a particular area. When
the pressure is reduced, movement of some of the material
occurs and work is done.
The pressure energy of a fluid (liquid or gas) is its
pressure multiplied by its volume.
Conservation of energy
The law of conservation of energy states that energy
cannot be created or destroyed. Einstein showed that
energy can be converted to matter and visa versa. Apart
from nuclear reactions, the law of conservation of energy
holds true.
What happens when
energy is used or "consumed"?
Energy is the capacity to do work. We say that energy is
consumed when work is done but what actually happens
during work is that energy is converted into a less
useful form. For example, a bucket of warm water may
contain more energy than a cup of boiling-hot water but
the energy in the cup of water is more useful.
Heat
The word "Heat" tends to be used very loosely.
Heat is not a form of energy but is energy in motion (or
in transit.) Heat is the transfer of energy. Heat usually
refers to movement of energy from one point to another as
a result of a difference in temperature.
There are three types of
heat: Conduction, Convection and Radiation. They are not
forms of energy but processes by which energy is
transferred.
Thermal Energy
Thermal Energy is related to the temperature of an object.
All materials are made up of very small particles: atoms,
ions or molecules. These are constantly moving and the
higher the temperature, the faster they tend to move.
We'll take a closer look at temperature, enthalpy and
thermodynamics in Unit 2 of this program.
Chemical Energy
Chemical potential energy is energy that can be released
(or absorbed) during a chemical reaction. Fuels release
energy when they react with oxygen. Exothermic reactions
release energy to the surroundings. In endothermic
reactions, energy is absorbed from the surroundings.
Fuels tend to release controlable amounts of energy
during combustion with air. Explosives tend to release
energy much more quickly and are more difficult to
control.
Force Fields
The simplest definition of a force is that it is a push
or a pull. Forces are needed to make things move or to
slow down things that are moving. Certain forces such as
gravity, magnetic forces and electrostatic forces create
fields. Force fields are regions in space where forces
can be detected within certain limits. Strictly speaking,
every force field extends to the edge of the Universe but
it's potential to do anything is usually limited to a
very small portion of space.
Magnetic Potential
Energy
An object that is influenced by a magnetic fiels can have
magnetic potential energy. For example: If I hold a steel
object close to a magnet, it will travel towards the
magnet if I let it go. There may be a way of making the
metal object do work as it moves towards the magnet and
it thus has potential energy. This is called magnetic
potential energy. Another way of looking at this is to
say that work is needed to remove a steel object from a
magnet. By doing work on the object, it gains potential
energy. This potential energy depends on the magnetic
force field and is thus called Magnetic Potential Energy.
Elastic Potential
Energy
A common method of storing energy is to distort the shape
of an object. When we compress a spring, stretch an
elastic band or hit a ball, particles that make up the
spring, elastic or ball change position within the force
fields inside the material. This increases their
potential energy. (Under normal circumstances, the
particles are in positions where forces of attraction and
repulsion between particles are balanced.)
The energy needed to
distort a spring by a particular amount is known as the
spring constant.
The equation used to
estimate the elastic potential energy of a spring is as
follows:
Espring
= ½ k D l 2 :
Energy stored in spring =
½ x spring constant x (increase in length of spring)2
Where: Espring = energy stored
in spring (J)
k = spring constant
(N/m)
and D l =
change in length of spring (m)
Pressure Energy
Pressure is the force that can act on a particular
surface area. The SI unit for pressure is the Pascal (Pa).
This is equivalent to a force of 1 Newton acting on 1
square meter of surface. In some countries (notably the
UK) people prefer to report pressures in Newtons per
square meter (N/m2). A Pascal is the same as a
N/m2
Work is done when the
pressure is reduced and movement of some of the material
occurs.
The pressure energy of a
fluid (liquid or gas) is its pressure multiplied by its
volume.
The equation used to
calculate the pressure energy of a certain volume of
fluid is as follows:
Epress
= P x V : Pressure energy = pressure x volume
Where: Epress
= pressure energy of a certain volume of
fluid (J)
P = pressure of
fluid (Pa or N/m2)
V = volume of fluid (m3)
Entropy
is a measure of the usefulness of energy. The entropy of
an object or a system increases as its energy becomes
less useful.
For example: If a cup of boiling water is mixed with a
bucket of warm water, there may be no net increase or
decrease in the amount of energy in the combined volume
of water but the entropy of the mixture will increase as
the water is mixed. (It is a law of nature that the
entropy of the universe is constantly increasing. This
means that, without intervention, things in the universe
are moving towards disorder rather than order. We will
look at entropy in greater detail when we study
thermodynamics in Unit 2 of this curriculum.)
Temperature
All materials consist of smaller particles such as
molecules, atoms and/or ions. These particles move
constantly. We cannot easily observe their movement but
if we had microscopes that were powerful enough, we would
see that they can vibrate, rotate and migrate (move
around). As a result of this constant movement, they
contain kinetic energy. Temperature is an indication of
the average kinetic energy of the particles in an object.
Sensing
Temperature: The particles in "hotter"
object move more vigorously than those in cooler ones and
have more kinetic energy. They can easily transfer some
of this kinetic energy by collision with objects they
come into contact with. (If you touch a hot surface,
rapidly vibrating particles at the hot surface collide
with your finger. These cause particles in the tip of
your finger to vibrate more vigorously and thus increase
the temperture of your finger tip. This is a transfer of
energy by conduction.)
Absolute Zero
When substances cool down, the particles inside the
material move more slowly. If the material continues to
cool, it will eventually reach a point at which the
particles stop moving. The temperature at which this
occurs is called Absolute Zero. (Absolute Zero is roughly
-273 degrees Celsius or 0 Kelvins.) It is impossible to
reach Absolute Zero because an object that cools needs to
be able to transfer energy to another object that is at a
lower temperature.
Expansion:There
are forces of attraction and repulsion between particles.
If the average kinetic energy of the particles in a
liquid, solid or gas at constant pressure increases, the
average distance between particles will increase. The
material will expand.
Thermometers are
instruments that provide a relative indication of the
average kinetic energy of the particles in a material or
object. Simple thermometers use the expansion and
contraction of a liquid or solid to indicate temperature
according to a defined scale. (We'll discuss temperature
in greater detail in Unit 2.)
Example
1.2.1: Calculation of work
How much work is done in lifting a mass of 5 kilograms
through a vertical distance of 4.5 meters?
Solution
The gravitational force acting on 5 kilograms at the
Earth’s surface is 5 x 9.81 Newtons or 59.05 N.
The work done in lifting 5
kilograms vertically through 4.5 meters is thus 5 x 9.81
x 4.5 Joules.
Work done = 220.73 J.
Example 1.2.2: Conversion of Energy
A concrete block with a mass of 20 kilograms falls from
the scaffold on a building site. If the scaffold is 10
meters above the ground, how much energy is converted to
other forms of energy when it strikes the ground?
Solution
At 10 above the ground, the concrete block has a
gravitational potential energy = 20 kg x 9.81 m/s2
x 10 m = 1962 Joules.
This energy is converted to kinetic energy as it falls
and this energy is converted to other forms of energy
when the block collides with the ground.
Example 1.2.3: Conservation of Energy in a Pendulum
(Assume that no energy is lost by a pendulum bob as it
swings back and forth.)
A pendulum consists of a metal object (mass = 100 grams)
suspended on a thin string. If the pendulum is pulled
back and released at a point where its vertical distance
above the lowest point of its swing is 30 centimeters (0.3
meters), how much kinetic energy will the pendulum bob
have as it passes its lowest point.
Solution
When the
pendulum bob is pulled back, its vertical height
increases and it gains gravitational potential energy.
When it is released and starts to move towards its lowest
point, it gathers speed and its kinetic energy increases.
The increase in kinetic energy is equal to the decrease
in gravitational potential energy that occurs as it loses
height.
When it is pulled back to
a height of 30cm, its gravitational potential energy
relative to its lowest point, mgh = 0.1kg x 9.81J/kg.m x
0.3m.
PE= 0.294 Joules.
If all of the
gravitational potential energy is converted to kinetic
energy, the kinetic energy of the bob at its lowest point
is the same:
KE = 0.294 Joules.
We can calculate its speed
at the lowest point by using the equation for kinetic
energy: .KE = ½mv2
v2 = (2 x 0.294J)/ .1 kg.
. . . . .___________
v = Ö (2 x 0.294)/ .1 = 2.425 m/s
Example 1.2.4: Calculation of pressure energy
Calculate the pressure energy of 2 cubic meters of water
with a pressure of 2000 Pa.
Solution
Pressure
energy is calculated by multiplying the pressure by the
volume of the object or material.
The pressure energy of 2
cubic meters of water with a pressure of 2000 Pa. is = 2
x 2000 = 4000 Joules.
REVIEW QUESTIONS
- In nuclear reactions
(and explosions) matter is apparently converted
to energy. Does this disprove the law of
conservation of energy?
- If 200 Joules are
used to wind up the spring of a clockwork motor,
neglecting friction, how much work is done on the
spring?
- If a person pushes a
car through a distance of 2 meters in 2 seconds
by applying a force of 300 N in the direction of
movement: How much work is done? How much power
is applied?
- Relative to ground
level, an object with a mass of 5 kg at a height
of 10 meters has gravitational potential energy
equivalent to 490.5 Joules. If it is dropped, how
much kinetic energy will it have as it strikes
the ground? (Neglect loss of energy due to
friction with the air)
- If a water bomb
weighing 200 grams (0.2 kg) is dropped and
strikes the ground at 20 meters per second, what
is the maximum amount of kinetic energy that can
be converted to other forms of energy during
impact?
- A pendulum has a bob
with a mass of 0.5 kilograms and swings in such a
way that the difference in height between its
highest point and lowest point is 30cm. Relative
to its lowest point, how much gravitational
potential energy does the bob have when it is at
its highest point?
How much kinetic energy does the bob have as it
passes its lowest point?
- Calculate the speed
of the bob as it passes its lowest point.
- An oscillating spring
has a mass of 500 g bobbing up and down on its
end. The mass travels 30cm between its lowest
point and its highest point during a cycle.
Relative to its lowest point in the cycle, what
is the gravitational potential energy of the bob
at its highest point?
Relative to the highest point of the bob in the
cycle, how much elastic potential energy is
stored in the spring when the bob is at its
lowest point?
- The water pressure in
a pipe at the outlet of a pump is 300,000 Pascals.
How much pressure energy is contained in 0.5
cubic meters of water leaving the pump?
HOMEWORK
Select one or more of the recommended
activities for Lesson 1.3, collect the items needed and test the
procedure before demonstrating the activity during the
next theory lesson.
Epress
= P x V : Pressure energy = pressure x volume
Where: Epress
= pressure energy of a certain volume of
fluid (J)
P = pressure of
fluid (Pa or N/m2)
V = volume of fluid (m3)
Espring
= ½ k D l2 : Energy stored in spring
= ½ x spring constant x (increase
in length of spring)2
Where: Espring
= energy stored in spring (J)
k = spring constant
(N/m)
and D l = change in length of
spring (m)
W = F
x d : Work =
Force x distance.
Where: W = work in
Joules (J)
F = force in
Newtons (N)
and d = distance in
meters (m)
KE = ½mv2
: Kinetic energy = ½ mass x (velocity
squared)
Where: KE = kinetic
energy in Joules (J)
m = mass in
kilograms (kg)
and v = velocity in
meters per second (m/s)
PEg
= mgh : Gravitational potential energy =
mass x gravitational acceleration x height above
reference point.
Where: PEg
= gravitational potential energy in Joules
m = mass in
kilograms (kg)
g = acceleration
due to gravity in meters per
second squared (m/s2)
and h = height in
meters (m)
Chemical energy:
Energy stored in substances during chemical reactions or
as a result of their ability to release energy during
chemical reactions
Elastic potential
energy: This is also called strain energy. This is
molecular potential energy stored as a result of
stretching or compressing an object.
Internal energy:
Internal energy (sometimes called thermal energy) is the
sum of the kinetic energy and molecular potential energy
of each molecule or particle of an object.
Heat: Heat is
energy in motion. When energy is transferred from one
substance or object to another, heat is transferred.
Enthalpy:
Enthalpy is used to describe energy that is contained in
a material as a result of the kinetic and potential
energies of the particles that make up the material. The
enthalpy of an object changes when the temperature of the
object changes or when it changes phase (from gas to
liquid, liquid to solid, gas to solid or visa versa).
Entropy: Entropy
is a measure of the usefulness of energy. The entropy of
an object or a system increases as its energy
becomes less useful.
Pressure energy:
This is energy stored in a substance as a result of the
pressure exerted on the object or substance.
Magnetic potential
energy: Magnetic potential energy is the energy
that an object that can be influenced by magnetic forces
has as a result of its position in a magnetic force field.
Force fields:
Force fields are regions in space where forces can be
detected.
Temperature: Temperature
is an indication of the average kinetic energy of the
particles in an object.
ANSWERS TO REVIEW QUESTIONS
- Yes. Einstein showed
that matter could be converted to energy and visa
versa. Apart from nuclear reactions though,
energy and matter are both indestructible.
- 200 Joules
- Work = force x
distance. 300 N moved through 2 meters = 600
Joules.
Power is the rate at which work is (or can be)
done.
The power consumed in moving a force of 300 N
through 2 meters in 2 seconds (300 x 2) Joules
divide by 2 = 300 Watts.
- 409.5 Joules.
As the object drops, it accelerates and its
gravitational potential energy is converted to
kinetic energy.
- 40 Joules. KE = ½mv2.
KE = ½ x .2 kg x (2 m/s)2 = 40
J.
- 1.4715 Joules. PEg = mgh.
PEg = .5 kg x 9.81 m/s2
x .3 m = 1.4715 J
- The kinetic energy of
the bob as it passes its lowest point = 1.4715 J
The speed of the bob as it passes its lowest
point = 2.426 m/s.
KE = ½mv2. v2
= (2 x 1.4715 J)/ .5 kg.
. . . . .____________
v = Ö (2 x 1.4715)/ .5 = 2.426 m/s
- Relative to its
lowest point in the cycle, the gravitational
potential energy of the bob at its highest point
= 1.4715 Joules.
PEg = .5 kg x 9.81 m/s2
x .3 m = 1.4715 J
Elastic
potential energy stored in the spring when the
bob is at its lowest point = 1.4715 J. Neglecting
friction, the energy of the system consisting of
the spring and bob remains constant at all times.
At its lowest point, the bob has no gravitational
potential energy or kinetic energy. The elastic
potential energy of the spring is thus equal to 1.4715
Joules.
- 150,000
Joules. Epress
= P x V. Epress = 300,000
Pa x .5 m3 = 150,000 J.
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