PHY_Unit3_Sep4

Unit 3
Work, Energy and
Power
P1106
P1107
P1108
In This Unit
Lesson 3.1: Work and Energy
Lesson 3.2: The Conservation of Energy
Lesson 3.3: Power and Efficiency
92

Unit 3
Unit Introduction
Energy is one of the most basic and important concepts in physics
and a critical aspect of human technology. The terms energy and work
mean different things in physics . We will learn to calculate the work
done and energy spent. We will also learn to calculate kinetic energy,
gravitational potential energy and elastic potential energy.
One of the most important laws in physics is that the total energy
remains the same before and after changes to a closed system.
The principle of conservation of energy is a powerful way to solve
problems and analyze many kinds of situations.
A very popular misconception is that power and energy are the same
thing. They are related, but not the same. We will define power as the
rate at which energy is exchanged. Systems that waste a lot of power
are inefficient. Engineers all around the world work hard, day and
night to develop efficient devices and systems. We will learn how to
calculate efficiency and apply the concept to our everyday lives.
Learning Experiences
3.1 Work done
3.2a Flow of energy
3.2b Energy of a coffee filter
3.3a How powerful are you?
3.3b Efficiency of different balls
93

Lesson 3.1
Work Done and Energy
Imagine what it would take to dig the foundation for a modern bulding
with a shovel. The amount of soil, sand, and rock that needs to be
removed for the foundation of a reasonable size building is about
100,000 m 3 . A large shovel has a volume of about 0.01 m 3 . If you dug
four shovels per minute, you would have to work every minute, 24
hours per day, for five years.
A human worker has a maximum
output of a few hundred watts of
power. A hydraulic excavator has
a power output of 500,000 watts
and can do the job in two weeks.
This less is about the fundamental
physics of work, forces, and energy.
These ideas are the foundation
of much of human mechanical
technology, including hydraulic
excavators.
200 watts 500,000 watts
Figure 3.1 Two ways to dig
the foundation for a building.
Learning Outcomes
P1106.1 Define the work done by a
force as the product of the force and
the displacement in the direction of
the force: W = Fd
P1106.2 Describe how energy can
be stored in different ways/parts of a
system, e.g. energy stored thermally,
gravitationally, etc.
P1107.1 Derive and apply the
formulae E k
= ½ mv 2 , E p
= mgh and
use the principle of conservation of
mechanical energy in problem solving
Key Vocabulary
work done
joule (J)
energy
kinetic energy
reference frame
potential energy
gravitational potential
energy
elastic potential energy
spring constant
94

Work done
What is work? Is reading a book or writing an
assignment work? In physics, work is done by
forces that cause objects to move. you may think
that studying for a test is work. But, in physics, if
there isn’t a force that causes something to move
then there is no work being done.
The amount of work done on an object is the force
multiplied by the distance the object moves in the
direction of the force. If you use a force of one
newton to lift a cup up a distance of one meter,
you do one newton-meter (N·m) of work on the
cup (Figure 3.2). Work has a quantity such as 1
N·m or 10 N·m is done when energy is transferred
through the action of a force.
(3.1)
Work
W=Fd
Lesson 3.1: Work Done and Energy
In the SI system, one joule (J) is defined as one newton-meter (N·m).
The unit of work, the joule, is also the basic unit of energy. Throughout
science, a joule is the standard unit of energy. It is not, however, the only
unit of energy. Calories and kilowatt-hours are other units of energy that are
commonly used.
10 N
W
F
d
Discussion question
How much work do
you do in a day?
work (J)
force (N)
distance (m)
1 m
1 N
Figure 3.2 One joule of
work
1 N
1 m
work = 10 N x 1 m = 10 J
Figure 3.3 Two ways to do 10 J of work
10 m
work = 1 N x 10 m = 10 J
We can do 10 J of work by applying a force of 1 N and moving an object a
distance of 10 m, as shown in Figure 3.3. We can also do the same amount
of work,10 J, by applying a force of 10 N and moving an object a distance
of 1 m.
One joule of energy is equivalent to one
newton-meter of work
95

Unit 3: Work, Energy and Power
Positive and negative work
Discuss teh sign of work and whether it is done by a system or on a system.
When done by the system word reduces the energy of the system and vice
versa.
96

Work done when the force is not constant
Lesson 3.1: Work Done and Energy
Consider pushing a heavy box with an initial force of 10 N (Figure 3.4).
After moving the box a distance of 5 m, you get tired and the force you are
applying gradually diminishes until the force becomes zero. To calculate the
work done by a force that changes over time we draw a graph that shows the
force on the vertical axis and the displacement on the horizontal axis. The
amount of work done is equal to the area under the force vs. displacement
graph as shown in Figure 3.5.
Force vs. displacement
Force
10
Force (N)
Displacement
5
Displacement (m)
20
Figure 3.4 Force
and displacement.
Figure 3.5 Graph showing the change in force over a distance
In this example, first the force is constant between the start and d = 5 m.
Between 5 meters and 20 meters the force decreases, making a triangle on
the graph. To find the area, we split the graph into a rectangle and a triangle.
We then find the areas of both shapes and add them.
The work done to complete the task is 50 N m + 75 N m= 125 N m or 125 J.
The area under the force vs. displacement graph is
equal to the work done by the force.
97

Unit 3: Work, Energy and Power
Energy
Energy measures the capacity for change and is measured in joules (J).
Energy can create changes in many quantities such as speed, height, pressure,
or temperature. Energy is what changes matter from liquid into gas or back.
Work is one form of energy. A basic mechanical definition of energy is
the ability to do work. A system that has 10 J of energy can exert any
combination of forces and distances whose product is equal to or less than
10 N·m of work. Without the addition of more energy, the system cannot
produce more work than 10 N·m.
Mechanical Energy comes from position
or motion. Gravitational potential energy,
elastic potential energy and kinetic energy
are examples of mechanical energy.
Thermal Energy is another word for heat.
Thermal energy is energy that is attributed
to an object’s temperature. Hot objects have
more thermal energy than cold objects.
Chemical Energy is stored in the bonds
of chemical compounds. It can be released
by rearranging the atoms into different
molecules, such as by burning natural gas
and to produce water and carbon dioxide.
Electrical Energy moves in the form of
electric currents that flow in response to
electrical voltages, such as in a battery or
wall socket.
Nuclear Energy (atomic energy) is energy
contained in the bonds between protons and
neutrons in the nucleus of atoms. Nuclear
energy may be released when atoms change
from one element into another, such as in a
nuclear reactor or in the core of the Sun.
Radiant Energy includes all forms of
electromagnetic waves such as visible light,
microwaves, radio waves, x-rays. Almot all
the energy on Earth ultimately comes from
radiant energy that originates in the Sun.
98
Figure 3.6 Energy examples

Lesson 3.1: Work Done and Energy
3.1 Work done
Inquiry Question
Materials
How does the distance travelled by a paper airplane depend
on the applied force?
Spring scale, paper to make airplanes, meter sticks
Laboratory procedure
1. Make a paper airplane.
2. Choose 5 different forces on the spring scale.
3. Attach the paper airplane to the spring scale, and pull the scale back to
your first force as shown in Figure 3.7.
4. Release the spring and measure the distance covered by the airplane.
5. Complete the data table given below.
6. Make a graph plotting force on the horizontal (x) axis and distance on
the vertical (y) axis.
Force (N) Distance distance (d) (m) Work done done (N m) (N m)
Figure 3.7 Attach
the paper plane to
the spring scale
Questions
a) Is your slope a straight line?
b) Calculate the area under the graph.
c) What does the area represent? (Hint: units are N m)
d) What possible errors could have occured during this experiment?
e) Write down two improvements that could be made.
99

Unit 3: Work, Energy and Power
Kinetic energy
Kinetic energy (E k
) is the energy of motion. An object has kinetic energy
when the object has mass and is moving. To appreciate the changes caused
by kinetic energy, imagine two balls each about the size of your fist. The two
balls strike a wall and each makes a dent in the wall. One is moving fast and
the other is moving slow. The dents occur because the wall must absorb the
kinetic energy to stop each ball. Which ball will create a bigger dent? The
ball with the greatest kinetic energy makes the largest dent.
(3.2)
Kinetic energy
EK
1
= mv
2
2
E K
m
v
kinetic energy (J)
mass (kg)
velocity (m/s)
Kinetic energy depends on both mass and speed (Figure 3.8). Consider
the relationship with mass first. The kinetic energy of a moving object is
proportional to mass. If the mass is double, then the kinetic energy is also
double. A 2 kg ball moving at a speed of 1 m/s has 1 J of kinetic energy.
A 4 kg ball moving at the same speed of 1 m/s has 2 J of kinetic energy, or
twice as much.
E k
1 m/s
2 kg
= 1 = 0.5 (2 kg)(1 m/s)
2 mv2 2 = 1 J
1 m/s
E k
1 m/s
2 kg
= 1 = 0.5 (2 kg)(1 m/s)
2 mv2 2 = 1 J
3 m/s
Figure 3.8 Kinetic energy depends on mass and speed
According to equation (3.2) kinetic energy of a moving object depends on
the square of the speed. If you double the speed then the kinetic energy
increases by a factor of four (2 2 ). Consider the 2 kg ball traveling at 1 m/s
which has 1 J of kinetic energy. The same ball moving at 3 m/s has 9 J of
kinetic energy. If you multiply the speed by 3, then the kinetic energy is
multiplied by a factor of 3 2 = 9.
The relationship between kinetic energy and mass is a linear relationship.
Doubling one variable in a linear relationship also doubles the other
variable. The relationship between kinetic energy and speed is a nonlinear
relationship. There are many different forms of non-linear relationships.
One variable changing as the square of another variable is a very common
form of non-linear relationship.
100
E k
4 kg
= 1 2 mv2 = 0.5 (4 kg)(1 m/s) 2 = 2 J
E k
2 kg
= 1 2 mv2 = 0.5 (2 kg)(3 m/s) 2 = 9 J

Lesson 3.1: Work Done and Energy
Work and kinetic energy
We understand that a quantity of energy represents the maximum amount
of work that can be done. The converse is also true. Think about a force
accelerating an object. You can think of energy as the accumulated work
done to the object to change its speed from zero to speed, v. This can be
proven mathematically by calculating the work done by a constant force, F,
that accelerates a body of mass, m, from rest to speed v.
W = Fd and F = ma
Figure 3.9 The kinetic energy is the work done to accelerate a mass, m,
from rest to speed, v.
We are looking for an expression for the work in terms of the variables m
and v. We need equations that relate acceleration and distance to velocity.
Fortunately, there are two such equations.
v = at → t = v a
Start at rest
m
F v = 0 F
and
d = 1 2 at2 → d = 1 2 a ⎛ v ⎞
⎝
⎜
a⎠
⎟
2
→ d = 1 2
If we substitute the expression for the distance, d, into the equation for work
we obtain the result we want.
W = ( ma)d → W = ma
( )
d
⎛
⎜
⎝
1 v 2
2 a
Finish with speed, v
⎞
⎟
⎠
2
→
W = 1 2 mv2
The work done is exactly equal to the kinetic energy of the moving mass!
This is a very general result with application to all of physics. The change
in kinetic energy of an ideal system is equal to the work done on the system.
By “ideal,” we mean no friction. If friction is considered some of the work is
done against friction leaving less to be “stored” as kinetic energy.
If work is done on an ideal system the energy of the
system increases by the amount of work done.
The energy of a system can be calculated by finding the work done to change
the system from one state, such as rest, to another state, such as moving with
speed, v.
v
v 2
a
101

Unit 3: Work, Energy and Power
Example problem
1
A sports car with an empty fuel tank has a mass of 1600 kg.
1. Calculate the kinetic energy of the car when it’s velocity is 90 km/h with
the fuel tank empty.
2. Calculate the the mass of petrol if the car has the same kinetic energy at
88 km/h when the fuel tank is full.
Asked
Given
1) Kinetic energy
2) mass of petrol
mass m = 1600 kg
velocity v = 90 km/h,
and v = 88 km/h
Relationships
Solution
EK
=
1
2
mv
2
1. The units for the velocity are km/h and need to be converted to m/s.
90 km
1 hr
1000 m
1 km
1 hr
3600 s = 25.0 m/s 88 km
1 hr
1000 m
1 km
1 hr
3600 s
= 24.44 m/s
Using the equation for kinetic energy we find :
E k
= 1 2 mv2 = 1 ( 1600 kg) ( 25 m/s) 2 = 500,000 J
2
2. The kinetic energy in this case is the same but the velocity is now 24 m/s.
We solve the kinetic energy for the unknown mass.
E k
= 1 2 mv2 → m = 2E k
v 2
( )
( )
= 2 500,000 J = 1674.2 kg
2
24.44 m/s
m = 1674.2 kg is the mass of the car with the fuel. The mass of the petrol
is calculated from the difference.
1674.2 kg – 1600 kg = 74.2 kg.
102

Lesson 3.1: Work Done and Energy
Gravitational potential energy
Potential energy (E P
) is the energy of position. The word “potential”
means this energy is available to transform into other forms of energy.
A good example of potential energy is to
compare the energy of a brick on the table
to that of a brick on the floor. The brick
has more potential energy on the table
than it does on the floor (Figure 3.10).
This potential energy can be transformed
into kinetic energy by letting gravity pull
the brick back down again.
mass, m
height
h
Figure 3.10 Mass and height
Potential energy from height exists because work must be done against the
force of gravity to raise the brick from the floor to the table. The work done
is equal to the amount of potential energy. Since gravity is the force, energy
of height is called gravitational potential energy.
(3.3)
Gravitational potential Energy
EP
=
mgh
E P
m
h
kinetic energy (J)
mass (kg)
height (m)
Equation 3.3 shows that gravitational
potential energy (E p
) depends on mass,
gravity and height. The amount of
energy varies in a linear relationship
with mass, gravity and height.
Consider three identical 1 kg balls at
three different heights as shown in
Figure 3.11. If we take gravity to be a
constant: 9.8 N/kg, then the potential
energy is 19.6 J when the ball is at a
height of 2 m. The potential energy
is 39.2 J when the ball is at 4 m. The
height doubled and the potential
energy also doubled. The potential
energy is 49 J when the ball is at 5 m.
Lowest
E p
2 m
Highest E p
4 m 5 m
Figure 3.11 Potential energy
depends on height
103

Unit 3: Work, Energy and Power
Work and gravitational potential energy
We have discussed that gravitational potential energy is gained because work
is done against gravity. To derive the equation for gravitational potential
energy we equate the gain in potential energy to work done.
The work done by a force, F, acting over
a distance, d, in the same direction as the
force is given by:
W = Fd
The force is equal to the weight (mg) of
the object. The distance is equal to the
height, h, the object is raised.
d = h and F = mg
The work done is therefore the same
expression as the gravitational potential
energy.
W = mgh
The proof above assumes the object
moves in a straight vertical path to
reach its final height, h. What if the
object moves in a different path? Is the
gravitational potential energy different if
the objects takes a longer path?
The proof above assumes the object
moves in a straight vertical path to reach
its final height, h. What if the object
moves in a different path (Figure 3.12)?
If you think about it, the gravitational
potential energy must be the same
independent of the path the object takes!
The work calculation is still correct
because work is done against gravity only
by the vertical components of movement,
parallel to the direction of gravity.
Horizontal components of any movement
do not cause any work to be done against
gravity.
104
Figure 3.13 Qatari high jumper
Mutaz Barshim, doing work
against gravity
E p
= mgh
(a)
(b)
(c)
Figure 3.12 Potential energy is
the same independent of path (a),
(b) or (c).
h

Reference frames
What is the potential energy of the 1 kg
red ball in Figure 3.14? The ball is 1.5 m
above the floor, or 4 m above the ground, or
6 m above the bottom of a hole outside the
window. Calculations give E p
= 14.7 J,
39.2 J and 58.8 J depending on which height
you choose.
Lesson 3.1: Work Done and Energy
1 kg ball
1.5 m
The energy of an object depends on
the reference frame in which things are
measured. In the reference frame of the E p
= mgh
room, the 1 kg ball that is 1.5 m from the
floor has a potential energy of 14.7 J. If the
E p
= (1 kg)(9.8 N/kg)(1.5 m) = 14.7 J
reference frame is the ground six meters
E p
= (1 kg)(9.8 N/kg)(4 m) = 39.2 J
below the ball then the potential energy is
E p
= (1 kg)(9.8 N/kg)(6 m) = 58.8 J
39.2 J. Values of energy often depend on the Which one is the right answer?
choice of reference frame.
Figure 3.14 Potential energy
reference frames.
The choice of a reference frame (such as where “zero” is) is arbitrary
because only differences in energy matter, not absolute values. A ball that
falls 1.5 m loses 14.7 J of potential energy. It does not matter if the ball falls
from 1.5 m to zero or from 7.5 m to 6 m. The potential energy lost or gained
is independent of where zero is defined. We are free to choose any reference
frame as long as we stay consistent when solving a problem.
Kinetic energy also depends on reference
frames. A ball at rest in your hand has
E k
= 1 2 mv2
zero velocity, doesn’t it? In your reference E k
= (0.5)(1 kg)(29,780 m/s) 2
frame, which is fixed to the Earth, the ball’s = 443,424,200 J
kinetic energy is zero. Consider, however,
that Earth is moving through space at
29,780 m/s. Relative to the Solar System,
E k
= 0
the ball on the table has a kinetic energy of
443 × 10 6 J!
In the next Lesson we will see how the
exchange of energy is used to analyze and
predict the changes in systems. It is very
useful to be able to choose a reference frame
best suitable to the problem.
4 m
6 m
29,780 m/s
Figure 3.15 Kinetic energy
reference frames.
105

Unit 3: Work, Energy and Power
Example problem
2
The current weightlifting world record of 263 kg was set by Hossein
Rezazadeh of Iran in 2004.
1. How much gravitational potential energy does a 263 kg barbell have if it
is held 2.0 m above the floor?
2. How much work is done to lift the barbell from the ground to the
overhead position 2.0 m high?
3. Lifting the same barbell to the same height on Mars only takes 1946 J of
work. Calculate the value of g on Mars.
Asked
1) potential energy E P
of the barbell over head.
2) work W done to lift the barbell 2 m overhead
from the floor.
3) acceleration due to gravity, g, on Mars.
263 kg
2.0 m
Given
Relationships
barbell mass m = 263 kg,
barbell final height h = 2.0 m
work on Mars W = 1946 J
E p
=mgh, g=9.8 m/s 2
Solution
1. E p
=mgh= (263 kg)(9.8 m/s2)(2.0m)=5,155J
2. As given in part (1), the change in potential energy of the barbell from the
floor (E p
=0) to its overhead position is 5,155J. The minimum work done by
the weightlifter is the same as the change in E p.
3. On Mars: E p
= mgh = (263 kg)(g)(2.0 m) = 1946 J
g =
1946 J
263 kg
( )( 2 m) = 3.7 N/kg
106

Elastic potential energy
Potential energy exists any time a force is
restrained from acting. If the restraint is removed
than the energy can be released. In gravitational
potential energy, it is the force of gravity that is
restrained. Compressing or extending a spring
also creates potential energy.
Lesson 3.1: Work Done and Energy
Work has to be done against the force of a spring to deform the spring into
a new shape. The spring stores elastic potential energy long as it is
deformed. The energy is released when the spring is allowed to return to its
non-deformed shape.
(3.4)
Elastic potential energy
EE
=
1
2
kx
2
Discussion question
Can you think of
another system that
stores potential
energy?
Equation 3.4 is a model for the elastic potential energy of a spring that has
been deformed an amount, x, from its free length. The free length is the
length of the spring under zero force. The quantity, k, is called the spring
constant and describes how much force the spring exerts per meter of
deformation. The spring constant is a property of the spring itself and is
different for every spring or other elastic materials. A stiff spring resists
compression or stretching, so it has a large value of the spring constant k; a
loose spring has a low value of k.
E E
k
x
elastic potential energy(J)
spring constant (N/m)
compression (m)
Oud
strings
Human
muscles
Figure 3.16 Examples of elastic potential energy
Rubber band
Spring
Elastic potential energy is stored in most objects when the object changes
its form, shape, or length. The force exerted by an elastic object acts in a
direction to return it back to its original shape or position. Some examples of
objects that can store elastic potential energy are shown in Figure 3.16.
107

Unit 3: Work, Energy and Power
Example problem 3
A spring with a spring constant of 1000 N/m is compressed by 1 cm.
1. How much energy is stored in the spring before it is released.
2. How does the answer change if the spring is compressed by 2 cm.
3. What is the relationship between the two energies stored.
Asked
Elastic potential energy stored
Spring before compression
Given
spring constant k = 1000 N/m
compression x = 1 cm; 2 cm
Relationships
EE
=
1
2
kx
2
Spring after compression
x
Solution
0.01 m
1. The compression is given in cm, so it must be converted to m tp match the
units of the spring constant (1 cm = 0.01 m)
Elastic potential energy stored in the compressed spring is calculated by
using the given relationship.
EE
1 1 2
kx 1,000 0.01
= =
2 2
= 0.05J
2. The compression is 2 cm = 0.02 m.
( )( ) 2
E E
= 1 2 kx2 = 1 ( 1000 N/m) 0.02 m
2
( ) 2 = 0.2 J
3. By increasing the compression by a factor of 2, the energy has increased
by a factor of 4. This is because energy is directly proportional to the
square of the compression or expansion.
108

Lesson 3.1: Work Done and Energy
Lesson 3.1 Review
1
2
3
A 30 kg boy is sitting on a 10 kg cart on top of a hill that is 10 m
high
a) What is the initial potential energy of the boy and cart together?
b) What is their initial kinetic energy?
A 1,000 kg car traveling 15.0 m/s brakes and comes to a stop after
traveling 20.0 m.
a) What is the car's initial kinetic energy?
b) What is the car's final kinetic energy?
c) How much work does it take to stop the car?
d) What is the average force applied in bringing the car to a stop?
A vertical spring with k = 100 N/m is compressed
10 cm by a 100 g mass.
a) How much elastic potential energy does the
compressed spring store?
b) How much elastic potential energy would the
compressed spring store if it were compressed
the same distance by a 300 g mass?
x
10 cm
100 g
4
If a the mass of a box is cut in half, but the box is raised to a height
four times higher. Does its potential energy change? Show your
work to explain your answer.
5
How far is a spring extended if the spring has 1.0 J of potential
energy and the spring constant is 1,000 N/m?
6
a) How much work do you do when you push a 400 kg car for 6 m
with a force of 300 N?
b) What is the car's final speed if all your work becomes kinetic
energy?
300N
109

Lesson 3.2
Conservation of Energy
There are many thrilling rides
at an amusement park but the
popular rollercoaster usually has
the longest lines. No amusement
park is complete without one.
The thrill factor in a roller coaster
comes from the exchange of
gravitational potential energy to
kinetic energy and vice versa.
Figure 3.17 A roller coaster
The first ascent in a roller coaster is usually the highest point of the ride
and the maximum potential energy that the ride will have. As gravity
pulls the car down, all of the potential energy converts into kinetic
energy causing the car to accelerate. The more potential energy the
car has to start with, the higherthe final speed it achieves. Most roller
coasters contain a seccession of hills that get smaller and smaller until
all of the energy is converted into heat through friction.
Learning Outcomes
P1106.3 Recall the principle of
conservation of energy
and apply it to simple
examples
Key Vocabulary
system
open system
close system
mechanical energy
110

Lesson 3.2: Conservation of Energy
The transformation of energy
In almost every process that occurs in nature and
technology we find energy is transformed between
one form and another. In the previous lesson we
learned about objects and systems having kinetic
and potential energy. These are two forms of
energy common in physics problems. Figure 3.18
shows a few of the many energy transformations
that occur before and during a car race.
Discussion question
What kind of energy
does a car have when
it is moving?
Where did the car’s
energy come from?
Chemical energy
in fossil fuels
Radiant energy
in sunlight
Nuclear energy (sun)
Heat energy
from combustion
Mechanical
energy
Energy
of a gas
Figure 3.18 Energy flow from the Sun to a race car.
The invention of the automobile is the single largest personal multiplier
of energy that most of us will ever regularly use. In one minute, a very fit
human, working constantly, might do 14,000 J of mechanical work. An
average car can do 7,000,000 J of work in the same minute. The car does
500 times as much work as a very strong person.
Consider the source of the energy that powers a race car. The energy of
the car is mechanical kinetic energy. Working backwards from the car
the engine transforms energy from the pressure of a hot gas into kinetic
energy. The energy of the hot gas comes from burning fuel that transforms
chemical energy into heat energy. The chemical energy is trapped in oil
that accumulated over millions of years from decayed plants. Those ancient
plants received radiant energy from the Sun. Over a 400-million-year cycle
you could say that a race car is actually solar-powered! If you trace back far
enough, virtually all the energy we use is ultimately derived from nuclear
energy in the Sun.
111

Unit 3: Work, Energy and Power
3.2a Flow of energy
Inquiry Question
Materials
Laboratory procedure
How does energy flow from one form to the other?
bunsen burner, match, coupled pendulum, 2 masses, spring,
pulley, string, 2 carts
Perform each activity and make an outline of how energy is flowing from
one form to the other. Try to include as many forms as you can think of.
1. Light a bunsen burner with a match.
Energy transformations:
2. Swing one side of a coupled pendulum.
Energy transformations:
3. Pull down the weight of the spring and then let it go.
Energy transformations:
4. Wrap a string with a weight around the pulley and then let it go.
Energy transformations:
5. Push one car so it crashes into another car making it move.
Energy transformations:
112

What is a system
Lesson 3.2: Conservation of Energy
The understanding of energy starts with the definition of a system. A system
is a group of objects and interactions that we choose to focus our attention
on. If we are trying to understand the speed of a falling ball, we might
choose a system to include the ball's initial height, mass, and speed, as
well as the force of gravity. We choose a system to include only the objects
and interactions that are important to what we are investigating. Choosing
a system frees us from having to consider everything, which would be an
impossible task.
Every system has a boundary, which is an
imaginary box that encloses the system. A
system is an open system, if we allow
matter or energy to cross the boundary.
A cup of hot coffee on a table is an open
system (Figure 3.19). In a few hours the
thermal energy flows into the room and in
a few days the water evaporates away. Both
matter and energy have left the system.
HEAT
System
Evaporation
HEAT
Figure 3.19 Example of an
open system
Figure 3.20 Example of
a closed system
A system is a closed system, if no matter or
energy is allowed cross the boundary. Closed
systems are useful to think about because in a
closed system the total energy remains constant.
The total energy at one time will be the same as
the total energy at any later time. Imagine the
coffee cup in a perfectly sealed and insulated box.
The energy and matter stay within the boundaries
because this is a closed system (Figure 3.20).
The total energy of an open system may change.
The total energy of a closed system remains the same.
There is no such thing as a truly closed system. However, it is often a
very good approximation to assume a closed system as a starting point
for understanding something. The analysis is much easier. Scientists often
start with a simple model of a closed system and then add details based on
comparing the model's predictions with actual data.
113

Unit 3: Work, Energy and Power
Law of conservation of energy
The total energy in a closed system remains constant. If one form of energy,
such as kinetic energy, increases then another form of energy must decrease
by the same amount. The law of conservation of energy states, 'Energy
cannot be created or destroyed; it can only be transformed from one form to
another'.
Closed system
E k
= 1 mgh v = gh
2
E p
= 1 2 mgh
h
(a) (b) (c)
1
2 h
Figure 3.21 Conservation of energy on a rollercoaster
Consider closed system of a roller coaster and car, including the effect of
gravity, as shown in Figure 3.21. The energy at the start is all potential
because the car is at rest on top of the hill. Energy conservation tells us
that if potential energy and kinetic energy are the only forms of energy in
the system, then the car's kinetic energy gain can only come from potential
energy lost. At the bottom of the hill (h = 0 ) the potential energy is
completed converted to kinetic energy. Conservation of energy tells us that
the speed of the car is completely determined by the change in height h. The
speed at points (a), (b), and (c) is the same because the potential energy lost
is the same so the kinetic energy must be the same.
The total energy is the same at any point in time in the ideal closed system
above. For frictionless mechnical systems it is usually enough to consider
kinetic energy, gravitational potential energy and elastic potential energy. A
more general analysis might include chemical energy, nuclear energy, and
thermal energy.
In a real rollercoster, some of the energy is converted by friction into heat
and wear. This energy is not “lost” but is no longer either potential or kinetic
energy and so is not counted in the simple analysis.
114

Conservation of energy in mechanical systems
Lesson 3.2: Conservation of Energy
Kinetic energy, gravitational potential energy, and elastic potential energy
are collectively called mechanical energy (Figure 3.22). For example,
an airplane in the air has kinetic energy due to motion and gravitational
potential energy due to height. A car moving on a level road might only have
kinetic energy. A compressed spring has elastic potential energy. A person
running has elastic potential energy in their muscles and also kinetic energy
due to their motion.
(3.5) Conservation of energy
E initial
=E final
E initital
E final
initial energy (J)
final energy (J)
In a frictionless system the total mechanical energy remains constant
according to the law of conservation of energy (equation 3.5). Energy can
only increase if external forces do work on the system. Energy can decrease
only if the system does work on something external to the system.
Elastic potential
energy due to
compression
(a)
E = mgh + 1 2 mv2
(b)
E = 1 2 kx2
(c)
E = 1 2 mv2
(d)
E = 1 2 kx2 + 1 2 mv2
Figure 3.22 Examples of mechanical energy. (a) A jet on takeoff is
increasing gravitational potential energy and kinetic energy. (b) A
compressed spring stores elestic potential energy. (c) A moving race car on
a level track has kinetic energy. (d) Running uses elastic potential energy in
muscles and kinetic energy of whole-body movement.
115

Unit 3: Work, Energy and Power
Understand energy conservation problems
Using the law of conservation of energy proceeds in three steps.
1. Define your system and the types of energy you will count - kinetic
energy, gravitational potential energy, elastic potential energy and work are
common choices for what to count in a mechanical system.
2. Energy conservation is applied before and after a change in the system
that rearranges the energy into different forms. Let the total energy before the
change equal the total energy after the change.
3. Solve the equation for your answer.
A ball that is moving with speed, v, on a frictionless track that launches the
ball straight up in the air. What is the maximum height the ball reaches?
Step 1: The system changes from a ball moving with velocity, v, to the
same ball at height, h, with v = 0. We choose the system and write down all
the forms of mechanical energy before and after the change.
System
m
v
h
Before the change
E = mgh + 1 2 mv2 + 1 2 kx2 + Fd
After the change
E = mgh + 1 2 mv2 + 1 2 kx2 + Fd
Step 2: We set the total energy before the change equal to the total energy
after the change and eliminate all terms we know to be zero.
Before the change
After the change
mgh + 1 2 mv2 + 1 2 kx2 + Fd
=
mgh + 1 2 mv2 + 1 2 kx2 + Fd
0 0 0 0 0 0
1
2 mv2 = mgh
h = v2
2g
Answer
Step 3: The equation for the total energy before and after the change is
solved for the height.
116

Lesson 3.2: Conservation of Energy
Example problem 4
A cart of mass, m, starts at rest and rolls down an frictionless, uneven hill.
Calculate an expression for the speed of the cart at height, h, given a starting
height of h 0 .
m
h 0
v
Figure 3.23 Car rolling down the track
h
Asked:
Given
Relationships
expression for speed, v
mass, m, initial height, h 0 , height, h, and initial speed = 0.
Total mechanical energy:
E 1 1
total
= mgh + mv + kx
2 2
2 2
Solution
1. Write down the relevant forms of energy at the start and later at height, h.
2. Apply the conservation of energy and eliminate terms that are zero.
3. Solve for the speed, v.
1
Start at h 0
0
Later at height, h
2
3
0
mgh
0
0
0
Answer
117

Unit 3: Work, Energy and Power
Solving energy problems involving springs
A spring allows for a third form of energy: elastic potential energy.
In problems with springs, the total energy has three terms: one each for
gravitational potential energy, elastic potential energy, and kinetic energy.
Consider a 2.0 kg ball that drops onto a vertical spring with a spring constant
k of 1,000 N/m (Figure 3.24). From what height did the ball drop if the
spring compresses by 25 cm?
To solve the problem we
follow the same three steps.
Step 1: write down the
total energy of the system in
the initial and final states.
Step 2: Equate energy
before and after the change
then eliminate terms that are
zero.
Step 3: Rearrange the
equation to find the variable
needed.
Before
(initial state)
2.0 kg
h
k = 1,000 N/m
After
(final state)
x = 0.25 m
Figure 3.24 A ball dropped on a spring.
1
Initial state
Final state
2
0 0 0 0
3
Answer
To find the height we must first convert 25 cm in to m.
25 cm = 0.25 m
Subsititute the values to calculate the initial height of the ball.
h = kx2
2mg
Answer
118

Lesson 3.2: Conservation of Energy
Example problem 5
A horizontal spring is used to launch a 2.0 kg ball. The spring is compressed
by 0.25 m and has a spring constant k of 1,000 N/m. What is the maximum
speed of the ball? What is the total mechanical energy of the system?
Asked
Given
Relationships
total mechanical energy
and speed v
k = 1,000 N/m;
x = 0.25m;
m = 2.0kg
Before
(initial state)
Total mechanical energy:
E 1 1
total
= mgh + mv + kx
2 2
After
(final state)
2 2
k = 1,000 N/m
2.0 kg
x = 0.25 m
v
Solution
Total mechanical energy of the system is the same in the initial and final
state. In the initial state the mechanical energy depends on only the elastic
potential energy and in the final state the mechanical energy depends on the
kinetic energy alone. We can solve for either one to find out the answer. To
solve for kinetic energy we first need to know the speed. So, in this case, we
will solve for elastic potential energy.
Solving the velocity we get:
E 1 1
P
= kx = (1,000 N / m )(0.25 m )
2 2
E = 31.25J
2 2
P
Write down relevant
forms of energy.
Initial state
Final state
= mgh + 1 2 mv2 + 1 2 kx2
Eliminate zero terms.
Solve for the
variable you want.
mgh + 1 2 mv2 + 1 2 kx2
mgh + 1 2 mv2 + 1 2 kx2 =
0
1
2 kx2
=
mgh + 1 2 mv2 + 1 2 kx2
0
1
2 mv2
0 0
v = ( 0.25 m) ( 1,000 N/m)( 2.0 kg)
= 5.6 m/s
v = x
Solution
k
m
119

Unit 3: Work, Energy and Power
3.2b
Inquiry Question
Materials
Laboratory procedure
Energy of a coffee filter
How does the final velocity of a coffee filter depend on its
height? Calculate and compare the initial potential energy
and final kinetic energy.
coffee filters, high speed cameras, 2 m paper strip with 5cm
marks, meter sticks or tape, chair, long blank wall space.
1. Create a 2 m long strip of paper and place long lines every 5
cm. Place this paper on a wall.
2. Use different heights as the starting point of the coffee filter.
3. Position the camera to face the strip of paper. The camera
should be placed so it can focus on the entire length of the
measuring tape.
4. Stand on a chair and hold the coffee cup at the 0 cm mark.
5. Begin recording the video, drop the coffee filter.
6. Stop recording when the filter reaches the last mark.
(Ideally it should be 2 m)
7. Repeat steps 4-6 but change the starting position by 5 cm
each time to decrease the height. Repeat this with 4 different
heights.
Results
a) Using the video record the time taken for the filter to reach the end of
the paper in a table.
b) Record the distance travelled by the coffee filter and calculate the
speed by analyzing the frames. (Your teacher can help you with that).
c) Calculate the initial gravitational potential energy using the height of
each descend.
d) Calculate the final kinetic energy using the speed from your video
analysis.
e) Compare the two energies. Are they the same? If there are differences,
what might have caused it?
120

Lesson 3.2: Conservation of Energy
Lesson 3.2 Review
1
You shoot a 2.0 kg basketball toward the hoop with an initial total
energy of 500 J. (Neglect air friction on the ball.)
a) When the ball reaches the top of its arc, what is its total energy?
b) When the ball is just about to hit the rim, what is its total energy?
c) What principle are you demonstrating?
2
A roller-coaster cart,
initially stationary at
position a, is given
a gentler push to the
right. As it glides along
the track, it passes
through positions b, c,
and d. Assume there is
no friction.
10 m
a
b
c
d
5 m
a) At which of the four positions is gravitational potential energy
greatest?
b) At which position is the cart moving fastest?
c) At which postion(s) is/are potential and kinetic energy equal?
3
4
5
A ball is dropped from two heights, one four times as high as the
other. What is the ratio of the speeds in the two cases just before the
ball hits the ground? (Assume that air resistance can be ignored.)
A 20 kg chair has 250 J of potential energy relative to the ground.
If the chair is dropped from its position, what is its speed when it
strikes the ground?
A 60 kg diver drops from a ledge that is
15 m above the water. What is the speed
of the diver upon hitting the water?
15m
121

Lesson 3.3
Power and Efficiency
When comparing and contrasting a car engine, the term horsepower is
used extensively. The word seems to be an odd choice since we don't use
it when we calculate power of an object ourselves. Even the light bulbs
use the term Watts. Horsepower was first an idea developed by Thomas
Savery in 1702. People relied on horses as their means of transport and
labor.In his work, Savery, compared the work done by a steam engine to
that of horses. This idea was later investigated and used by James Watt to
sell his own steam engines.
Watt measured how long it takes a pony to
turn a grindstone in a mill. He multiplied
the distance the pony walked by it's mass
and divided it by the time it took. Since this
investigation was done using ponies, Watt,
made an assumption that a horse must be
twice as powerful. Today we know that a
horse's power is actually only 0.7 hp.
Figure 3.25 Power of 1
horse = 0.7 hp
Learning Outcomes
P1108.1 Define power as the rate
of doing work or the rate of energy
transferred and solve problems using
P = W/t = E/t
P1108.2 Explain that power is
associated to the transfer of energy
between different parts of a system and
it is measured in watts (W)
P1108.3 Explain that in all energy
transfers some energy is dissipated
(wasted) and can no longer be stored
usefully
P1108.4 Calculate the efficiency
of a system as: Efficiency = Energy
transferred usefully / Total input energy
Key Vocabulary
horsepower (hp)
power
watt (W)
efficiency
sankey diagram
122

Lesson 3.3: Power and Efficiency
Power
The words energy and power are often used
interchangeably, but the true meanings are
different. Energy is the ability to do physical work
and is measured in joules.
Consider that an amount of work, can be done
either slowly or quickly. For example, imagine
taking a full bag of groceries upstairs. You can
walk up the stairs slowly in three minutes or run
up in 30 seconds. How are the two different?
Discussion question
What makes a person
energetic?
What makes a person
powerful? Are the
criteria for both the
same or different?
The total work done is the same in both scenarios but the power required is
different. Power is the rate at which work is done or the rate at which energy
is transferred. Work is measured in joules and power is measured in joules
per second. A power of one joule per second (J/s) is one watt (W). The watt
is named in honor of James Watt, a Scottish engineer who developed the
first practical steam engine and thereby provided the power for the industrial
revolution.
(3.5)
Power
P
E
power (W)
energy change (J)
W
t
work done (J)
time duration (s)
Power is the indication of the level
of "effort" required to perform a
given amount of work. Lifting a 1
kg ball by 1 m takes a minimum of
9.8 J of work (Figure 3.26). Doing
this work in 60 s requires 0.16 W;
approximately the power output of
a small mouse. Doing the same 9.8
J of work in 1 s requires 9.8 W of
power, which is 60 times greater.
The work is the same
but the power is different.
1 kg
Time
1 kg
9.8 J in 1 s 9.8 J in 60 s
9.8 W
1 m
0.16 W
Time
1 m
Figure 3.26 Example of power when
lifting a ball
Work done is independent of time taken.
Power depends on how fast or slow the work is done.
123

Unit 3: Work, Energy and Power
3.3a
Inquiry Question
Materials
How powerful are you?
What is the power output of your muscles when doing an arm
curl?
500 g mass, measuring tape or ruler, stopwatch
Laboratory procedure
1. Measure the length of your arm with the
help of a partner, as shown in Figure 3.27.
2. Calculate the work done in lifting a
mass of 500g to the length of your arm.
(Hint: You need the formula W = F ×
d. Remember to convert the mass in to
weight.) This is the amount of energy spent
during one arm curl.
3. Now with the help of a partner and a
stop watch, count how many arm curls you
can do in 60 seconds.
4. Divide the number of arm curls by 60 s
to get the time for one arm curl.
5. Multiply the time for one arm curl by the
energy spend during one arm curl.
6. Repeat the experiment by using different
masses.
Questions
a) How accurate do you think your answer is?
Starting position
Ending position
b) Suggest 3 things you can do to improve your answer.
c) Suggest 2 ways that you can increase the power output of your
muscles.
d) Can you think of another method to calculate a person’s power?
Measure the
complete
length of arm
Figure 3.27 Starting and
ending positions of the arm
curl
124

Lesson 3.3: Power and Efficiency
How much energy does an incandescent light bulb rated at 100 W use in one
hour and in one full day of 24 hours?
Asked
Example problem
6
energy
Eused by the light bulb.
Given
power of the light bulb P=100 W
time that bulb is on t= 1 hr
time that bulb is on t= 24 hr
Relationships
power
P = E t
Solution
Time is must be expressed in seconds, but we are given it in hours. Convert
time to seconds:
⎛ 60min ⎞⎛ 60s ⎞
∆ t = 1hr⎜ ⎟⎜ ⎟ = 3,600s
⎝ 1hr ⎠⎝1min
⎠
Solve for E by multiplying the power equation by the elapsed time ∆t:
∆E
P × ∆ t = × ∆t ⇒ ∆ E = P∆t
∆t
∆ E = P∆ t = (100W)(3,600s)=360,000J
To see how much energy is consumed in 24 hours by the same bulb, we
need to simply multiply the time from the first part by 24.
3,600s × 24hr
∆ t = = 86,400s
1hr
∆ E = P∆ t = (100W)(86,400s)=8,640,000J
A single 100W light bulb uses 8.64 million joules of energy in one day.
125

Unit 3: Work, Energy and Power
Power in everyday use
When you think of how "strong" something is
you are often thinking about how much power
it produces. Many appliances and cars provide
power in units of horsepower (hp), which is
equal to 746 W.
The electric motor in a typical washing
machine is 1/2 hp or 373 W, about the same as
the power output of a very fit athlete during a
competition. The motor in an electric saw is
about 1.5 hp. A small car engine operates at
around 100 hp. A blue whale can develop 500
hp, or 370,000 W. It takes 0.13 hp to power a
standard 100 W bulb. Some more examples are
shown in Figure 3.28.
Think of all the appliances found in your
house. How often are they used? and for
how long? Can we cut down our daily
consumption? You can use Table 3.1 to help.
Discussion question
How many horses
would it take to power
your house?
23 W
75,000 W
746 W
Figure 3.28 Everyday
examples of power
Table 3.1 Power consumption of everyday appliances
Appliance
Power consumption (hp) Power consumption (W)
Air conditioner 4.7 3,500
Vacuum cleaner 1.9 1,400
LCD/LED TV 0.13 91.5
Microwave oven 1.6 1,200
Desktop PC 0.4 300
Phone charger
Washing machine
iron
hair dryer
Refrigerator
0.003-0.008 2-6
1.3 1000
2 1,500
2 1,500
0.3 200
126

Transmission of power
Lesson 3.3: Power and Efficiency
Discuss how a machine can have the same power at the input and output but
different speeds and forces. Start with lever and show the work done is the
same on both input and output sides. Then divide by time to get power out =
power in for an ideal machine. This developes the framework to appreciate
efficiency.
127

Unit 3: Work, Energy and Power
Efficiency
Imagine dropping a beach ball from the top of a
building (Figure 3.29). The speed would agree very
well at first with the formula derived from energy
conservation. However, air friction soon increases
so much that the ball cannot fall any faster. The
efficiency of a process describes how well the process
transforms input energy into output energy. The
measured speed of the beach ball is slower than the
theoretical speed because the efficiency of converting
potential energy to kinetic energy is decreased (to zero)
by the effect of air friction.
You can easily see efficiency by bouncing a rubber ball off the floor. The
ball never bounces back up to the same point that it started from. This is
because each bounce converts elastic energy into kinetic energy with less
than 100% eficiency. The efficiency of a system is the ratio of energy output
divided by energy input (equation 3.6)
(3.6)
128
Efficiency
E
η =
E
out
in
η
E out
E in
How fast
will the
beach ball
fall?
How about
the bowling
ball?
Figure 3.29
Dropping different
balls from a height
efficiency
output energy of a system (J)
input energy of a system (J)
Since work and energy are directly related, the definition of efficiency can
also be expressed as the ratio of the work performed by a system to the work
input to the system.
2 joules of light
98 joules of heat
100 joules
electrical energy
2 joules of light
21 joules of heat
23 joules
electrical energy
Figure 3.30 Comparisson between
incandescent and flourescent bulb
A very common inefficient system
is the incandescent light bulb. The
incandescent bulb takes an input of
100 J of electrical energy and only
provides an output of 2 J of light
energy. The efficiency is only 2%.
The other 98 J are are wasted as
heat energy. A flourescent bulb has
a much higher efficiency of 9%. An
input of 23 J of electrical energy
and provides the same 2 J output of
light energy (Figure 3.30).

Lesson 3.3: Power and Efficiency
Example problem
7
A man does 2,000 J of work when pushing a box up a ramp. If 800 J of
energy was spent overcoming friction,
a) How much useful work did he do?
b) How efficient was the process? State efficiency as a percentage.
Asked
Given
Relationships
Solution
useful work done.
efficiency
potential energy gained
input energy E in
=2,000 J
energy spent on friction E f
=800 J
efficiency
E
η =
E
a) First we need to calculate the useful work
done, which is also the output energy.
out
in
E in
=2,000 J
What is the efficiency of
the system?
b) Calculating efficiency:
E = E − E
out in f
= 2,000J − 800J
= 1,200J
Converting it into a percentage:
0.6× 100 = 60%
E
out
η =
η =
E
E
out
in
1,200J
2,000J
= 0.6
In some cases it is preferable to convert the efficiency in to a percentage.
It is easier to perceive that a system is 60 % efficient then a system’s
efficiency is 0.6.
129

Unit 3: Work, Energy and Power
Sankey diagrams
Energy chains give an outline of how the energy flows from one form to
another including the origin of the energy. Sankey diagrams also depict
the energy flow but they are more precise and represent actual quantities. The
width of the arrows is proportional to the flow quantities.
100 J of
Electrical
energy
2 J useful light
energy
98 J wasted
heat
Figure 3.31Sankey diagram for an
incandescent bulb
500 J of
Electrical
energy
150 J light energy out
100 J sound energy out
250 J wasted heat
Figure 3.32Sankey diagram for a TV
100 %
Fuel
energy
25% useful work
5% lost in friction
30% transferred to coolant
40% exhaust gas
Figure 3.33Sankey diagram for an
engine
130
Sankey diagrams are mainly used
when referring to efficiency. This
bulb takes in 100 J of electrical
energy and only produces 2 J of light
energy. 98 J of the remaining energy
are converted to heat energy(Figure
3.31). This is why incandescent
bulbs are very hot to touch and
replace as soon as it goes off. Notice
that arrows that represent wasted
energy diverge downwards.
Law of conservation of energy is
applied, the amount of energy that
goes in is the amount of energy that
comes out. However, all of the output
energy is not useful to us and is
thus considered as waste.A modern
television set takes in around 500
J of electrical energy(Figure 3.32).
In this scenario there are two useful
outputs, light and sound. This makes
a modern television set around 50%
efficient.
We don't have to only rely on joules
in Sankey diagrams. We can use
watts or even percentages. A typical
car engine only uses 25% of fuel
for traveling and accessories(Figure
3.33).The rest of the energy is wasted
or used to refrain the car from over
heating.

Lesson 3.3: Power and Efficiency
Example problem 8
Here is a sankey diagram representing the energy transfer of an ipod. Each
box in the grid represents 10 J of energy. Calculate the input energy, useful
output energy and wasted energy. Is energy conserved?
light energy
input
electrical
energy
sound energy
thermal
energy
Asked
input energy,
useful output energy
wasted energy
Solution
To calculate the input energy, we must count the boxes and
multiply it by 10 J.
There are 13 boxes and 13 × 10 J = 130 J
Input energy = 130 J
There are two useful energies: light and sound. Light energy is 1 box wide.
1 × 10 J=10 J
Sound energy is 3 boxes wide. 3 × 10 J = 30 J
Total useful output energy = 30 J + 10 J = 40 J
Wasted energy is thermal energy. Thermal energy is 9 boxes wide.
9 × 10 J = 90 J
Total output energy is: 90 J + 40 J = 130 J
Here we can see that input energy = total output energy. So, energy is
conserved!
131

Unit 3: Work, Energy and Power
3.3b
Inquiry Question
Efficiency of different balls
How does the efficiency of a ball depend on its temperature?
Materials
Laboratory procedure
measuring tape or ruler, balance, slow motion camera,
different balls, fridge, freezer, hot plate and a pan, gloves for
safe handling, infra-red thermometer.
1. Select one type of a ball (tennis ball, football
etc). Find out it's mass and record it on the
investigation sheet.
2. Place a measuring tape or ruler along an
empty wall. Make sure that the zero is aligned
with the ground.
3. Using the infra-red thermometer, find the
temperature of the ball.
4. With the help of a partner set up the camera
and begin recording.
5. Place the ball at a 1m mark and let go. Analyze the point on on the tape/
ruler where the ball bounces back to, by using the slow motion camera.
6. Repeat this experiment 3 times and calculate the average height of the
return.
7. Now place the ball in the fridge, for 30 minutes or more.
8. Repeat steps 2-5.
9. Repeat the experiment after placing the ball in the freezer for 30 mins
or more and then again by heating it in a pan for 5 minutes.
10. Practice caution by wearing gloves when the ball is too hot or too
cold.
11. Calculate the gravitational potential energy before the ball is
released and after.
12. Collect the data from different groups to add to your data table. Plot
a line graphs for each type of a ball with Efficiency on the x-axis and
temperature of the ball on the y-axis.
132

Lesson 3.3 Review
Lesson 3.3: Power and Efficiency
1 A 40 kg wheeled cart needs to be moved to the top of a platform
that is 1.0 m high.
a) How much power is required to pick up the cart and place it on
the platform in 3.0s?
b) How much power is required to roll it 6 m up a ramp, a process
taking 20s?
c) How much power is required to roll it 12 m up a shallower ramp,
a process that also takes 20s?
2 a) What are the advantages for a car with high horsepower?
b) What are the disadvantages for a car with high horsepower?
3 A man rides a bicycle that is connected to an electrical generator.
If he rides as hard as he can, his body can produce a mechanical
power of 500 W, but the generator is only 40% efficient at
converting mechanical energy into electrical energy.
a) How many 100 W incandescent light bulbs can he power?
b) How many 100-W-rated compact fluorescent light bulbs can he
power?
4 A fully charged cellphone battery contains 20,000 J of stored
energy. The cellphone uses 2 W of power.
a) How long will the battery last in seconds?
b) How long will the battery last in minutes?
c) How long will the battery last in hours?
5 When a falling object has reached terminal velocity, what is its
efficiency in converting potential energy to kinetic energy?
6 A boy walks up a 10 meter tall hill and rolls down on a skate
board. When he reaches the bottom, the boy is moving at 7 m/s.
What is the efficiency of the boy's skate board?
133

134
Unit 3
Summary
Lesson 3.1: Work Done and Energy
• Work is done when a force is applied on an object causing the object to
move a certain distance.
• Joule (J) or newton-meter (N m) is the unit for work.
• Energy and work are similar but not the same. Energy is the ability to do
work and work is the amount of energy that is actually used up.
• Kinetic energy is the energy in an object that is moving. Objects at rest
have 0 J of kinetic energy.
• Gravitational potential energy is the energy stored in an object that
is placed at a height. The energy is released when the object moves back
down. An object on the ground has 0 J of gravitational potential energy
• Elastic potential energy is the energy stored in an object that is
stretched of compressed. The energy is released when the material goes
back to its original shape. Only materials that can change shape can store
elastic potential energy, such as, rubber bands, springs, strings or muscles.
Lesson 3.2: Conservation of Energy
• Law of conservation of energy states that energy changes from one form
to another. Energy is not destroyed and it doesn’t disappear; most lost
energies have changed into thermal energy or sound energy.
• Energy flow diagrams are used to represent the flow of energy.
• Mechanical energy is the total energy in a system, it is usually the
sum of kinetic energy, gravitational potential energy and elastic potential
energy. Individually, each form of energy changes as the work is done but
mechanical energy always remains the same.
Lesson 3.2: Power and Efficiency
• Power is the rate at which work is done. The unit for power is watts (W),
sometimes, horsepower (hp) is also used.
• Efficiency is the ratio of the output energy to input energy. We can make
better judgement about the performance of a system by calculating its
efficiency. Efficiency is sometimes converted into percentages.
• Sankey diagrams are precise energy diagrams that represent input
and output energies. The width of the arrow in a sankey diagram is
proportional to the percentages of input and output. It also represents
wasted energy.

Lesson 3.3: Power and Efficiency
Scientist Spotlight
James Prescott Joule
Like everything in science, our understanding
of power, energy and efficiency has had many
contributors over the years. The earliest efforts and
research allowed other scientists and engineers to
build on and develop more efficient devices and
technologies.
The unit Joule is named after the physicst and
mathematician James Prescott Joule. Joule
was born in England in 1818 and discovered
the "Joules Law" in 1840. He discovered the
relationship between current, resistance and power.
His work also established that heat and mechanical
work are both forms of energy and it became the
foundation to the First Law of Thermodynamics.
Invention of the steam engine
It was the invention of the steam engine and the
drive to make it more and more efficient that shapes
our life today. The first steam engine was developed
by Thomas Savery in 1698 to pump water out of
flooded mines. Savery’s engine was very inefficient
and his ideas were improved by Thomas Newcomen
in 1712. The Newcomen steam engine was also
used to pump the water out of coal mines.
Figure 3.34 James
Prescott Joule
Figure 3.35 One
of the first steam
engines
James Watt
James Watt was a Scottish inventor and he
was asked to repair a Newcomen engine. Watt
discovered that the engine was extremely
inefficient. Over a period fo years, Watt improved
the design, creating a seperate condensing chamber
which helped in maintaining the temperature of the
steam engine. Watt publicized his steam engine by
comparing it's power to that of horses.
Figure 3.36 James
Watt
135

Unit 3: Assessment
Multiple choice questions
136
1 A large electric motor is used to lift a container off a ship. Which
of the following values are enough to allow the power of the motor
to be calculated.
2
4
5
a) the current used and the work done
b) the work done and the time taken
c) the force used and the distance moved
d) the mass of the container and the distance moved
A a constant force is applied to a frictionless car for 13 meters. The
car gains 91 J of energy. What is the minimum average force used?
a) 7 N
b) 3 N
c) 10 N
d) 16 N
3 Saeed and Nasir run up a hill in the same time. Saeed weighs 600
N and Nasir weighs 500 N. Which statement is true about the
power produced?
a) Saeed produces more power.
b) Nasir produces more power.
c) They both produce the same power.
d) It is impossible to tell who produces more power.
Marwan does 18 J of work to lift a 1 kg box at a constant speed. If
he drops it, how fast will the box be going when it hits the ground?
a) 1.8 m/s
b) 6 m/s
c) 16 m/s
d) 36 m/s
How much energy is stored in a spring with a spring constant of
500 N/m if it is compressed a distance of 0.4 m?
a) 20 J
b) 40 J
c) 80 J
d) 100 J

9
7
8
Unit 3: Assessment
6 How much energy does it take to accelerate a 90 kg object from
rest to 13 m/s?
a) 3,681 J
b) 6,943 J
c) 7,605 J
d) 9,810 J
A dock worker pushes a 50 kg crate up a 1-m-high, 3-m-long ramp.
Ignoring friction, how much work did he do?
a) 150 J
b) 490 J
c) 1,470 J
d) 1,960 J
Ahmed is standing on the top of a building 10 m high holding a 7
kg bowling ball. Mazin dug a 2-m-deep hole next to the base of the
building. What is the gravitational potential energy of the bowling
ball relative to the bottom of the hole?
a) 137.2 J
b) 548.8 J
c) 686.0 J
d) 823.2 J
Which of the following energy flow diagrams might describe the
path of the energy that powers the electric light in your classroom?
a) nuclear energy > thermal energy > light energy
b) mechanical energy > light energy > pressure energy
c) light energy > electrical energy > nuclear energy
d) chemical energy > electrical energy > light energy
10
A 15 kg ball is thrown straight upward with a speed of 20 m/s.
What is the maximum height the ball reaches?
a) 14.0 m
b) 19.8 m
c) 20.4 m
d) 40.8 m
137

Unit 3: Assessment
11
A 0.70 kg ball is placed on a vertical 200 N/m spring that is
compressed 40 cm. When the spring is released, how high above
its starting point will the ball go?
a) 0.40m
b) 2.3 m
c) 5.8 m
d) 80 m
12 For a typical car, approximately 65% of the energy in the fuel is
radiated away as heat, 13% is output as work in moving the car,
10% is spent overcoming friction, 7% is spent idling rather than
moving, and 5% runs accessories (e.g., the heater). What is the
efficiency of the typical car?
a) 13%
b) 20%
c) 23%
d) 30%
13 A 40 W lamp wastes 34 J of energy every second by heating its
surroundings.What is the efficiency of the lamp?
a) 0.15%
b) 15%
c) 18%
d) 85%
14 A 70 kg man who wants to climb up a 900 m cliff wonders what
would happen if he falls without using a safety rope. How fast
would he be traveling at the bottom when he hits the ground, if he
fell from the top of the cliff?
a) 13.6 m/s
b) 93.9 m/s
c) 132.8 m/s
d) 17,640 m/s
138

Unit 3: Assessment
Lesson 3.1: Work Done and Energy
15 How much work does it take to hold a dumbbell motionless over
your head for 10 s?
16 A car with its engine off moves on a horizontal level road. A
constant force of 530N opposes the motion of the car. The car
comes to rest after 84m. Calculate the work done on the car by the
opposing force.
17
18
String and nylon thread will stretch when pulled with a moderate
force, but only a small amount. If you apply the same force to a
spring and it stretches much further than the string and thread, how
do the spring constants of the string and thread compare to the
spring?
Two brothers in an apartment are arguing over the potential energy
of a 10 kg TV that hangs on the wall. The first person claims that
the television is 2 m from the floor so its potential energy is 10 kg
× 9.8 N/kg × 2 m = 196 J. The other claims that since they are on
the second floor, the TV is 12 m above the ground so the potential
energy is 10 kg × ×9.8 N/kg × 12 m =1,176 J. Who is right or are
they both right? Explain.
19 You stand on roller skates facing a wall. You push against the wall
and you move away. Discuss whether the force exerted by the wall
on you performed any work.
20 What is the elastic potential energy of a rubber band with a spring
constant of 25.0 N/m if it is stretched by 10.0 cm from its original
length?
21 What is the kinetic energy of a 6 kg bird moving at a speed of 15
m/s?
22
A mobile that weighs 28 N is
hanging 2 m below a ceiling
that is 5 m high. What is its
potential energy with respect
to the floor, the ceiling, and a
point at the same height as the
mobile?
2 m
mg = 28 N
5 m
139

Unit 3: Assessment
23
A ball with a mass of 150 g
rolls due north along the deck
of an ocean liner at a speed of
2.0 m/s. The ocean liner is also
moving north, with a speed of
2 m/s 10 m/s
10.0 m/s relative to a nearby
island.
a) What is the kinetic energy of the ball as measured from the
reference frame of the ocean liner?
b) What is the kinetic energy of the ball as measured from the
reference frame of the island?
Lesson 3.2: Conservation of Energy
24 According to physics, energy can never be created or destroyed
and the energy content of the universe is constant. So why are
people worried about “conserving energy lest we run out”?
25 A roller coaster car begins at rest at the top of the first hill.
a) Draw a sketch of a roller coaster with a second hill where the
roller coaster cannot reach the top.
b) Draw a sketch of a different roller coaster with a second hill that
the roller coaster can get over.
26 A bowling ball and a tennis ball are dropped separately in such
a way that both have the same kinetic energy when they hit the
ground. Were they dropped from the same height or a different
height? If the latter, which one was dropped from a higher point?
27 A 1.0 kg brick falls off a ledge of height 44 m and lands on the
ground 3.0 s later.
a) Find the final velocity of the brick using the equations of
motion.
b) Find the final velocity of the brick using conservation of energy.
28 A frictionless roller coaster with a mass of 200 kg starts 15 m
above the ground with a speed of 10 m/s. When it is 5 m above the
ground what is its speed?
140

Unit 3: Assessment
29 Karim weighs 80 kg, and eats a 1,000 J candy bar. If his body
perfectly transforms the energy in the chocolate into kinetic energy,
what is the fastest he can run?
30 A block of mass 3 kg slides on a rough horizontal surgace. The
initial speed of the block is 6 m/s. It is brought to rest after
travelling a distance of 15 m. Calculate the frictional force.
31 A 60 kg diver jumps off a diving board upward with an initial
velocity of 5 m/s. The diving board is 10 m higher than the water.
What is the diver’s speed when just entering the water after the
dive?
Lesson 3.3: Power and Efficiency
32 Is it possible to have very little power but use a lot of energy?
How?
33 Estimate the minimum power required to lift a mass of 60 kg up a
vertical distance of 14 m in 5 s.
34 A small electric motor produces a force of 5 N that moves a
remote-control car 5 m every second. How much power does the
motor produce? Give your answer in watts and horsepower.
35 What is the maximum height a 5 hp engine could push a 10 kg box
in 5s? Assume you could attach the engine to an ideal mechanical
device with perfect (100% efficient) transfer of energy.
36 A boy, who is 60 kg, falls from a height of 20 m on a strange
plantet that has a large amount of air resistance and a gravity equal
to Earth’s. When he reaches the ground, he is traveling 2m/s.
a) How efficient was his jump at converting potential to kinetic
energy?
b) How much energy do his surroundings gain as he jumps?
37 Consider a rubber ball whose bounce has an efficiency of 80%.
That means 80% of the kinetic energy before the bounce remains
kinetic energy after the bounce. (The rest of the energy is
converted to thermal energy.)
a) If the ball drops from a height of 5 m, how high does it bounce
back on the first bounce?
b) How high does the ball bounce on the second, third, and fourth
bounces?
141

Unit 3: Assessment
38 Here is a sankey diagram for a power plant producing electrical
energy.
Electrical
Chemical
energy
5000 J
Energy transferred
to coolant
Thermal
energy
a) How much electrical energy is produced?
b) How much energy is used in the coolant?
c) How much thermal energy is wasted as gases?
d) What is the efficiency of the power station.
39 Suppose you have a solar energy conversion system with a sunlight
collecting area of 10 m 2 . On a cloudless day sunlight has an
intensity of about 600 W/m 2 .
a) How much energy is collected in 1 hr?
b) A single electric light bulb uses 25 W of power. How long could
the collected energy keep the bulb lit?
c) A very efficient cabin uses about 400 W on average over 24
hr. If the solar conversion to electricity is 15% efficient, can this
collector supply the average power draw for the cabin?
40 A 1,500 kg car begins at rest. A force of 2,000 N is applied to the
car for a 20 m stretch in order to accelerate it. At the end of the 20
m, the car is going 5 m/s, and the road gains 21,250 J of thermal
energy.
a) Is energy conserved?
b) Why does the road gain thermal energy?
142

Unit 3: Assessment
41 The top speed of a car whose engine is delivering 300kW of power
is 280 km/h. Calculate the value of the resistance force on the car
when it is traveling at its top speed on a level road.
42 The motor of an elevator develops power at a rate of 2500W.
a) Calculate the speed that a 1200kg load is being raised at.
b) In practice it is found that the load is lifted more slowly than our
theoretical value. Suggest reasons why this is so.
43 Ziad, whose mass is 60 kg, is traveling on a bike at 15 m/s at the
top of a 3.0 m hill. Ziad continues down this hill without pedaling.
Assume friction is negligible.
a) What energy transformation is occurring as he travels down the
hill?
b) How fast is he traveling when he reaches the bottom of the hill?
44 A 0.3 kg battery operated toy train moves with constant velocity
0.30 m/s along a level track. The power of the motor in the train is
2.5 W and the total force opposing the motion of the train is 4 N
Determine the efficiency of the train’s motor.
Research problem
Industrial plants in Qatar
Research ways in which dissipated energy (by heating) is minimized, used or
dispersed, in Qatar industrial plants such as power stations.
• Choose an industrial plant.
• Research it's functions.
• How much heat energy is usually dissipated in such processes?
• How much heat energy is dissipated in this particular industrial plant?
• Is there a method used to minimize the heat dissipated?
• Is the heat produced from the process used in another process?
• Is it dispersed throughout the plant to avoid over heating?
• What do your findings conclude about the efficiency of the plant?
143