Chapter 5 Notes page 174-219
Energy and Motion
5.1 Analyzing and Measuring Motion page 176
Distance, displacement, and position are some of the
most fundamental quantities of mechanics.
The definitions are precise and many other
quantities depend on the correct
definitions of these basic quantities.
Scalars and Vectors
Scalar quantities or Scalars: Quantities that
describe magnitude (size or amount) but not
direction. Ex: speed, distance and time.
Vector quantities or vectors: Quantities that do
include direction as well as magnitude. Ex: velocity,
displacement, and position.
 To distinguish between these quantities, symbols for
vectors are written with arrows above them while
symbols for scalars are not.
 Example the symbol for velocity is
for speed is v .
v
and the symbol
1
Defining Distance, Displacement, and Position
 Distance is NOT simply the magnitude of displacement.
 Distance is dependent on the path but displacement is
not.
 Displacement depends only on the initial and final
positions.
 For example, consider a runner who is racing on a
oval track. If finish line is the same as the
starting line, then the runners’ displacement for
the race is zero although the distance that he/she
ran might be 1.0 km.
 Displacement has not been fully reported unless both the
magnitude and direction have been includes.
 Symbol for distance ∆d. Is this a scalar or vector
quantity? Scalar
 The ∆ in the case of distance means the change in the
location of an object when it moves from one point to
another.
 Symbol for displacement ∆ d . Is this a scalar or vector
quantity? Vector
 The ∆ in the case of displacement means the change in
the position of an object when it is displaced.
2
 Position infers the existence of a frame of reference.
Position cannot be expressed without a reference point
and a definition of direction.
 An x-y coordinate system must be defined in order to
describe a position.
 Symbol for position d . Is this a scalar or vector quantity?
Vector

See Figure 5.3 page 177 to see the relationship between
displacement vectors and position vectors.
Displacement
∆d =
d2
-
d1
∆ d is displacement
d 2 is the final or ending position
d 1 is the initial or starting position
The SI unit for position and displacement in
metres, m.
Where
 See example in page 177 Figure 5.4
Calculating Distance and displacement
 Even when working on one dimension, distance is
not the same as the magnitude of the displacement.
 When an object goes back and forth along the same
line, the entire path is included in distance.
3
 Once again, displacement depends only on the
starting and ending points.
 Calculation of displacement in one dimension
involves only addition and subtraction.
 The direction of the vectors will be indicated by
compass directions (N,S,E or W) or by positive
and negative signs (+ or -).
 The direction “west” is equivalent to the
negative of “east”.
 So, the displacement has not been properly reported
unless the sign (+ or -) has been defined and is
included in the statement of the answer.
 Although a plus sign is not required on a positive
number, it is often helpful to use plus signs when
working with vectors in one dimension.
 Vectors in one dimension: up, down, right, left.
 Vectors in two dimensions: upward and westward,
eastward and downward, etc
 See Model problem 1 page 178. (Make on overhead)
 When you subtract a vector, you point it in the
opposite direction but keep the length the same.
 Do BLM 5-1 Interpreting Vectors
 Do Practice Problems 1 to 9 page 181
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Speed and Velocity
 The relationship between speed and velocity is the
same as the relationship between distance and
displacement.
 You cannot assume that speed is the same as the
magnitude of velocity.
 Speed is the distance travelled by an object during a
given time interval divided by the time interval
 Velocity is the displacement of an object during a
time interval divided by the time interval.
 Velocity depends only on the initial and final
positions but speed depends on the path.
 The time interval has the same meaning for both
speed and velocity.
 The relationship between time interval and time is
similar to the difference between displacement and
position.
 Time (t) and position are specific points.
 Time interval (∆t) and displacement are a difference
between those two points.
 Reporting direction in compass directions can be
very confusing. Just remember to point in the
direction of the first symbol then rotate the number
of degrees specified toward the second direction.
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Velocity
Speed
d
v ave =
t
Where v ave is average speed in metres per
second,m/s.
d is distance in meters, m
t is the time interval in seconds, s.
v ave 
d
t
or
v ave 
d 2  d1
t2  t1
where v ave is average velocity in
meters per second,m/s.
∆ d is the displacement in meters,m.
d 2 is the final position in metres, m.
d 1 is the initial position in metres,m.
∆t is the time interval in seconds,s.
t2 is the final time in seconds, s.
t1is the initial time in seconds,s.
 See example on page 182183
 See Model Problem 2 page 183
 Do practice Problems 11 to 22 page 184 – 185
 Do Find out Activity Measuring Velocity in One
dimension page 186
Graphing Velocity
 Examine Figure 5.7 page 187and analyse how the
motion of the sprinters matches the graphs below
them.
 Uniform motion: motion with no change in velocity.
 Since velocity is the rate of change of position, the
velocity is the slope of the position versus time graph.
 Slope =
rise
run
6
 Slope =
d
t
d
t

v
=

v
= slope
 See example on page 188
 Don’t assume that the point (0,0 s, 0,0m) is a data
point but, unless specifically stated in the data, the
origin cannot be considered a data point.
 Line of best fit: leave an equal number of points
above and below the line.
 When you calculate the slope of the line, do not use
any of the actual data points because most of them do
not lie directly on the line.
 For most accurate calculation, choose two points on
the line that are near the opposite ends of the line.
 Calculate the slope from those points.
 See example page 189.
 Do Find out Activity Graphing Position-Time Data
page 190.
 Do worksheets package
7
Defining Acceleration
Acceleration: A change in the velocity during a time
interval. Is Acceleration a scalar or Vector quantity?
Vector
Calculation Acceleration
Acceleration
a ave 
d
t
or
a ave 
Unit Analysis
v 2  v1
t2  t1
a ave 
Where a ave is average acceleration in
d
t
m
m
 s
2
s
s
Meters par second squared, m/s2
∆ v is the change in velocity in meters per
m m s
 
s2 s 1
second, m/s.
v1 is the initial velocity in meters per second, m/s

m 1

s s

m
s2
v2 is the final velocity in meters per second, m/s
t2 is the final time in seconds, s
t1 is the initial time in seconds, s.
The direction of acceleration is not necessarily the same
as velocity but is the direction of the change in velocity.
You can use the concept of force as
a “push” to determine the direction
of the acceleration. It is the
direction that you would have to
push on the object to cause the
observed change in velocity.
See diagram page 191
8
When solving problems, the sign – positive or negative –
of the answer will tell you the correct direction of the
acceleration.
Look at Model problem 3 page 192
Do Practice Problems 23 to 31 page 192 193
Graphing Accelerated Motion
 The slope of a position versus time graph is the
velocity. When the slope is changing, the velocity is
changing.
 Acceleration is a change in velocity. Thus a curved
position versus time graph is a clear indication of
acceleration. See Figure 5.12 page 193.
 The slope of a velocity versus time graph is the
acceleration.
 If the velocity versus time graph is a straight line,
then the acceleration is constant. See Figure 5-13 A
page 194.
 If the velocity versus time graph is a curve, then the
acceleration is changing. See Figure 5-13 B and C
page 194
 Motion with a constant velocity is called uniform
motion,
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 Motion with a constant acceleration is called
uniformly accelerated motion or non-uniform
motion.
 In the absence of air friction, an object falling under
the influence of gravity is uniformly accelerated
motion.
 Do Check Your Understanding questions 1to 9
5.2 Energy of Motion
The energy transformation involved to produce all motion
is due to a force, whether provided by gravity or by
applied force.
Energy of Motion = Kinetic Energy
Calculating Kinetic Energy
Ek 
1 2
mv
2
where Ek is the kinetic energy in Joules (J)
m is the mass of the object in kilograms (kg)
v is the speed in meters par second (m/s)
 Joule = (kg) ( m )(
s
m
)
s
= Kg ●
m2
s2
 See Model problem 4 page 198
 Do Practise problems 32 to 40 page
200
 Do BLM 5-5 Kinetic Energy
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Work and Kinetic Energy
The relationship between kinetic energy and work is
often studied using the first law of thermodynamics. It
suggests that work done (joules) to make an object move
from rest is equal to its kinetic energy (joule) once it is in
motion.
Some work must always be done
against friction. Thus some
energy goes into heat.
Do Find out Activity Driving
Safely page 201.
Do Check your Understanding questions 1 to 8 page
204.
5.3 Potential Energy
Potential energy is often described as the energy stored
in a substance or object due to its position or condition.
An example of condition is the compression of a
spring.
Form of Potential Energy
1. Elastic Potential Energy
An object is elastic if it always
returns to its original form.

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Elastic potential energy: Energy stored in an elastic
object when work is done to distort the shape of the
object.
2. Chemical Potential Energy
Does gasoline contains potential energy?
Chemical potential energy: energy stored in the
bonds of chemical compounds which is released when
bonds in a molecule break or are rearranged.
Chemical potential energy is the difference in the
potential energy of reactants and products. See Figure
5.19 page 206.
 Some chemical reactions release energy when they
Proceed (exothermic)
 Some chemical reactions require an input of energy
in order to proceed. (endothermic)
 Nearly all chemical reactions that form compounds
from their elements release energy when they
proceed.
3. Nuclear Potential Energy
The energy stored in the bonds between
protons and neutrons in the nuclei of atoms.
electron
neutron
Fission : When the nucleus of an atom splits
into smaller nuclei. See Figure 5.21
proton
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Chain reaction: the process continues
The nuclear potential energy that is released when the
large nuclei fissioned is transformed into thermal energy.
This thermal energy in nuclear reactors converts water into
the steam that drives an electric generator.
4. Graviational Potential Energy
Gravitational potential energy is stored as a result of an
object’s position (height above surface). See Figure 5.22
Potential energy exists in many objects due to the
potential effect of gravity on the object.
Potential energy is a property of a system –like the Earth
and a mass above the Earth’s surface.
Explaining Gravity
Gravity is a property of anything that has mass.
Gravitational potential energy depends
only how far an objects is lifted vertically.
Objects fall straight down (neglecting
friction).
Acceleration due to gravity: the acceleration with
which all objects near Earth’s surface would fall if there
were no air friction; approximate value is 9.81 m/s2.
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Calculating Gravitational Potential Energy
 Mass and weight are not the same.
 Masse affects the weight
 Mass never change.
 Weight is the force of gravity acting on a mass
Weight
Fg = mg
Where Fg is used to represent weight and the units are newtons (N)
m is the mass in kilograms (kg)
g is the acceleration due to gravity in meters per
second squared (kg ●m/s2)
Whether using ma or mg to calculate force, both multiply
mass times acceleration
The direction of the motion must be parallel to the
direction of the force.
If you move the object horizontally while lifting it, the
horizontal motion does not contribute to the work done
against gravity. Therefore, you do not include horizontal
distance in your calculation. See Figure 5.23
When all of the work done on an object give the object gravitational
potential energy, the amount of work done is equal to the amount of
gravitational potential energy gained by the object or
W = ∆Eg
14
Formula for gravitational potential energy
If : W = F∆d
So W= Fg ∆h
W = mg∆h
Eg = mg∆h
Gravitational Potential Energy
Eg = mg∆h
Where Eg is the gravitational potential energy in joules (J)
m is mass in kilograms (kg)
g is the acceleration due to gravity in meters per second squared
(m/s2)
∆h is the height in meters (m)









See Model problem 5 page 210
Do Practice Problems page 212
See BLM 5-6
Do BLM 5-7
Do Investigation 5-B Gravitational
Potential Energy and Work page
213
Do Investigation 5-C page 215
Do Check Your understanding page 216 questions
1to 9
Do chapter at glance page 217 questions a to 0
Do chapter review page 218 questions 1 to 20 and
21 to 30
Chapter test on __________________________
15
Chapter 6 Notes page 220-245
Energy Conversion and Efficiency
6.1 Efficiency of Energy Conversions
What form of energy nearly always accompanies energy
transformations? See Figure 6.1. Heat is a by-product of
most energy transformation.
Efficiency and the Second Law of Thermodynamics
Second Law of Thermodynamics
“No process can be 100 percent efficient. Some energy
will always remain in the form of thermal energy.
All machines convert one form of energy into another
form in order to accomplish a specific task.
Useful energy: Energy that performs a task.
During any process, some energy is always converted
into a form that is not useful. This energy is often said
to be “wasted”.
Do BLM 6-1 Analyzing Machines for
Efficiency (Together with the class)
Calculating Efficiency
Efficiency = useful output energy × 100%
total input energy
Efficiency is a ratio so it has no units.
The output and input energies must be in the
same units so they will cancel.
16
If for example, a system is 30 percent efficient (i.e., has a
useful energy output of 30 percent), this means that 70
percent of the energy going into the system is wasted.
Simple systems
 Study Figure 6.3 Energy
transformation in a pendulum
 Look at Model Problem 1 page 225226
 Do Practice Problems page 227
 Do BLM 6-2 Calculating Efficiency
 Do Check Your Understanding page
231 questions 1 to 5 and 7
6.2 Energy Efficiency and the Environment
Because no system is 100 percent efficient all energy
conversions result in an unavoidable waste of energy as
heat (thermal energy).
This wasted energy is often referred to as “thermal
pollution”.
Installing technology to capture the neat normally given
off into the environment requires large capital
expenditures, but is environmentally beneficial and often
economically beneficial as well.
Efficiency of Some Common Technologies
17
1. Internal Combustion Engines
On average cars are only 20 percent efficient.
It’s mean that only 20 percent of the chemical potential
energy stored in the gasoline is transformed into the
mechanical kinetic energy.
Interior car heaters in vehicles provide an example of
using “waste” heat for the benefit of the occupants.
While they do not convert the heat to another form of
energy, car heaters do allow heat to from engine to be
used beneficially, and lowers the temperature of heated
air before it enters the environment.
The use of water to transfer the thermal energy from the
engine to the heater is also significant. Water provides
an excellent coolant due to its high heat capacity.
2. Electrical Devices




Light bulb : 5 % efficient
5 % of the electrical energy use is
converted into light energy
Compact fluorescent bulbs:20% efficient
See Figure 6.7
Generating Electrical Energy
18
Which electrical generating method –coal-burning,
nuclear, or hydro-electric generation of electrical energy
is more efficient because the energy-transformation
“route” is shorter and more direct?
Coal-burning and nuclear reactors 30% efficient
Hydro-electric 90 % efficient
 Do Investigation 6-B Energy Transformations in
Electrical Energy Generation page 235
Drawing Conclusions about Efficiency
After the thermal energy has turned a turbine or moved a
piston, the steam or hot gases still contain much of the
thermal energy. This thermal energy is usually lost to the
environment.
Efficiency of Energy Transformations in Living Plants
Photosynthesis: Process by which
plants use light energy to produce
food in the form of carbohydrates.
Photosynthesis is very inefficient (1
%) in terms of energy conversion, it
is the only process that produces
this specific conversion, and this
conversion is necessary for nearly all
life on Earth to exist.
In case of photosynthesis the total input energy is all the
light energy that is converted into chemical potential
energy.
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Saving Energy
Cost effectiveness is probably the greatest challenge to
innovative techniques and processes that conserve
energy.
Cogeneration
Method of conserving energy by using “waste” heat from
a thermoelectric-generating system to heat a building.
The system use 80 percent of the input energy for both
electrical energy and space heating.
However, thermal energy cannot be transported over long
distance.
 Do Check Your Understanding page
242 questions 1 to 6
 Do Chapter at a glance page 243
 Do BLM 6-6 (Word splash)
Chapter 6 Review page 244 -245
questions 1 to 12, 17 and 18 to 25
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Scientific Theories of Heat (page 150)
Each early theory of heat was an important step in the
development of scientific knowledge. Theories and
models are based on the knowledge of the time. Each
theory could explain the observation that “scientist” of
the time had made. It was only when new information
became available that a theory was modified or
discarded.
Early Theories of Heat (page 150)
What was the theory of the
1. Greek philosopher Empedocles: All matter consisted
of some combination of four elements: earth, air, fire,
and water According to this theory, many objects
contained fire. When these objects burned, the fire
was released (Figure 4.12)
When: (492 –435 B.C.E.)
2. Phlogiston: Substances that could burn contained an
invisible fluid. Scientist called this fluid phlogiston. It
was believed that the phlogiston flowed out of an
object when the object burned.
When: Early 1700s
3. Caloric: Caloric – or heat – was a massless fluid that
was found in all substance. Caloric could not be
created or destroyed, but could flow from one
substance to another. The theory stated that caloric
always flow from warmer objects to cooler objects. Unit
of caloric – the calorie. 1 cal is the quantity of caloric
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that would increase the temperature of 1 g of water by
1° C.
When: Late 1700s
Modern Theories of Heat (page 151-153)Benjamin
Thompson (Count Rumford’s) was the first person to
reveal flaws in the caloric theory. He noticed that when
a hole was bored in metal to make
cannon, the tools, the metal, and the
metal shavings became very hot. Since
none of the objects had been hot before
the boring process, what could be the
source of the caloric, or heat?
1. Rumford Hypothesis: There is no
substance such as caloric. Instead, he
hypothesizes that some of the mechanical energy used
to bore the holes was converted into heat. He was
saying that heat is equivalent to energy.
When: 1798
2. Julius Robert Mayer : Found evidence supporting
the relationship between energy and heat. Mayer
was one of the first scientists to recognize that the
body uses oxygen to break down food and use it for
energy. He also reasoned that the same processes
that use oxygen to provide energy for the body must
also be providing heat. Therefore, heat is related to
energy.
When: 1840
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3. James Prescott Joules : Receives the credit for
discovering the mechanical equivalent to heat.
When: 1818-1889
Energy and Work (page 153-155)
 Work is always done by a force acting on an
object.
 The work done on an object changes the position or
condition of that object.
 More than one force can be acting on an object at the
same time but the work done by different forces is
reported separately.
 W = F • ∆d
Where W is the work in joules (J)
F is the force in newtons (N)
∆d is the distance in meters (m)
The GRASP (Given, Required, Analysis, Solution,
Paraphrase) Method for solving numerical problems.
(Page 153)




Do BLM 4-4 Using GRASP to solve Problems
See Model Problem 1 page 154
Do Practice Problems 1 to 9 in textbook
Do BLM 4-5 energy and Work Practice Problems
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1. Graphical Methods for Determining Work (page 155158)
 See Figure 4.17. This graph shows a constant force.
 The area of the rectangle equals the length times the
width.
A=l•W
 But on the graph the length is the Force and the width
is the distance.
 Substitute F for length and ∆d for width in the formula
for area.
A = F • ∆d so A = W
2. Graphs with Geometric Shapes
 See figure 4-18. This graph shows a changing force.
 The area under the curve determines the amount of
work done by a force.
 The shape under the curve is a triangle. The area of a
triangle is
A=½b•h
 On the graph the base is the distance and the height is
the force.
 Substitute d for the base and F for the height in the
formula.
A = ½ d • F so A = w
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3. Graphs with Non-uniform Shapes
 See figure 4.19. This graph show that the force starts
very small, but increases rapidly. Then it immediately
begins to fall to zero.
 You can calculate the work done by calculating the
work represented by each small square and then
counting the squares.
 See calculations page 156
 See Model Problem 2
 Do Practice Problems 10 and 11 page 157 –158
 Do BLM 4-6 Graphical Methods for Determining
work
Joule’s Method for Determining the Mechanical
Equivalent of Heat
 See Figure 4.20 Joule’s experiment to determine the
mechanical equivalent of heat.
 The unit of energy – the Joule
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What Exactly is “Heat?”
The work of Mayer and Joule led to the
law of conservation of energy. This law
states that energy cannot be created or
destroyed, but it can be converted from
one form to another.
The Kinetic-Molecular Theory of Heat
 Because particles are undergoing random motion,
they collide with each other and the walls of any
container. These collisions are the fundamental
step in the transfer of energy. See Figure 4.21
 Work and heat are closely related. When particles
collide, transferring thermal energy (heat), the
particles are doing microscopic work on each other.
 In a solid, the molecules do not move freely around
and away from each other. The molecules vibrate in
place. As the solid becomes warmer, the molecules
vibrate faster. See Figure 4.22
Heat and Thermal Energy
Define the following term:
1. Kinetic energy : Energy of motion
2. Kinetic-molecular energy : Theory stating that the
molecules of a gas are in constant random motion;
26
the energy associated with this motion is known as
thermal energy
3. Thermal energy : Energy related to the continual,
random motion of atoms and molecules
4. Heat : Transfer of thermal energy from one object to
another
5. Work : Transfer of mechanical energy from one
object to another
 When describing the interactions of a system with
its surroundings, work and heat are the two
methods by which energy enters or leaves a system.
Specific Heat Capacity
 Specific Heat capacity: amount of energy (J) to
increase the temperature of 1g of the substance by
1˚C.
 Symbol c
 Unit J/g˚C
 The specific heat capacity of a substance depends
on the interactions of the molecules of the
substance.
 Water molecule form relatively strong hydrogen
bonds with each other. Therefore, the kinetic energy
of individual molecules must be large in order to
break away from adjacent molecules.
 For water c = 4.186 J/g˚C
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Heat and Temperature
 While adding energy to a substance, some of the
energy goes into breaking interactions and into
rotational kinetic energy.
 These forms of energy do not contribute to
temperature. It is only the translational – straight
line – kinetic energy that contributes to
temperature
 Temperature: measure of the average kinetic
energy of the individual atoms or molecules in a
substance.
 Complete the activity on page 162 Heat versus
Temperature
The Laws of Thermodynamics
 Thermodynamics : field of physics that deals with
forces and motion involving heat – transfer of
thermal energy
First Law of Thermodynamics
Energy cannot be created or destroyed, but can
be transformed from one form to another or
transferred from one object to another.
Second Law of Thermodynamics
It is not possible for any process to remove
thermal energy from an energy source and convert
it entirely into work
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 Or no process can be 100 percent efficient. Some
energy will always remain in the form of thermal
energy (friction).
 Or thermal energy always spontaneously flows
from an object at a higher temperature to an
object at a lower temperature
Check your Understanding page 163. Answer questions
3,4,5,7,8,9,10
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