Unit B: Physics
Investigating the energy flow in technological systems
requires an understanding of motion, work and
energy
In this unit, you will learn about...

General Outcome #2: Explain and apply concepts used in
theoretical and practical measures of energy in mechanical
systems
◦ Define, compare and contrast scalar and vector quantities
◦ Describe displacement and velocity quantitatively
◦ Define acceleration quantitatively as a change in velocity during a
time interval (
)
◦ Explain that, in the absence of resistive forces, motion at constant
speed requires no energy input
◦ Recall, from previous studies, the operational definition for force as a
push or pull, and work as energy expended when the speed for an
object is increased or when an object is moved against the influence
of an opposing force
◦ Investigate and analyze one-dimensional scalar motion and work
done on an object or system using algebraic and graphical techniques
4.1 The Development of the Steam
Engine
Steam engine converts steam pressure
into mechanical motion.
 Take a look at page 144-147.
 Who was James Watt? What did he
improve and how?


Practice pg. 149
4.2 Scientific Theories of Heat

Three theories:
1) The Phlogiston Theory
2) The Caloric Theory
3) Count Rumford’s Hypothesis
5.1 Motion

Motion is everywhere and easy to
recognize, but it was not always easy to
describe. The early Greek philosophers
realized that motion involved an object
travelling a certain distance in a time
interval. However, they could not
describe motion because they did not
understand the idea of rate or how
something changes in a certain amount of
time
Uniform Motion

Reference point - the motion of an
object only if we compare the object’s
position to another point (eg. suppose
you’re floating on an air mattress in a
swimming pool; you may not realize you
are moving until you realize how far away
you have moved from the stairs where
you entered, the stairs are the reference
point
Uniform Motion
Motion – occurs when an imaginary line
joining the object to the reference point
changes in length or direction or both
 Uniform motion – describe an object
that is travelling at a constant rate of
motion in a straight line.

Uniform Motion

Many situations occur where an object
appears to have uniform motion, but this
type of motion is nearly impossible to
maintain for long periods. For example, a
car travels along a straight highway with the
cruise on at 100km/h, the car appears to
maintain a constant rate of motion, but
various forces act to slow the car down,
such as friction of the tires on the road and
wind resistance. Even on cruise control, the
car’s rate of motion fluctuates as the car
attempts to maintain that speed. It is almost
impossible to maintain motion in a perfectly
straight line in everyday situations.
Did you know??

In Japan, MAGLEV (short for magnetic
levitation) trains achieve uniform motion by
reducing friction. They do this by eliminating
wheels and tracks. Instead, the train hangs
down on either side of a guideway. Both the
train and the guideway contain very highpowered magnets. The two sets of magnets
repel each other, causing the train to rise
(levitate) above the guideway and move
forward. These trains can reach speeds of
about 400 km/h, much faster than the speed
of the fastest conventional trains!
Average Speed
 Average
speed – the distance
travelled in a specified time
◦ because uniform motion is difficult to
maintain, average speed is often used
Did you know??

Earth is travelling through space around
the Sun at an average speed of about
107 000 km/h !!
Significant Digits
Significant digits are the number of digits
used to communicate the accuracy
(degree of uncertainty) of the
measurement
 Rules for counting significant digits:
Digits 1 to 9 are significant. Trailing
zeros and middle zeros are significant.
Leading zeros are not significant.
 Eg) 320, 0.321, 0.000321, 3.21x103, 302
Sig digs: (3) (3)
(3)
(3)
(3)

How do you determine the significant
digits when adding or subtracting?
The calculated result will have the same
number of decimal places as the number
with the least amount of decimal
places.
Example: 2.2 kg + 8.267 kg + 12.32 kg
(1 dec) (3 dec)
(2 dec)
= 22.787 (need 1 dec)
= 22.8
(8 rounds the 7 to 8)

How do you determine the significant
digits when multiplying of dividing?
The calculated result will have the same
number of total digits as the number
with the least amount of digits.
Example: (3.87cm) (0.050cm) (208cm)
(3 dig)
(2 dig) (3 dig)
= 40.248 (need 2 dig)
= 40
(2 keeps the 0)

Using Formulas to Analyze Average
Speed

Use the following equation to determine
the average speed:
 where
 v = average speed (units: m/s)
 Δd = change in distance (units: m)
 Δt = change in time (units: s)
◦ therefore; you’re formula will look like:
Using Formulas to Analyze Average
Speed

Example:
◦ A person walks 10.0 m away from a stop sign
in 5.00 s. What is the average speed of the
person?
(always include formula!)
Next: what do we know??
di = 0 m (reference point) df = 10.0 m
ti = 0s
Make sure you include units!!
tf = 5.00 s
Using Formulas to Analyze Average
Speed
3.
Practice 10-22 pg. 184-185
Using Graphs to Analyze Average
Speed

For uniform motion, we can have two
different graphs to analyze data; they are
distance-time and speed-time
Plotting a Distance-Time Graph

Suppose a motorboat is travelling at a
uniform speed. The boat passes marker
buoys placed 5 m apart, which act as a
measuring scale. As the boat passes the
first marker, a person on shore starts to
record the distance the boat travels away
from the first marker every 2.0 s. These
are the measurements taken by the
person on shore.
Plotting a Distance-Time Graph

The line of best fit on the graph is a
straight line with a positive slope, this
indicates a direct linear relationship
between the distance travelled and the
time taken to travel the distance.
Therefore, as time increases the distance
travelled also increases hence the graph is
a straight line and the change in distance
travelled in relation to the time intervals
is constant, showing uniform motion.
Plotting a Distance-Time Graph

If the line of best fit were a curve of any
type, this would mean the object was
changing distance travelled in equal time
interval; in other words the boat would
be speeding up or slowing down.
Plotting a Distance-Time Graph

The slope of the graph tells you
something about the motion

You can find the slope using;
Plotting a Distance-Time Graph
Therefore the average speed, v, is 5.0 m/s
 A greater or steeper slope indicates a faster
speed and a lesser slope indicates a slower
speed!

Plotting a Distance-Time Graph

Let’s try this gizmo...
Plotting a Distance-Time Graph
c. The slope of the graph represents
average speed
Plotting a Distance-Time Graph
Line 1 – object with uniform motion
 Line 2 – object with slower uniform
motion than line 1
 Line 3 – uniform motion of 0 m/s; the
object is at rest (not moving)

Plotting a Distance-Time Graph

But what happens when the data is not
quite linear?

When data is not precisely linear, use a
line of best fit to determine the average
speed. The slope of the line of best fit
corresponds to the average speed.
Plotting a Speed-Time Graph

Suppose the motorboat mentioned
previously is travelling past the same
buoys. This time, a person on shore uses
a radar gun to record the speed of the
motorboat every 2.0 s. The data is shown
here:
Plotting a Speed-Time Graph

The line of best fit would be a straight
line indicating that as the time increases
the speed remains constant. This should
be the case since the boat has uniform
motion
Plotting a Speed-Time Graph

You can confirm this by calculating the
slope of the graph

A slope of 0.0 m/s2 confirms the motion
is uniform
Plotting a Speed-Time Graph

You can determine the distance the boat
travelled by calculating the area under the
line of the graph. The area under the line
of best fit of the speed-time graph is
determined by;
Plotting a Speed-Time Graph

Since the speed formula is v = Δd
Δt
the equation can be rearranged to
Δd = v(Δt), the area under the line is the
same as Δd. Thus, the area under the line
of a speed-time graph indicates the
distance travelled in the time period
Plotting a Speed-Time Graph
Line (a) – indicates that the speed is
increasing
 Line (b) – indicates that the speed is
decreasing

Plotting a Speed-Time Graph
5.
a. and b.
c.
This area represents the distance
travelled, 50 m.
Unit B: Physics
Velocity
In this section, you will learn about...

General Outcome #2: Explain and apply concepts
used in theoretical and practical measures of
energy in mechanical systems
◦ Define, compare and contrast scalar and vector
quantities
◦ Describe displacement and velocity quantitatively
◦ Investigate and analyze one-dimensional scalar motion
and work done on an object or system using algebraic
and graphical techniques
Did you know??

The numbering of airport runways illustrates
the importance of including direction when
describing motion. Airport runways are
numbered according to their angle from
magnetic north at 0o. The runway number
indicates the runway’s angle from magnetic
north in a clockwise direction, with the last
“0” omitted. If the runway’s heading is 40o
from magnetic north, the runway is called
runway 4.
Velocity
You have heard people use the term
“velocity” when they describe how fast a
car is going; however, most of the time
they are referring to “speed”.
 Velocity – describes the rate of motion
and the direction of an object

Speed and Velocity Practice

Practice 23-29 pg. 192
What if...

Imagine you’re a pilot flying from Calgary to
Vancouver. In order to know that you are
going to get to your destination and get
there at a certain time, you need to be
aware of both the speed and direction of the
airplane’s motion.You may be travelling at
the right speed; but if you head in the wrong
direction, you might end up in the wrong
province. Not only would this be
embarrassing as a professional pilot, but you
would most likely lose your job over
mistakes like this.
5.1 Scalar and Vector Quantities
Scalar quantity – indicates magnitude
only (eg. speed)
 Vector quantity – indicates magnitude
and direction (eg. velocity)

◦ a vector is written with an arrow above the
symbol for the measure quantity.
 symbol for speed – v
 symbol for velocity – v
Distance Travelled and Displacement

Distance travelled is a scalar quantity; it is
a measurement of the change in distance
of an object moving from a starting
reference point

This person has moved 10 m from the bus stop (reference
point), so the distance travelled is written as Δd = 10m
Distance Travelled and Displacement

Displacement is a vector quantity; it is a
measurement of the change in distance
and the direction or the change in
position of an object from a reference
point. In the last picture, the person’s
displacement would be Δd = 10m
[right]. This indicates that the object (the
person) ends up 10m from the reference
point (the bus stop) as well as the
direction of travel (right).
Distance Travelled and Displacement
Distance (Δd)
 Displacement (Δd)
What is the distance and displacement of
the following?



Distance – Δd = 3m + 5m = 8m
Displacement – Δd = 3m [right] + -5m [left] = -2m [left]
How to Identify Vector Directions

In the previous slide, the vector directions
we used were right and left, these were
determined using the x-axis method. You
can also use a compass, going [E] for
“east”, this is called the navigator method
How to Identify Vector Directions

The X-Axis Method
◦ uses “x” and “y” axis with a reference
point starting at 0o
◦ directions are determined in a counter
clockwise direction
How to Identify Vector Directions

Use the x-axis method to determine the
direction of vectors A, B, C, and D. Give
magnitude and direction for each
◦
◦
◦
◦
A – 6m [30o]
B – 10m [right]
C – -8m [down]
D – 2m [230o]
How to Identify Vector Directions

Try the following:
◦ A ball is rolling at a velocity of 2 m/s [135o].
Use the x-axis method to sketch this vector
on a grid
2 m/s [135o]
How to Identify Vector Directions

The Navigator Method
◦ uses north [N], south [S], east [E] and west
[W]
◦ north is the starting reference point of 0o
◦ directions are stated clockwise from north
How to Identify Vector Directions

Use the navigator method to determine
the directions of the vectors A, B, C and
D. Give the magnitude and direction for
each vector.
◦
◦
◦
◦
A – 6m [60o]
B – 10m [E]
C – -8m [S]
D – 2m [220o]
How to Identify Vector Directions

Notice that you were identifying the same
vectors but using different methods.
Remember to read vector problems
carefully to see which method you are
suppose to use to solve them.
Distance and Displacement
Practice Analyzing Distance and
Displacement mapping pg. 178
 Practice 1-9 pg. 181

Using Formulas to Analyze Average
Velocity


Average velocity is uniform motion that
involves changing a position in a specified
time. To determine average velocity, use
the following equation:
Velocity is a vector quantity so you must state its magnitude and
direction
Using Formulas to Analyze Average
Velocity

A person walks 10.0m [E] away from a
bus stop in 5.00s. What is the average
velocity of the person?
Using Formulas to Analyze Average
Velocity

Try the following:
◦ A student walks 10.0m [E] in 7.00s. Then he walks another
12.0m [E] in 8.00s. Determine
a. The displacement of the student in 15.00s.
The displacement of the student is 22.0 m [E].
b. The average velocity of the student.
The average velocity of the student is about 1.47 m/s [E].
Using Formulas to Analyze Average
Velocity

Try the following:
◦ A boat travels at a velocity of 8.00 m/s [N] for 14.0s. What is
the displacement of the boat?
The displacement of the boat is 112 m [N].
Plotting a Position-Time Graph

Suppose a motorboat is travelling east
past six marker buoys in the water placed
10.0m apart. A person on shore is
recording the time it takes for the
motorboat to pass each marker. Here are
the measurements;
Plotting a Position-Time Graph

The line of best fit indicates a linear or
straight-line relationship between position
and time; therefore as time increases, the
position also increases. The straight line
of the graphs shows that the motorboat’s
displacement in relation to the time
intervals is constant, therefore the
motorboat is moving with uniform
motion and it’s velocity remains constant.
Plotting a Position-Time Graph

You can use the slope to determine the
average velocity.
Plotting a Position-Time Graph
The average velocity is 25.0 m/s [E].
Plotting a Velocity-Time Graph
A velocity-time graph is similar to the
speed-time graph you studied earlier on.
 Suppose the motorboat is travelling east
at uniform velocity pas six marker buoys
10.0m apart. On shore, one person is
measuring the time using a stopwatch, and
another is measuring the speed with a
radar gun and is using a compass to
determine direction.

Plotting a Velocity-Time Graph

The following shows the measurements
they took;
Plotting a Velocity-Time Graph

The line of best fit is a straight line, which
indicates a linear relationship. Since the
line is horizontal, the velocity remained
constant during the time the motorboat
moved past the markers and is therefore
travelling in uniform motion
Plotting a Velocity-Time Graph

Let’s try this gizmo...
Unit B: Physics
Acceleration
In this section, you will learn about...

General Outcome #2: Explain and apply
concepts used in theoretical and practical
measures of energy in mechanical systems
◦ Define acceleration quantitatively as a change in
velocity during a time interval ( )
Did you know??

A jumbo jet can change its speed during
take-off from rest to 200 km/h (55.6 m/s)
in about 12 seconds! A NASA shuttle
craft moves from rest to 180 km/h (50
m/s) in the first 4 s of lift-off and then
increases its speed to 28 000 km/h
(7800 m/s) in the next 8.5 minutes!
Acceleration
 As
a passenger inside a jet airplane
streaking across the sky at 850
km/h, you may hardly be aware of
your velocity. As long as the
airplane is in uniform motion, you
may not even sense its high speed.
In contrast to uniform motion,
acceleration is easily sensed.
Acceleration
 Acceleration
– change in
velocity during a specific time
interval (eg. When you start to
run for the bus, you are
accelerating!)
Types of Acceleration

Uniform motion is the simplest type of
motion, but accelerated motion is the most
common type of motion. Like velocity,
acceleration is a vector quantity so you must
determine both its magnitude and direction.
Different types of acceleration are possible
because both the magnitude and direction of
velocity can change. When the object is
speeding up, the magnitude of velocity is
increasing, and when an object is slowing
down, the magnitude of the velocity is
decreasing.
Types of Acceleration

Positive acceleration occurs in two ways:
◦ when the change in both the magnitude of the
velocity and the direction are positive
◦ when the change in both the magnitude of the
velocity and the direction are negative
Types of Acceleration

Negative acceleration also occurs in two
ways:
◦ when the change in the magnitude of the
velocity is negative while the direction is
positive
◦ when the change in the magnitude of the
velocity positive while the direction is
negative
Using Formulas and Graphs to
Analyze Accelerated Motion

To calculate acceleration;
acceleration = change in velocity
units (m/s2)
time interval
Remember that acceleration is a vector so you must
determine the magnitude and the direction.
Using Formulas and Graphs to
Analyze Accelerated Motion

Example:
◦ A racing car accelerated from rest to a speed
of 200 km/h (55.6 m/s) [E] in 6.00s. What is
the acceleration of the car?
Using Formulas and Graphs to
Analyze Accelerated Motion

Try the following;
◦ A shuttle craft accelerates from rest to a
velocity of 50 m/s [upward] in 4.00s. What is
the acceleration?
The acceleration of the shuttle craft is 13 m/s2 upwards.
Using Formulas and Graphs to
Analyze Accelerated Motion

Try the following;
◦ A baseball thrown at 25.0 m/s strikes a catcher’s
mitt and slows down to rest in 0.500 s. What is
the magnitude of the ball’s acceleration?
The magnitude of the ball’s acceleration is 50.0 m/s2.
(In some situations, only the magnitude of the acceleration is required, and the direction
is ignored)
Plotting Position-Time Graph

Thus far, you have seen that uniform
motion is represented by a straight line
sloping upwards on a position–time graph.
The position–time graph of accelerated
motion is not represented by a straight
line on a position–time graph. It is
represented by a curved line.
Plotting Position-Time Graph

Suppose that a motorboat is travelling
with accelerated motion in an easterly
direction. It passes marker buoys placed
5 m apart. As the boat passes the first
marker buoy, a person on shore starts to
estimate and record the position of the
motorboat every 2 s relative to the first
marker buoy.
Plotting Position-Time Graph
The following is the data collected as well
as the graph.
◦ The slope of the line is gradually increasing, which indicates that
the velocity of the boat is gradually increasing or accelerating.
Plotting Position-Time Graph

The shape of the curve indicates whether
a positive or a negative acceleration.
◦ positive acceleration
(increasing slope)
◦ negative acceleration
(decreasing slope)
Plotting Position-Time Graph
i. Between t = 0.0 s and t = 3.0 s, there is accelerated motion.
This is shown by the curve of the graph.
ii. Between t = 3.0 s and t = 6.0 s, there is uniform motion. The
graph is linear during this time interval.
iii. Between t = 6.0 s and t = 8.0 s, the graph is curved with a
decreasing slope. This indicates a negative acceleration.
Plotting a Velocity-Time Graph

Again...suppose that the motorboat is
accelerating in an easterly direction. A
person on the shore uses a radar gun and
records the velocity of the motorboat
every 1.0 s, as soon as it passes the first
marker buoy. Here are the
measurements taken;
Plotting a Velocity-Time Graph

On the graph, the straight line with an
increasing slope indicates that the velocity
of the motorboat is increasing with time.
The slope can be calculated as follows:
The acceleration of the boat would be 2.0 m/s2 [E]
Plotting a Velocity-Time Graph

You can have two velocity-time graphs
positive acceleration
negative acceleration
Plotting a Velocity-Time Graph
i. Between t = 0 s and t = 3.0 s, the object is accelerating.
ii. Between t = 3.0 s and t = 5.0 s, the object is moving
with uniform motion. The graph is horizontal during this
interval.
iii. Between t = 5.0 s and t = 8.0 s, the object is
undergoing a negative acceleration. The graph has a negative
slope during this interval.
Activity

Describing Motion pg. 195
Unit B: Physics
4.2 Work and Energy pg. 150-163
In this unit, you will learn about...

General Outcome #2: Explain and apply
concepts used in theoretical and practical
measures of energy in mechanical systems
◦ Explain that, in the absence of resistive forces,
motion at constant speed requires no energy
input
◦ Recall, from previous studies, the operational
definition for force as a push or pull, and work as
energy expended when the speed for an object is
increased or when an object is moved against the
influence of an opposing force
Force
Recall:
Force – push or pull on an object
(measured in Newtons (N))

◦ With an unbalanced force, the force acting in
one direction is greater than the force acting
in the opposite direction. If a person hits a
stationary ball with a cue, he used energy to
apply the force. The energy was transferred
from the person to the ball through the cue.
The ball then gained energy and acquired a
change in motion
Force
◦ Once an object is in motion, it tends to
remain in motion, moving at a constant speed
in a straight line, however, if an unbalanced
force is applied to the moving ball, it will
either speed up or slow down (accelerate).
Force

In the absence of any external unbalanced
forces, such as resistive forces, all objects
tend to maintain uniform motion or stay
at rest. An object n motion will stay in
motion and no energy input is required to
maintain uniform motion.
Force

When a ball is lifted an held above the
floor, the person had to apply a force in
the opposite direction to the downward
force of gravity. The person doing the
lifting is doing the work and the energy is
transferred to the ball. This energy
transfer results in a change in the ball’s
position relative to the Earth’s surface.
Work

Whenever a force moves an object
through a distance that is in the direction
of the force, then work is done on the
object.
Work
 There
are three conditions for
work to be done on an object
◦ There must be movement.
 Someone pushing against a wall with 100
N of force is NOT doing any work on
the wall because the wall does not move
Work
◦ There must be force.
 A person riding a bike that is coasting is not doing
any work on the bike because even though there is
movement, the person is not applying a horizontal
force to the bike.
◦ The force and the distance the object
travels must be in the same direction.
 A person is NOT doing any work on a backpack
when she’s carrying it parallel to the ground
because the force of her hand on the pack is
vertical and the distance the pack travels is
horizontal.
The Relationship Between Work
Output and Work Input

When a force is applied to move an object
through a distance, work is done on the object. If
the force applied to the object is constant
throughout the distance that it acts on the object,
then a force-distance graph should be a straight
line. The area under the line of best fit can be
used to determine the work input. The object
gains energy as a result of this work done on an
object, the energy is the work output. In absence
of any outside forces, such as friction, the total
work input should equal the total work output.
The Relationship Between Work
Output and Work Input

Example:
◦ A weightlifter lifts a barbell a vertical distance
of 2.40 m. If the average force required to lift
the barbell is 2.00×103 N, how much work is
done by the weightlifter on the barbell?
The work done by the weightlifter is 4.80×103 J or 4.80kJ
The Relationship Between Work
Output and Work Input

Practice 1-9 pg. 154-155
Graphical Method's for determining
Work
Practice 10 pg. 157
Energy
Energy – the ability to do work
 If a body has energy, then the body can do
work by transferring the energy to
another object.
 Work and energy are essentially the same
thing, if a body does work on an object,
then the body doing the work loses
energy and the object that has work done
to it gains energy.

Energy

Since work and a change in energy are
the same, then they must have the same
units.
Energy

Example
◦ A weightlifter does 4.80×103 J of work in
lifting a barbell. How much energy is gained
by the barbell?