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Cambridge University Press
978-0-521-68359-3 - Study and Master Physical Sciences Grade 11 Learner’s Book
Karin Kelder
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Einstein
MODULE 1
force
Mechanics
motion
accelerate
Galileo
Newton decelerate
moment of force
momentum
movement
In Grade 10 we investigated kinematics, or movement described
in terms of velocity, acceleration, displacement, and so on.
This module focuses on the reasons for motion – what makes an
object at rest begin to move, what causes an object to accelerate or
decelerate. It invites you to explore the relationship between
motion and the forces that cause motion.
In this module you will work your way through the following units:
•
•
•
•
Newton’s laws of motion
Newton’s Law of Universal Gravitation
momentum
moment of a force.
From everyday experience, we know that an object cannot move
unless a force is applied to it. In the early 1600s Galileo observed
this phenomenon. We will start our study with Galileo and progress
to Isaac Newton, the father of classical physics. Newton formulated
the laws of motion and the Universal Law of Gravitation in 1687.
We still use these laws today, although Albert Einstein formulated
new laws in 1905. To understand the link between these two great
scientists, we will look briefly at their contributions to science.
In sport, we talk about a rugby or soccer player’s momentum
that carries him forward. We will investigate how momentum can
be defined scientifically, and also how we can calculate its change.
The relationship between motion and the forces that cause
motion is called dynamics. We will also look at the relationship
between dynamics and machines. In science we consider a machine
to be any device that makes it easier for us to do work.
1
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Cambridge University Press
978-0-521-68359-3 - Study and Master Physical Sciences Grade 11 Learner’s Book
Karin Kelder
Excerpt
More information
inertia
newton
UNIT 1
mass
motion
force
friction
acceleration time
NEWTON ’ S LAWS OF MOTION
KEY CONCEPTS
When you have completed this unit, you should be able to:
• mass
• inertia
• forces
• force diagrams
• acceleration
• equilibrium
• net force
• action-reaction
pair
• define Newton’s three laws of motion
• explain what inertia is and how it is related to mass
• understand and define the mathematical and graphical
relationship between force, acceleration and mass
• understand how this relationship between force, acceleration and
mass led to Newton’s Second Law
• draw a force diagram and label the forces acting on an object
• distinguish between balanced and unbalanced forces
• calculate the net force and use it in Newton’s Second Law
• identify action-reaction pairs according to Newton’s Third Law.
Newton’s First Law
In the 17th century, scientists invented the telescope. At this time,
astronomers began to study the movement of planets in the heavens
(or solar system). They noticed that the planets moved freely
through space, without any force to push them. Galileo came to the
conclusion that this was the natural motion of objects:
• An object at rest will stay at rest, unless a force causes it to start
moving.
• A moving object will continue to move at a constant speed in a
straight line, unless a force acts on it.
(a)
2
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Galileo devised several experiments to test his ideas. In one
experiment, a ball rolls down a curved ramp, speeds up, and then
runs up the other side. If there is no friction, it reaches the same
height as the starting height, as seen in (a). If the second part of the
ramp is lowered to a less
steep slope, the ball
reaches the same height as
before, but now travels
further horizontally, as
(b)
original height
seen in (b). What happens
if the ramp is lowered to a
horizontal position?
(c)
Galileo suggested that the
ball would roll on forever,
as seen in (c).
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Cambridge University Press
978-0-521-68359-3 - Study and Master Physical Sciences Grade 11 Learner’s Book
Karin Kelder
Excerpt
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To have a better understanding of Galileo’s idea, let us look at another
example. When you push a brick with a rough surface along a table
top at constant speed, you have to exert a certain amount of force. To
push a smooth wooden block with the same mass across the table at
the same speed requires less force. If a layer of oil is poured onto the
table, the force required to move the block will be very small. Imagine
if the block was not touching the table at all. Once started, the block
should move across the table with no further force applied.
F
v
F
rough surface
v
smooth surface
v
no contact
Newton used Galileo’s results and formulated his theory of motion
in three laws.
His First Law summarises Galileo’s original ideas:
Newton’s First Law
An object will remain at rest or continue to move at a constant velocity
in a straight line, unless an external net force acts on it.
Inertia and mass
The tendency of a body to maintain its state of rest or constant
motion in a straight line is called its inertia. Let’s look at the
following examples:
• It is easier to catch a tennis ball than a cricket ball.
• It is easier to move a stationary bicycle than a stationary car.
• It is easier to turn an empty supermarket trolley than a fully
laden one.
From these examples, we can deduce that the greater the object’s
mass, the more difficult it is to change its motion.
Newton used the term mass for the quantity of matter of an
object. Another way to define mass is to say that it is a measure of a
body’s inertia. The more mass a body has, the harder it is to change
its state of motion.
DID YOU KNOW?
In Grade 10 we learnt that mass is a property of a body itself. Mass is
measured in grams and kilograms. Weight is the force of gravity acting
on a body and is measured in newtons.
3
© Cambridge University Press
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Cambridge University Press
978-0-521-68359-3 - Study and Master Physical Sciences Grade 11 Learner’s Book
Karin Kelder
Excerpt
More information
Examples: Demonstrating Newton’s First Law and inertia
The mass of an object is a measure of its inertia. The following demonstrations explain this
property of matter.
Example 2
Example 1
ball
When the cardboard is flicked away from the top of
the glass, the coin drops in the glass. The force
applied to the cardboard is not relayed fast enough
to the coin to accelerate it with the cardboard.
pull
Example 3
A quick jerk breaks the string
at the bottom. There is not
enough time to overcome
the inertia of the ball, and
the pulling force breaks the
string at the bottom.
A steady, slow pull breaks
the string at the top. There is
enough time to overcome
the inertia of the ball, and the
weight of the ball together
with the pulling force breaks
the top string.
jerk
When the paper is jerked away, the glass of water
lands on the table. The friction between the table and
the paper cannot overcome the inertia of the glass.
Before we can continue our investigation into the effect of force on
the motion of an object, we need to refer back to the concepts we
used in Grade 10 to describe motion. The quantities of displacement
(s), initial velocity (u), final velocity (v), acceleration (a) and time (t)
all contribute to the type of motion of an object. This motion can be
described and calculated by using words, graphs and equations.
Displacement-time graphs plot the rate at which the displacement of
an object changes, and velocity-time graphs plot the rate at which
its velocity changes. Any of the above quantities can be calculated
by using a set of equations called the equations of motion. They are:
(u v)t
v u at
v2 u2 2as
s ut 1/2at2
s
2
4
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Cambridge University Press
978-0-521-68359-3 - Study and Master Physical Sciences Grade 11 Learner’s Book
Karin Kelder
Excerpt
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Acceleration, force and mass
Newton’s First Law describes an object at rest or with constant
motion. But what happens if an unbalanced external force is exerted
on the object? Newton realised that the velocity of the object will
change. If the object experiences an increase or decrease in velocity,
it will have acceleration. To understand the relationship between
acceleration, force and mass, we will investigate the motion of a
minibus taxi.
Relationship between acceleration and force
A minibus taxi driver is waiting for the traffic lights to change. When
the lights turn green, the driver pulls away and moves forward. The
force provided by the engine causes the minibus to accelerate. The
arrow in the sketch shows the force pushing the minibus forward. If
the driver wants to move away from the lights more quickly, he can
push down harder on the accelerator. The forward force is then
stronger, and the minibus’s acceleration will be greater than before.
v
a
v
a
F
F
The graphic representation of the motion of the minibus is:
v (m)
v (m)
t (s)
t (s)
a
(m s2)
a
(m s2)
t (s)
t (s)
5
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Cambridge University Press
978-0-521-68359-3 - Study and Master Physical Sciences Grade 11 Learner’s Book
Karin Kelder
Excerpt
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At the next traffic light, the driver must stop. He applies the brakes,
which provides another force to slow down the minibus. Although the
minibus is moving forward, the braking force is directed backward to
decelerate the minibus. If the driver wants to stop in a hurry, he must
apply a stronger force by pushing down harder on the brake pedal. The
minibus’s deceleration will therefore be greater than before.
a
v
a
F
v
F
The graphic representation of the motion of the minibus is:
v (m)
v (m)
t (s)
t (s)
a
(m s2)
a
(m s2)
t (s)
t (s)
Now we can deduce from our observations on the minibus that:
• A force can make an object accelerate. The object accelerates in
the direction that the force is being exerted.
• The stronger the force acting on an object,
the greater the acceleration of the object.
a
We say that the acceleration a produced by a
force F is directly proportional to the force.
The mathematical relationship is written in
symbols: a ⴤ F
F
We can also represent the relationship
Acceleration is plotted
graphically, as shown on the right.
against force
6
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M O D U L E 1 : U N I T 1 : N E W T O N ’ S L AW O F M O T I O N
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Cambridge University Press
978-0-521-68359-3 - Study and Master Physical Sciences Grade 11 Learner’s Book
Karin Kelder
Excerpt
More information
DID YOU KNOW?
Because acceleration is directly proportional to the force which produces
it, doubling the force will produce twice the acceleration, three times
the force will produce three times the acceleration, and so on.
You can find out
more about the
mathematical and
graphical
representations of
the relationship
between
quantities in the
introduction.
v
Relationship between acceleration and mass
Another factor that influences an object’s acceleration is its mass.
The taxi driver knows that when his taxi is full of people, he will not
be able to accelerate fast when he pulls away from a traffic light.
Similarly, when he applies the brakes, the taxi will decelerate more
slowly than when it is empty. A good driver takes these differences of
mass into account when driving and stopping the taxi safely.
a
v
a
F
F
We can deduce from our observations on the minibus that:
• If a constant force is applied, the greater the mass of an object, the
smaller its acceleration.
We say that the acceleration a of an object produced by a force F is
inversely proportional to the mass m of the object.
The mathematical relationship is written in symbols: a ⴤ 1/m
The graphical representation is:
a
a
m
Acceleration is inversely
proportional to mass
1
m
Acceleration is directly proportional
to 1/m
7
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978-0-521-68359-3 - Study and Master Physical Sciences Grade 11 Learner’s Book
Karin Kelder
Excerpt
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DID YOU KNOW?
Since acceleration is inversely proportional to the mass of an object,
doubling the mass of the object will halve acceleration if the force
remains constant.
Newton’s Second Law
We can now combine the relationship between acceleration and
force with the relationship between acceleration and mass:
F
a
or F ma
m
Newton’s Second Law
When a net force is exerted on an object, it causes the object to
accelerate in the direction of the force. This acceleration is directly
proportional to the force and inversely proportional to the mass of the
object.
This proportionality is not an exact relationship yet. To insert an
equal sign (), the total numerical value of the SI units on the left of
the proportionality must equal the total numerical value of the SI
units on the right. To achieve this, we have to include a
proportionality constant k:
F kma
By setting k equal to 1, our formula becomes:
F ma
DID YOU KNOW?
The unit of force,
the newton, was
named after Sir
Isaac Newton,
who played a
great part in
developing the
scientific concept
of force. The
newton is one of
seven basic SI
units. Read more
about these units
in the introduction
on page vi.
8
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We have now defined the magnitude (size) of the unit of force
(newton) in terms of existing units, the kilogram, metre and second.
One newton is the force that will give a mass of one kilogram
acceleration of one metre per second squared:
1 N 1 kg m s–2
The quantities are related by the formula F ma
Quantity
Symbol
Unit
Force
F
N (newtons)
Mass
m
kg (kilograms)
Acceleration
a
m s–2 (metres per second squared)
Note: Different scientific sources use different names for the force
that results in acceleration of an object – net force; unbalanced force;
resultant force. They all refer to exactly the same force.
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Cambridge University Press
978-0-521-68359-3 - Study and Master Physical Sciences Grade 11 Learner’s Book
Karin Kelder
Excerpt
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WORK IN GROUPS
Activity 1: Investigating Newton’s Second Law
LO1: AS1, AS2, AS3, AS4; LO2: AS1, AS2
Note: To compare
two values
experimentally, all
other factors must
remain constant
during the course
of the experiment.
The trolley experiments are used to investigate the relationship between
the applied force, acceleration and mass of an object. Ask your teacher
for details on the experimental procedure. The concepts of the
experiments are explained here briefly so that you can answer the
questions in the activity.
In this activity, two relationships are investigated:
• the effect of force on acceleration, and
• the effect of mass on acceleration.
ruler
mark
ticker-timer
tape
elastic band
trolley track
In the experiments, a force is applied to a trolley which is on a slightly
raised trolley ramp. The trolley ramp is raised to compensate for friction.
When the trolley is given a light push, the ticker-tape that shows the
trolley’s displacement at constant time intervals, resembles the tape in
the sketch.
1. What does the spacing of the dots on the ticker-tape tell you about
the motion of the trolley?
2. What is the value of the net force on the trolley that produced the
ticker-tape?
3. Draw an example of a ticker-tape in which the trolley accelerates.
Stretched elastic bands provide the force that accelerates the trolley.
Care is taken to stretch the elastic bands to the same length all the time
so that a constant force is applied. All the elastic bands are tested
beforehand to ensure that they all give the same force. Ticker-tapes from
each run are collected and processed. The results are recorded in tables
and graphs to show the various relationships.
9
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978-0-521-68359-3 - Study and Master Physical Sciences Grade 11 Learner’s Book
Karin Kelder
Excerpt
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Investigation 1: Determining the relationship between force and
acceleration on an object with constant mass
The trolley is accelerated with one, two and three elastic bands in
succession. The results are used to draw velocity-time graphs.
4. What conclusions can you make from
these graphs?
3 elastic bands
v
1
5.
What is the mathematical relationship
(m s )
2 elastic bands
between v and t?
6. Draw a sketch graph to show the
relationship between the net force on the
1 elastic band
trolley and the acceleration it produces.
7. The following ticker-tape gives you the
t (s)
experimental values for one force (one
Velocity is plotted against time
elastic band).
A
B
C
D
E
F
•••••••••••••• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •
0,125 m
0,178 m
0,238 m
0,292 m
0,353 m
Use the displacements above to complete the following table and to
calculate the acceleration of the trolley.
Displacement
s (m)
Time
between
10 dots
⌬ t (s)
A to (reading 1 2) 0,2
C
Average
velocity
s
v (m s1)
t
Instantaneous
velocity
v (m s1)
Change in
velocity
⌬ v (m s1)
Acceleration
⌬v
a = (m s2)
⌬t
(value 7 value 6
value 10)
(value 10 0,2)
(value 8 value 7
value 11)
(value 11 0,2)
(value 9 value 8
value 12)
(value 12 0,2)
(reading
1 2 0,4
value 6)
B
(value 6)
B to (reading 2 3)
D
0,2
(reading
2 3 0,4
value 7)
0,2
(reading
3 4 0,4
value 8)
0,2
(reading
4 5 0,4
value 9)
C
(value 7)
C to (reading 3 4)
E
D
(value 8)
D to (reading 4 5)
F
E
(value 9)
10
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