1.
X INTRODUCTION
We apply measurements in almost everything we do. For example, how much
time does it take to bake a cake? Or how far away is the school from your house?
Or what is your weight? Each of these quantities needs to be measured using
different measuring tools. You need to be able to determine the proper measuring
tool for each measurement that you make so that you can get the best results from
the activities that you do.
PHYSICAL QUANTITIES AND SI UNITS
All measurements in physics are related to fundamental quantities such length,
mass and time. In the earlier times, until about the year 1800, workers in various
countries used different systems of units. Thus, while the English used inches to
measure length, a scientist from another country would measure lengths in
centimetres. This made it difficult for people from different countries to compare
1.1
TTooppiicc
11
X Measurement
By the end of this topic, you should be able to:
1. Define physical quantity;
2. Describe base and derived quantities and their respective SI units;
3. Determine the appropriate measurement tools for measuring different
physical quantities;
4. Discuss the precision, accuracy and sensitivity of measuring tools;
and
5. Use the graph technique to analyse measurements and data.
LEARNING OUTCOMES
2.
X TOPIC 1 MEASUREMENT2
the measurements that they have made. Fortunately, this situation has now been
changed by the efforts of various international committees of scientists who have
met for discussion regularly over many years.
In 1960, the General Conference of Weights and Measures in France
recommended the use of a metric system of measurement called the International
System of Units*. The SI units are derived from the earlier MKS system, so called
because its first three basic units are the metre (m), the kilogram (kg), and the
second (s). Most countries including Malaysia have adopted this system.#
A pphysical quantity is a quantity that can be mmeasured. Examples of physical
quantities are length, mass, time, weight, electric current, force, velocity and
energy. NNon-physical quantities are quantities that ccannot be measured such as
colour, feelings or beauty.
To describe a physical quantity, two things need to be specified. The first is its
numerical value and the second is its uunit. For example, the distance between
your house and school is five kilometres. The distance has a numerical value of
five and the unit is kilometre (km).
On the other hand, colour, feelings and beauty cannot be stated in numerical
form and do not have units. Thus these quantities are subjective, as in the famous
saying, „beauty is in the eye of the beholder‰.
1.1.1 Base and Derived Quantity
Now let us get to know base and derived quantity.
(a) Base Quantity
There are two types of physical quantities; the base quantity and the
derived quantity.
________________________________
* (Le Systeme International (SI))
# To date, there are three countries known not to adopt this system: the United States, Myanmar
and Liberia.
A bbase quantity is a physical quantity that cannot be defined in terms
of any other physical quantity.
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TOPIC 1 MEASUREMENT W 3
Table 1.1 shows five base quantities and their respective SI units.
Table 1.1: Base Quantities and Their Respective Base Units
Base Quantity BBase Unit (SI Unit) SSymbol of Unit
Length, l Metre m
Mass, m Kilogram kg
Time, t Second s
Temperature, T Kelvin K
Current, I Ampere A
Scientific investigations usually involve quantities with values either very
big or very small. For example, the height of Mount Everest is 8848 m or
the diameter of a cell is 0.000002 m. Quantities written this way take up
much space and are difficult to use in calculations. Thus we can write them
as numbers which are base of 10s to make them simpler to use.
M u 10n where 1 ª M d 10 and n is an integer
By using the above multiplication factor, the height of Mount Everest is
written as 8.848 u 103 m and the diameter of the cell is 2.0 u 10ă6 m. The
magnitudes of physical quantities are usually rounded up to three or four
significant figures. The list of prefixes and multiplication factors is shown
in Table 1.2.
Prefixes in the SI unit represent the multiplication factors. For example, the
multiplication 103 is represented by the prefix, kilo.*
Similarly, 1,000 m can be stated as 1 km. 1 cm can be stated as 0.01 m or
1 u 10ă2 m.
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X TOPIC 1 MEASUREMENT4
Table 1.2: Prefixes and Multiplication Factors
Prefix SSymbol MMultiplication Factor
Tera T u 1012
Giga G u 109
Mega M u 106
Kilo k u 103
Deci d u 10ă1
Centi c u 10ă2
Milli m u 10ă3
Micro ø u 10ă6
Nano Ș u 10ă9
Pico p u 10ă12
When we want to change a prefix to the base unit, we need to use suitable
multiplication factors. The example below shows the conversion of units.
Example 1.1:
6.78 mm = __________________ km
Solution:
6.78 mm = 6.78 u 10ă3 m
= 6.78 u 10ă3 u 10ă3 km
= 6.78 u 10ă6 km
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TOPIC 1 MEASUREMENT W 5
(b) Derived Quantity
What does derived quantity mean?
Physical quantities are related to one another by mathematical equations.
These quantities can be expressed and derived from base quantities.
For example,
Velocity = Displacement/Time
Table 1.3 shows some derived quantitties, their units and how their units
are derived from base units.
A derived quantity is a physical quantity that is produced from a
combination of base quantities through some operation such as
multiplication, division or both.
1. Search the values of the following constants in prefixes and convert
them to real numbers:
(a) Speed of light in vacuum;
(b) Mass of an electron; and
(c) Distance from Earth to the Sun.
2. Convert the following numbers using suitable prefixes.
(a) 23,000,000 kg; and
(b) 7,500 nm.
ACTIVITY 1.1
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X TOPIC 1 MEASUREMENT6
Table 1.3: Derived Quantities
Derived Quantity
Relationship with
Base Quantities
Relationship with
Base Units
Derived Unit
Area, A Length u Breadth m u m m2
Volume, V
Length u Breadth u
Height
m u m u m m3
Density, U
Mass
Volume
3
kg
m
Kgmă3
Velocity, v
Length
Time
m
s
m să1
Acceleration, a
Velocity
Time
m
s
m să2
Work, W
Force u
Displacement
kgm să2 u m
kgm2 să2 or
Nm or J
Power, P
Work
Time
2 2
s
kgm
s
kgm2 să1 or
Nm să1 or
J să1
Example 1.2:
Based on the formula given, derive the SI units of the following quantities.
(a) Force = Mass u Acceleration
(b)
Force
Pressure =
Area
Solution:
(a) Force = Mass u Acceleration
Unit of (Force) = Unit of (mass) u Unit of (acceleration)
= kg u msă2
= kg msă2
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TOPIC 1 MEASUREMENT W 7
(b) Pressure =
Force
Area
Unit of (Pressure) =
Unit of (Force)
Unit of (Area)
=
2
2
kgms
m
= kgmă1să2
1.1.2 Length
Length is a measure of displacement between two points within a single
dimension. Different terms are used for measurement in two other perpendicular
dimensions: width and height. You have learnt that length is measured using the
SI unit, metre. It is defined as:
Other than the metre or its prefixes (centimetre, kilometre etc), the US customary
units, English or Imperial System of units uses other units for the measurement
of length such as inch, foot, yard or mile.
1.1.3 Area
Area is defined as the amount of the two-dimensional space within a boundary.
For a square or a rectangular,
Area = Length u Width
Thus, the SI unit for area is m2.
If symbols are used to represent quantities as in table 1.1 (where l = length), and
let A = Area; and b = width or breadth, we obtain the following equation for area
of a square or a rectangle:
A = l u b
Metre is the length of path travelled by light in vacuum during an interval of
1/299,792,458 of a second.
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X TOPIC 1 MEASUREMENT8
If length and width are measured in cm as in Figure 1.1, area is measured in cm2.
Figure 1.1: A square of 1 cm u 1 cm
1 cm2 = 1 cm u 1 cm
= 0.01 m u 0.01 m
= 0.0001 m2 or 1 u 10-4 m2
You must try out similar problems to improve your problem solving skills.
The area for various shapes can be determined by using the formulae for area.
Some examples are shown in Figure 1.2.
Figure 1.2: Area of some regular shapes
You can also measure the area of an object by placing uniform objects such as a
stamp over the object. In order to measure the area using uniform objects, you
must count the number of uniform objects covering the surface area.
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TOPIC 1 MEASUREMENT W 9
For example, if you want to measure the area of a textbook, you should fill as
many stamps as possible on the surface of the book. The number of stamps
covering the surface of the book is the area of the book. Look at the diagram in
Figure 1.3. The area of the book is covered by 12 stamps.
Figure 1.3: Stamps cover book surface
Although the stamps can be used to measure the area of the book, this method is
considered as a non-standard method. Again, there is a need to use a
standardised unit in order to make the method a standard one.
A simple method to measure the area of a rectangular or square is by using
graph paper. The advantage of using graph paper is that it has uniform squares
printed on it. To measure the area of a rectangular or square object, place the
graph paper on the surface of the object. One square on the graph paper is 1cm2.
Thus, the number of squares on the graph papers can be counted to measure the
area of the objects being covered. By using the previous example, let us replace
the stamps covered on the book with the graph paper (as shown in Figure 1.4).
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X TOPIC 1 MEASUREMENT10
Figure 1.4: Graph squares cover book surface
The area of the book is 48 squares. Since the area of each square is 1 cm2, the area
of the book is 48 cm2.
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TOPIC 1 MEASUREMENT W 11
To find the area of a non-regular shape, you can trace the shape on centimetre
grid paper (see Figure 1.5).
Figure 1.5: A non-regular shape
Then, count the number of full centimetre squares inside the shape. Then, piece
together the remaining parts (for example, halves) into full squares. This method
will give you a good estimate of the shapeÊs area.
We have learned how to use graph paper to measure an area of a
rectangular and a square object. Imagine, if the area you want to
measure is big, like a badminton court or a football field. Is it practical
to use graph paper as a tool to measure those big areas? There are other
alternatives we can use to measure such big areas. The area of a square
or a rectangle is measured by using the formula: A = l u b.
Calculate the area of your classroom by using the given formula.
SELF-CHECK 1.1
As a teacher, you can ask your students to do this activity:
They have already learned that a graph paper can be used as a tool to
measure the area of a rectangular and a square object. Now, ask them to
measure the area of their own books by using graph paper.
ACTIVITY 1.2
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X TOPIC 1 MEASUREMENT12
1.1.4 Volume
Think about this situation. You need to estimate the amount of petrol that you
need to drive your car from Ipoh to Malacca. You already know the distance
between Ipoh and Malacca, but now you need to estimate how much petrol you
need to reach Malacca. The further the distance you drive, the larger the volume
of petrol that you need for the journey. This indirect relationship can be
explained in a simple manner by referring to the following situation shown in
Figure 1.6.
Figure 1.6: Comparing a big and a small bowl for volume
When you compare bowl A and bowl B, which bowl has a bigger space to be
filled by a liquid? Why can one bowl be filled with more volume of the liquid
compared with the other bowl? These two questions can be answered when we
understand the definition of volume. Basically, the volume of an object is the
total amount of space occupied by the object. Thus, a bigger object has a
bigger volume.
Volume is a three-dimensional space occupied by an object. The units for volume
reflect its three-dimensional form such as cubic metres, cubic feet or cubic miles.
The volume of a regular shape or geometric shape can be determined by using
mathematical formulae shown in Figure 1.7.
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TOPIC 1 MEASUREMENT W 13
Figure 1.7: Volume of some geometric shaped objects
Volume of Cuboid
The volume of a cuboid can also be determined experimentally by filling the box
completely with cubes of equal sizes. This is because the cubes can completely fill
the box. In order to measure the volume of an empty cuboid with cubes, we need
cubes with sides of 1cm and volume of 1cm3. We can measure the volume of an
empty box by filling it up completely with cubes with a volume of 1cm3 each.
The number of cubes which fill the box completely is the volume of that
particular box. If 36 cubes fill up the box completely, that means the volume of
the box is 36cm3.
The second method to measure a volume of cuboid is by using a mathematical
formula. First of all, we need to understand the basic characteristics of a cuboid.
The length, width and height of a cuboid are different. Even so, we can still
calculate the volume by using the following formula shown in Figure 1.8.
Figure 1.8: Formula to calculate the volume of a cuboid
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X TOPIC 1 MEASUREMENT14
Example 1.3:
Given the length of the cuboid is 5cm, its width is 4cm and its height is 2cm, its
volume can be calculated by using the formula:
Volume = Length u Width u Height
= 5 cm u 4 cm u 2 cm
= 40 cm3
For irregular shaped objects, the volume cannot be determined using formula, we
can use the displacement of liquid as a way to determine its volume. When an
object is placed into a measuring cylinder, the level of water will rise. The
difference in the volume of water is the volume of the object, Vobject.
The water in the first cylinder in Figure 1.9 has a volume of 200 cm3.
Figure 1.9: Measuring the volume of a liquid
The level of the water rises to 260 cm3 when the object is placed in it. Thus the
volume of the object is:
Vobject = 260 cm3 ă 200 cm3
= 60 cm3
Vobject = Vobject + water ă Vwater
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TOPIC 1 MEASUREMENT W 15
1.1.5 Time
Time is a non-spatial continuum measure of existence and events. The unit of
time, second (ss), was defined originally as the fraction 1/86 400 of the mean solar
day. However, the irregularities of the rotation of the Earth do not allow accuracy
to be achieved for the measurement of a second. The second was redefined in the
year 1967 to take advantage of the high precision attainable with an atomic clock,
which uses the characteristic frequency of the light emitted from the cesium-133
atom as its „reference clock.‰
1.1.6 Mass
When you walk around in a supermarket, you will see many things sold in
packets. If you read the packets carefully, you will notice the amount of mass
printed on the packets, such as 1 kg, 5 kg, 10 kg etc. We use the concept of mass
in daily life situations. Can you give examples of daily situations related to mass?
All objects have mass. Mass is the quantity of matter present in the object. An
object which has larger quantity of matter in it has larger mass. The mass of an
object is the same even though it is measured at different places. This is because
the mass of an object depends on the amount of matter present in the object.
Thus, a 50 cent coin has a bigger mass than a 20 cent coin.
The standard unit for mass is kilogram (kg). The standard mass is an
international prototype of mass 1 kilogram kept at the International Bureau of
Weights and Measures near Paris.
A kkilogram is equal to the mass of the IInternational Prototype Kilogram
(IPK), a platinum-iridium cylinder kept by the BIPM at Sèvres, France.
The ssecond is defined as the time required for 9,192,631.770 periods of
radiation of caesium atoms as they pass between two particular states.
Metric Units
1 kilogram (kg) = 1000 grams (g)
1 gram (g) = 1000 milligrams (mg)
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X TOPIC 1 MEASUREMENT16
1.1.7 Temperature
You are probably familiar with the weather report aired in the news which
predicts the weather for the next day. You may have noticed that some numbers
appear on the screen which indicate how hot or cold the day would be. The
numbers may be relatively higher or lower in some places. These are called
temperatures.
Temperature is used to indicate how hot or cold an object is. Usually, a hot object
is indicated by having a high temperature. In contrast, a cold object has a low
temperature. You cannot measure temperature of boiling or cold water
accurately by dipping in your fingers into it. You may only be able to estimate
the temperature of the water. A thermometer is used to measure temperature
accurately.
Temperature is a physical property of matter which quantitatively expresses the
common notion of hot or cold. If the temperature of an object is low, the object is
cold; various degrees of higher temperatures are referred to as warm or hot.
Temperature can be measured using various kinds of thermometers. The basic
unit of temperature in the International System of Units (SI) is Kelvin and has the
symbol K. It is named after the British physicist, Lord Kelvin.
On the scale commonly used in laboratories, the number 0 is assigned to the
temperature at which water freezes and the number 100 as the temperature at
which water boils. The space between is divided into 100 equal parts called
degrees, hence, a thermometer so calibrated is called a centigrade thermometer
(from centi, „hundredth‰, and gradus, „degrees‰). It is now called a Celsius
thermometer in honour of the man who first suggested the scale, Swedish
astronomer Anders Celsius (1710-1744). This unit is used by many customers.
Tc = Tk ă 273.15
The United States uses a different unit do measure temperature. In United States,
number 32 is assigned to the temperature when water freezes. Boiling water is
assigned to number 212. This scale is known as the Fahrenheit scale.
TF = 1.8 Tc + 32À F
Kelvin is the fraction 1/273.16 of the thermodynamic temperature of the
triple point of water.
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TOPIC 1 MEASUREMENT W 17
MEASUREMENT TOOLS
In the following subtopics we are going to look at some of the tools that we
commonly use scientifically to measure. When we make measurements, there are
certain things that we need to know about the measuring tools that we use so
that we can get the best results for our measurements, which are precision,
accuracy and sensitivity.
1.2.1 Precision, Accuracy and Sensitivity
In everyday life, no measurement is exactly accurate. All of the physical
quantities are only estimations. For example, 500 g of sugar bought from a mini
market may be 500.2 g or 499.8 g. There will always be a slight difference
between the observed value and the real value of the quantity. The difference
1.2
ABSOLUTE ZERO TEMPERATURE
Absolute zero temperature, OK (corresponds to ă273.15À C on the Celcius
temperature scale and ă459.67 À F on the Fahrenheit temperature scale) is the
temperature at which a thermodyname system has the lowest energy.
Riddles related to temperature.
1. Why should someone wear a hat on a cold day?
2. Why can you warm your hands by blowing them gently, and cool
them by blowing hard?
3. Air and water, both at 25ÀC, do not feel the same. You notice this
temperature difference upon jumping from 25ÀC air into a
swimming pool of 25ÀC water. Why are there differences?
4. Can an ice cube be so hot that your fingers will burn when in
contact?
(Source: Jargodzki Potter, 2001)
ACTIVITY 1.3
18.
X TOPIC 1 MEASUREMENT18
between the real value and the observed value (OObserved value ă Real value, ')
is known as tthe error of uncertainty.
There are many reasons for errors of measurement, such as:
(a) Using unsuitable measuring instruments;
(b) Personal error when reading the scale; and
(c) The measuring process itself.
The three important aspects of a measurement are explained in Table 1.4.
Table 1.4: Three Important Aspects of Measurement
Aspect Description
Precision Ability of the instrument to give consistent readings when the same
physical quantity is measured more than once. In other words, there is
no or little deviation among the measurements taken.
Accuracy How close is the measured value compared with the actual value?
Sensitivity The ability of detecting small changes in the measured quantity.
Sensitive instruments can detect and react fast to small changes in the
quantities.
Now let us learn more on these three aspects.
(a) PPrecision
Let us look at two examples to understand precision.
Example 1.4: Precision
Table 1.5 shows two sets of readings taken by using two different
measuring instruments; A and B:
Table 1.5: Example for Precision
Instrument A IInstrument B
6.5 7.2
6.4 6.6
6.5 5.9
6.6 5.2
6.5 7.9
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From the readings in Table 1.5, the values taken by instrument A are closer
to one other compared with instrument B. The readings taken by
instrument B are scattered, where the five values are quite far from one
another. Thus, when comparing instruments A to B, the readings taken by
instrument A are more precise than instrument B.
Example 1.5: Consistency in the form of deviation
Relative deviation = Average deviation/Average reading u 100%
Steps in finding relative deviation:
The readings taken by an instrument G are shown below. Find the relative
deviation of the readings.
2.2 m, 2.3 m, 2.5 m, 2.1 m and 2.2 m
Solution:
(i) Find the average reading.
Average reading = (2.2 + 2.3 + 2.5 + 2.1 + 2.2)/5 = 2.26 m
(ii) Construct a table as shown in Table 1.6:
Table 1.6: Sample Table
No. Readings Taken by Instrument G, (m) Deviation (m)
1 2.2 2.2 ă 2.26 = 0.06
2 2.3 2.3 ă 2.26 = 0.04
3 2.5 2.5 ă 2.26 = 0.24
4 2.1 2.1 ă 2.26 = 0.16
5 2.2 2.2 ă 2.26 = 0.06
Total 11 0.56
Average 11.3/5 = 2.26 0.56/5 = 0.11
(iii) Find the total deviation using the formula as shown below:
Deviation = Reading ă Average reading
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X TOPIC 1 MEASUREMENT20
(iv) Find the average deviation using the formula:
Average deviation = Total deviation/Number of readings
= 0.56/5
= 0.11 m
(v) Find the relative deviation using the formula given:
Relative deviation = Average deviation/Average reading u 100%
= 0.11/2.26 u 100%
= 4.86 %
If we use a 100% consistent measuring instrument to measure one of
the physical quantities, then the relative deviation of a reading taken
will be zero. This situation happens as there is no deviation in every
reading taken. On the other hand, if we use a measuring instrument
which is not 100% precise, we will get different readings for the
measurement of the physical quantities.
(b) AAccuracy
Let us look at an example to show the concept of accuracy.
Example 1.6:
A teacher asks two students, Afiq and Syazwan, to measure the height of a
chair in the physics laboratory. The actual height of the chair is 35.4 cm. The
following data table shows the obtained data:
Afiq 35.2 cm 35.6 cm 35.4 cm 35.7 cm 35.3 cm
Syazwan 36.2 cm 36.1 cm 36.2 cm 36.1 cm 36.2 cm
For Afiq:
(i) Since the readings taken are very close to the actual reading, his
readings can be considered as accurate.
(ii) But, there are variations between the readings, so his readings can be
considered as not precise (consistent).
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For Syazwan:
(i) Since the readings taken are far from the actual reading, his readings
can be considered as less accurate.
(ii) But, his readings are more precise compared with Afiq because the
readings are concentrated on two values, 36.1 cm and 36.2 cm only.
(c) SSensitivity
If we look at a ruler, we will observe that there are two scales ăă the
centimetre (cm) and millimetre (mm) scales. We can state that the
millimetre (mm) scale is more sensitive than the centimetre scale as
instruments with smaller divisions on the scale are more sensitive.
The sensitivity of a measuring instrument can be compared between
different measuring instruments.
Some examples:
(i) A ruler can measure to a smallest value of 0.1 cm, a vernier caliper to
a smallest value of 0.01 cm and a micrometer screw gauge to a
smallest value of 0.001 cm. So when we measure the diameter of a
glass rod, we will possibly get 0.8 cm from a ruler, 0.82 cm from a
vernier caliper and 0.823 cm form a micrometer screw gauge. Thus,
the micrometer screw gauge is more sensitive than a vernier caliper
which is more sensitive than a ruler.
(ii) A millimetre is more sensitive than an ammeter as it has a scale
which can measure currents accurately to a smallest value of
1 milliampere. An ammeter can only measure currents to a smallest
value of 1 Ampere only.
(iii) An electronic balance has a smallest value of 0.0001 g, while the
weighing balance has a smallest value of 100 g. Thus, the electronic
balance is more sensitive than a weighing balance.
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X TOPIC 1 MEASUREMENT22
1.2.2 Tools to Measure Length, Mass, Time, Electric
and Temperature
Now let us look at the tools that we can use to measure length, mass, time,
electric and temperature.
(a) Tools for Measuring Length
There are several methods we can use to measure length. A long time ago,
people used parts of their body to measure length. For example, they used
their legs, arms or fingers to measure the length of certain things.
Basically, there are five units of length when using parts of the body as a
measurement: a span, a foot, a cubit, an arm span and a stride (refer to
Figure 1.10).
Figure 1.10: Area of some regular shapes
Source: http://www.ilmoamal.org
Each has its own unique description. For example, the span is the distance
from the tip of the thumb to the tip of the index finger, whereas a foot is the
length of a human foot. Other than that, a cubit is the distance from the
elbow to the tip of the middle finger. In addition, an arm span is the
distance between an adult manÊs hands when the arms are outstretched.
Last but not least, a stride is the distance covered by one long step. Our
Is the diamond yours?
A friend asks to borrow your diamond for a day to show her family. You
are a bit worried, so you carefully have your diamond weighted on a
scale which reads 8.17 grams. The scale accuracy is claimed to be 0.05
grams. The next day, you weigh the returned diamond again, getting 8.09
grams. Is this your diamond?
Source: Giancolli (1998)
ACTIVITY 1.4
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TOPIC 1 MEASUREMENT W 23
ancestors also used terms like a hail (sepelaung) or a boil of rice (setanak
nasi) to describe a distance travelled.
Various tools have been designed so that we can measure length accurately
as the Laser Distance Meter which is designed to measure length up to 100
metres using laser rays. Another common tool to measure length is the
measuring tape. It measures lengths in millimetres (mm), centimetres (cm)
and metres (m). It is often used to measure larger objects (more than 1 m).
In this topic we will to discuss three measuring instruments for length
which is mmetre rule, vernier caliper and mmicrometer screw gauge.
(i) Metre Rule
A meter rule is used to measure length of an object in the laboratory.
It can give reading to 0.1 centimetre (cm) or 1 millimetre (mm)
depending on its type.
(ii) VVernier Caliper
A vernier caliper is a measuring tool which can measure the length of
small objects between 0 and 10 cm. It has an accuracy of up to
0.01 cm. Figure 1.11 shows a vernier caliper.
Figure 1.11: Vernier caliper
Source: www.tutorvista.com
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X TOPIC 1 MEASUREMENT24
There are two scales in the vernier caliper:
x Main scale - Main scale is in cm where 1 cm is divided into 10
equal parts, and 1 part is equivalent to 0.1 cm (or 1 mm).
x Vernier scale - Vernier scale is a short scale of 0.9 cm long divided
into 10 equal parts, where 1 part is equivalent to 0.09 cm. Thus, the
difference in length between vernier divisions on the main scale is
0.1cm ă 0.09 cm = 0.01 cm.
A vernier caliper can be used to measure the external and internal
diameter of an object. When we want to measure the outer diameter
of a container, we may use the outside jaws, while we use the inner
jaws to measure the inner diameter of a container or tube.
Steps in reading the vernier caliper:
(i) Determine the zero mark Â0Ê on the vernier scale. Check that
there is no zero error;
(ii) Between the jaws, place the object that you want to measure.
Then, rotate the screw until the jaw is gripping the object, do
make sure that it does not squeeze the object;
(iii) Next, start taking the reading, write down the value shown
on the main scale before or exactly touching the Â0Ê mark on
the vernier scale, for example, 2.1 cm;
(iv) Then, observe the mark on the vernier scale which coincides
with a mark on the main scale. For example, if the mark is at
6, then the value will be 0.06 cm; and
(v) Finally, add up the reading from the main scale with the
reading on the vernier scale to obtain the exact reading.
Total reading
= Reading on the main scale + Reading on the vernier scale
= 2.1 cm + 0.06 cm
= 2.16 cm
25.
TOPIC 1 MEASUREMENT W 25
If the vernier caliper has a zero error, then the readings need to be
corrected through the following formula:
To find out whether there is zero error or not, we must first close the
jaws. If the zero mark on the vernier scale coincides with the zero
mark on the main scale, then the vernier caliper does not have a zero
error (Figure 1.12).
Figure 1.12: A vernier caliper with no zero error
(iii) Micrometer Screw Gauge
If we want to measure the thickness or diameter of a small object, we
may use the micrometer screw gauge. It has an accuracy of up to
0.01 mm or 0.001 cm.
There are a few structures in a micrometer screw gauge ăă the anvil,
spindle, sleeve, thimble and ratchet. See Figure 1.13.
x Anvil and Spindle ă Used to grip the object that we want to
measure.
x Sleeve ă Used to determine the reading on the sleeve by referring
to the scale on the thimble.
x Thimble ă Thimble is actually connected to the graduated sleeve.
It can be rotated in order to tighten the anvil and spindle. One
revolution of the thimble will give 0.5 mm gap between the anvil
and spindle. The scale on the thimble has 50 equal divisions and
every division is 0.5/50 mm or 0.01 mm as we turn the thimble.
26.
X TOPIC 1 MEASUREMENT26
x Ratchet ă We rotate the ratchet for fines adjustment so as to exert
the correct amount of pressure on the object that we want to
measure.
If the micrometer screw gauge has a zero error, then the readings
need to be corrected through the following formula:
Figure 1.13:
Source: http://www.cyberphysics.co.uk/practical/skills/micrometer.htm
Procedure in using the micrometer screw gauge:
(i) Between the anvil and spindle, place the object that you
want to measure;
(ii) Grip the object gently with the anvil and spindle by rotating
the thimble; and
(iii) We may rotate the ratchet, but as soon as the first „clickÊ
sound is heard we should stop. This is because the „click‰
sound tells us that the anvil and spindle are gripping the
object gently without applying any pressure on it.
27.
TOPIC 1 MEASUREMENT W 27
(b) TTools for Measuring Mass
Imagine that you are now at the fish market. You see many different kinds
of fish sold at the stalls. Some are big and some are small. Each kind of fish
is sold at different prices. Some are cheaper while others are more
expensive. The price of the fish is not based only on its type but also on its
mass. As we have discussed in the previous section, the higher the mass of
the fish, the higher the price. The fishmonger will usually use a specific tool
to measure the mass of the fish. It is called a bbalance.
In general, the mass of an object can be measured using a balance. There
are several types of balance as shown in Figure 1.14, Figure 1.15 and Figure
1.16.
Both ruler and measuring tape are useful for measuring length or
distance. However, sometimes, one tool is more suitable than the other
depending on what kind of objects we want to measure. Based on this
assumption, fill in the following table.
Length Measured Tool Unit
Examples
Length of paper clip
Examples
Ruler
Examples
mm
Length and height of a refrigerator m
Length and width of a badminton court Measuring tape
Height of a classmate
Circumference of a ball
Height of a cat
Length of a necktie
Circumference of a marble
Height of a rambutan tree
SELF-CHECK 1.2
29.
TOPIC 1 MEASUREMENT W 29
In a formal setting like in the laboratory, a lever balance is used to measure
an objectÊs mass. Besides the above mentioned balances, there is also
another type of balance called ttriple-beam balance which is used to find the
mass of various objects (see Figure 1.17) in a laboratory.
Figure 1.17: Triple-beam balance
Source: http://www.southwestscales.com
When we use triple-beam balance, the objects are placed on the scale and
then we move the weights on the beams until we get the lines on the right-
side of the scale to match up. Once we have balanced the scale, we have to
add up the amounts on each beam to find the total mass.
Steps in using triple-beam balance to measure mass:
(i) Place the objects on the scale;
(ii) Slide the large weight to the right until the arm drops below the
line. Move the rider back one groove. Make sure it „locks‰ into
place;
(iii) Repeat this process with the top weight. When the arm moves
below the line, back it up one groove;
(iv) Slide the small weight on the front beam until the lines match up;
and
(v) Add the amounts on each beam to find the total mass to the
nearest tenth of a gram.
30.
X TOPIC 1 MEASUREMENT30
(c) Tool for Measuring Time
Stopwatch
We can use a stopwatch to measure a short period of time. Hence, a
stopwatch is usually used in a sports event or in a laboratory. On the
middle upper part of an analogue stopwatch, there is a knob. We press the
knob when we want to start the stopwatch. We need to press the knob a
second time in order to stop the watch. In order to restart again, we press
the knob for the third time. Alternatively, we can use digital stopwatch
which often have more features.
Figure 1.18: Reading in a triple-beam balance
Source: www.regentsprep.org
Based on the reading in Figure 1.18, what would be the mass of the
object measured in the picture?
_______ + ______ + _______ = ________ g
SELF-CHECK 1.3
There are many types of balances, such as lever, compression and
electronic. Search the Internet to find out more about these. You may
search for more information on their:
(a) Attributes;
(b) Functions and usefulnesses; and
(c) Advantages and disadvantages.
ACTIVITY 1.5
31.
TOPIC 1 MEASUREMENT W 31
(d) TTools for Measuring Electric Current
There are two tools that can be used to measure electric current . They are:
(i) Ammeter
An ammeter is used to measure the quantity of electric current. The
SI unit of electrical current is amperes (A). There are more sensitive
types of ammeter, which are the milliamperes (mA) and the
microamperes (ȝA).
In order to measure the current, we need to connect the ammeter in
series. We have to make sure that the positive terminal of the battery
is connected to the positive terminal of the ammeter and vice versa in
order to measure the electric current. The deflection of the ammeter
pointer shows the value of the current flowing through the circuit.
The pointer of the ammeter will deflect slightly below the zero mark
if the connection of the circuit is wrong.
1 ampere = 1,000 milliamperes (mA)
1 milliampere (mA) = 1,000 micoramperes (ȝA)
(ii) VVoltmeter
We use a voltmeter to measure the potential difference (voltage),
which is known as the difference in electrical charges between two
points in electric circuit. The SI unit of voltage is volt (V). Note that in
connecting a voltmeter, we should connect parallel across the battery
or other electrical components in a circuit. For example, let us refer to
Figure 1.19.
Figure 1.19: An electric circuit
The deflection of the voltmeter pointer shows the value of the voltage
across the bulb.
32.
X TOPIC 1 MEASUREMENT32
(e) TTool for Measuring Temperature
Thermometer
We use a thermometer to measure temperatures accurately. Usually we use
mercury thermometers to measure temperatures. A thermometer has its
own special sealed tube which contains either mercury or alcohol. Both
liquids are sensitive and will expand when they are heated and contract
when they are cooled. Usually, a dye is added to the alcohol to make it easy
to read the scales.
Temperature is proportional to the average kinetic energy of molecular
motion in a substance. Thus, when a thermometer is in contact with the
object whose temperature we wish to find, energy will flow between the
two media until their temperatures are equal and thermal equilibrium is
established. By reading the scales on the thermometer, we will know the
temperature of an object. A thermometer should be small enough and must
not alter the temperature of the object we are measuring.
There are many types of thermometers. The most commonly used
thermometers are:
(i) Laboratory thermometer
This thermometer is used specifically in the laboratory. It is used to
measure temperature when an experiment is being done in the
science laboratory (see Figure 1.20). The normal reading scale is from
-100C to 1100C.
Figure 1.20: Laboratory thermometer
Source: http://www.northernbrewer.com
33.
TOPIC 1 MEASUREMENT W 33
(ii) Clinical Thermometer
This thermometer is used by medical doctors to measure the
temperature of people. A healthy person should have a body
temperature of 37oC. This thermometer is designed to have a narrow
constriction in the tube to prevent the mercury from returning to the
bulb after it is taken out from the mouth. A sharp jerk is required to
make the mercury go back to the bulb.
Measuring Temperature and Correct Technique to use the Thermometer
In order to measure temperature using a thermometer in the correct
manner, hold the thermometer vertically. The eyes should be at the same
level as the curved surface of the mercury in the capillary tube of the
thermometer.
By getting accurate information about the temperature of an object, it will
tell us how cold or hot the object is. In everyday life, we often deal with
things related to temperature. For instance, if we want to eat instant
noodles, we need to boil water until it reaches a certain degree. Do you
know what temperature indicates the heated water has reached its boiling
point? The next activity will deal with measuring the temperature of water
when it is heated.
Measuring temperature of water when it is heated
Materials:
Bunsen burner, thermometer, beaker, retort stand, tripod stand,
stopwatch, wire gauze, distilled water.
Steps:
Place a wire gauze on a tripod stand and a beaker containing 100ml of
water on the wire gauze. Heat the water slowly with the Bunsen burner.
Read the temperature of the water every 30 seconds. Continue heating
until the water boils. Record the readings in the table below.
Time (Seconds) 30 60 90 120 150 180 210 240
Temperature (oC)
Draw a graph on a piece of paper to show the relationship between the
time and temperature of water.
ACTIVITY 1.6
34.
X TOPIC 1 MEASUREMENT34
GRAPH TECHNIQUE
In this subtopic, we will discuss on how to present data in a table, draw graph
and analyse graph.
1.3.1 Table of Data
Data is arranged so that it can be presented systematically. In order to ensure the
tidiness of the data, we may present the data in a table as shown in Table 1.7:
Table 1.7: How We Can Present Data in a Table
Name of the manipulated variable
(symbol, unit)
Name of the responding variable
(symbol, unit)
1st reading,
A
2nd
reading, BB
Average reading,
(A+B)/2
At least five sets of readings for
each table, decimal places
according to the sensitivity of the
instrument.
Readings must be consistent in
decimal places.
20
22.9
19.66
1.3
Avoid
inconsistent
decimal
places
Measuring the water when it is cooled
Steps
After the water has been boiled, remove the water from the Bunsen
burner. Let the water cool naturally to room temperature. Record the
temperature of the water every thirty seconds. Record the readings in the
table below.
Time (Seconds) 30 60 90 120 150 180 210 240
Temperature (oC)
Based on the information, draw a graph on a piece of paper to show the
relationship between the time and the temperature of the water.
ACTIVITY 1.7
35.
TOPIC 1 MEASUREMENT W 35
For example,
Length of the
Thread, l (cm)
Time Taken for 20 Complete Circulations, t (s)
t1 t2 taverage
10 20.2 20.4 20.3
20 19.9 19.9 19.9
30 19.7 19.8 19.8
40 19.0 19.0 19.0
50 20.0 20.1 20.1
60 19.5 19.5 19.5
1.3.2 Drawing Graph
In order to analyse the results of an experiment, we may use a graphical method.
The relationship between two physical quantities is shown through a graph, such
as the graph of time against length shows the relationship between the length of
a pendulum and the period of oscillation.
A Step-by-step Guide to Draw a Graph
(a) DDetermine the Axes (see Figure 1.21).
Figure 1.21: Determining the axes in a graph
36.
X TOPIC 1 MEASUREMENT36
(b) DDetermine the Scale of the Graph
We use scale to fit our data into the graph, and we may use the unit of
representation such as:
1cm represents 2 units (1 cm: 2 units),
2cm: 5 units, or
2cm: multiplication of 10 units.
But, avoid using odd scales like 1cm: 3 units and 1 cm: 9 units. This will
lead to some difficulties when we want to take readings from the graph.
(c) PPlot the Readings
Plotting the readings is a process where we transfer the data into the graph.
It is best to use a sharp pencil when drawing. A cross (X) is used to
represent the point of a graph. A graph should contain at least five points.
Figure 1.22: Example of a good graph
(d) JJoin the Points
In a straight line graph, one should try to join the points with the following
criteria. If possible, the line should:
(i) Pass through as many points and any one of the axis;
(ii) If the points cannot fit into the line, the number of the points above
and below the line should be approximately the same; and
(iii) Be smooth.
A good example of graph is shown in Figure 1.22.
37.
TOPIC 1 MEASUREMENT W 37
(e) DDetermine the Title of the Graph
A good graph will always contain the title of the graph which is written on
top of the graph by the following form:
A graph of responding variable against manipulated variable
For example: A graph of time against length
1.3.3 Analysis of Graphs
We can analyse a graph by finding its gradient.
The gradient of the graph can be determined by the following steps:
Pick two points that are far apart. Draw a right-angled triangle as shown in
Figure 1.23.
Figure 1.23: A right-angled triangle
Calculate the value of ’’'y (difference in the y-coordinates) and 'x (difference in
the x-coordinates).
'
'
2 1
2 1
, andy y y
x x x
38.
X TOPIC 1 MEASUREMENT38
'
'
2 1
2 1
Gradient
y
x
y y
x x
For example, if the two selected points are (s, 4) and (20, 24), then
3
3
27 4
The Gradient
20 5
2
15
1.5
PRACTICAL INVESTIGATIONS IN PRIMARY
SCIENCE CURRICULUM
In the primary science, measurements are taught at the Year 3 level. Pupils were
required to measure various physical properties such as length, area, volume,
mass and time using non-standard and standard measurements.
1.4.1 Measurement of Length
In the measurement of length, students were required to suggest and do
activities on different ways that they can measure length using non-standard
measuring tools such as using their hands or parts of their body. Other than
using parts of the human body, we can use other tools for measurement such as a
book, pen or box. These things are more uniform.
For example, take your own eraser and use it to measure this book. The diagram
below shows how an eraser can be used to measure the length of a book (see
Figure 1.24).
1.4
39.
TOPIC 1 MEASUREMENT W 39
Figure 1.24: Measuring length of a book using an eraser
Based on Figure 1.24, we can measure the length of the book by counting how
many erasers cover the length of the book. This diagram shows that the length of
the book is approximately equal to three times the length of the eraser.
Pupils were then required to measure length using standard measuring tools
such as measuring tape. The measuring tape will have standard units like
millimetres (mm), centimetres (cm) and metres (m). Another example is a ruler,
which measures lengths in millimetres (mm) and centimetres (cm). The
measurements will be recorded in a graphic organiser.
1.4.2 Measurement of Area
Knowing length, pupils need to apply the information to calculate area. They will
be given activities that will lead them to understand the concept area. For
example, a few 1cm u 1cm squares will be used to produce a 4 cm u 4 cm square
and 8 cm u 8 cm square, and make comparisons between the numbers of 1 cm u
1 cm squares that can make up the two bigger squares. Pupils were then required
to calculate the area using standard units in the metric system and use formulae
like area = length u width.
1.4.3 Measurements of Volume
Objects in the solid and liquid form are considered for the measurements of
volume. For solids, the suggested activity is to arrange a 1 cm3 cubes into a
bigger cube for example, a 4 cm3 cube or a 2 cm u 4 cm u 8 cm cuboid. Students
compare the total number of cubes that can fill up the bigger cube/cuboid to
40.
X TOPIC 1 MEASUREMENT40
discuss volume, or use the formula, volume = length u breadth u height to
calculate volume and state their answers in standard units.
Both the non-standard ways to measure volume such as using cups, cap of a
bottle and standard ways such as using beakers, measuring cylinders are used to
give pupils the idea on volume. Pupils make measurements of liquids given by
using different standard measuring tools and give their answers in the standard
metric units.
1.4.4 Measurement of Mass
Various tools for measuring mass are introduced in this topic such as lever
balance. Non-standard measurements can be used by comparing the mass of the
object measured with the mass of a book, glass or any available objects. Pupils
need to know the standard units for mass in the metric system such as mg, g and
kg. They will take measurements using the correct technique and record the
findings in the form of graphic organisers.
1.4.5 Measurements of Time
Non-standard ways to measure time will be discussed. Some examples are the
swinging pendulum, water dripping or the pulse. Pupils are required to measure
the time taken for an action using this non-standard time measurement
technique. They also need to know that they can only use things that repeat
uniformly to measure time.
The pupils are then required to choose appropriate standard tools to measure
time by using a stopwatch etc. They need to state the measurements in the
standard units for time such as seconds, minute or hour.
x A physical quantity is a quantity that can be measured.
x A base quantity is a physical quantity that cannot be defined in terms of other
physical quantities.
x Derived quantities are produced from the combination of base quantities
through some operation such as multiplication, division or both.
41.
TOPIC 1 MEASUREMENT W 41
x Some derived quantities are area (m2), volume (m3), density (kg/m3) and
velocity (m s-1).
x When we make measurements, there are certain things that we need to know
about the measuring tools that we use so that we can get the best results for
our measurements.
x The three important aspects of a measurement are precision, accuracy and
sensitivity.
x Precision is the ability of the instrument to give consistent readings when the
same physical quantity is measured more than once.
x Accuracy refers to how close is the measured value compared with the actual
value.
x Sensitivity is the ability of detecting small changes in the measured quantity.
x In order to measure the length of a small object between 0 and 10 cm, we may
use the vernier caliper, as it has an accuracy of up to 0.01 cm.
x If we want to measure the thickness or diameter of a small object, we may use
the micrometer screw gauge.
x The mass of an object can be measured using a balance.
x Stopwatch is used to measure a short period of time.
x Voltmeter is used to measure the potential difference (voltage), which is
known as the difference in electrical charges between two points in an electric
circuit.
x Thermometer is used to measure temperatures.
x Graphical method is used to analyse the result of an experiment.
x A graph is analysed by finding its gradient.
42.
X TOPIC 1 MEASUREMENT42
Accuracy
Base quantity
Derived quantity
Graph technique
Precision
SI unit
Sensitivity
Tools
Beyer, B. K. (1997). Improving student thinking: A comprehensive approach.
Boston: Allyn Bacon.
Giancoli, D. C. (1998). Physics: Principles with applications. New Jersey: Prentice
Hall.
Hartman, H. J. (2002). Tips for the science teacher. Thousand Oaks: Corwin Press.
Hewitt, P. G. (1998). Conceptual physics. (8th ed.). Reading: Addison-Wesley.
43.
X INTRODUCTION
The motion of objects such as cars, footballs, joggers or even the motion of
planets and their moons, is an obvious part of our everyday life. Our
understanding of motion was established in the 16th and 17th centuries when
two individuals made important discoveries: Galileo Galilei (1564-1642) and
Isaac Newton (1642-1727).
By the end of this topic, you should be able to:
1. State scalar and vector quantities;
2. Find the resultant of two or more vectors;
3. Define displacement, speed, velocity and acceleration;
4. Describe the graphs of motion;
5. Solve problems related to displacement, speed, velocity and
acceleration;
6. Define Newton Laws of Motion.
7. Relate mass to inertia;
8. Use the Principle of Conservation of Momentum to solve problems;
9. Solve problems related to collisions; and
10. Solve problems related to projectile motion.
LEARNING OUTCOMES
TTooppiicc
22
X Forces and
Motion
44.
X TOPIC 2 FORCES AND MOTION44
Mechanics is the field of physics that studies motion of objects. Mechanics are
divided into two parts called kinematics, which is a description of how objects
move, and dynamics, which describes movements of objects in relation to the
forces acting on them. Several concepts in kinematics and dynamics and their
application in daily life situations will be discussed in this topic.
VECTORS
We have learnt that a physical quantity has a value and a unit attached to it. This
is called the mmagnitude of a physical quantity. However, for some quantities, it
makes more sense if the directions are given as well.
For example, if you want to describe the movement of a car, stating its speed
alone in not enough. It will give a clearer picture when you describe the direction
as well. Thus physical quantities can be divided into sscalar quantity and vvector
quantity based on the information given.
2.1.1 Scalar Quantity
Scalar quantity means that the physical quantity only has mmagnitude but no
direction. Examples of scalar quantities are distance, speed, mass and volume.
Example 2.1:
Distance = 200 m.
Distance is a scalar quantity, 200 is a magnitude and m is a unit.
2.1.2 Vector Quantity
A physical quantity that has both mmagnitude and direction is called a vector
quantity. Examples of vector quantities are displacement, velocity, acceleration
and momentum.
Example 2.2:
Velocity = 70 kmh-1 to the east
Velocity is a vector quantity, 70 is a magnitude mkmh-1 and Âto the eastÊ is the
direction.
2.1
45.
TOPIC 2 FORCES AND MOTION W 45
2.1.3 Resultant and Resolution of Vector
An example of a vector quantity which has both magnitude and direction is
force. A vector quantity is represented by a long arrow whereby the length of the
arrow shows the magnitude of the force and the head shows the direction of the
force (see Figure 2.1).
Figure 2.1: Addition of vector
The force obtained from the addition of two or more forces is called the rresultant
force. Additions of vector quantities such as force must take into account both the
direction and magnitude.
For vectors which are parallel (whether in the same direction or in opposite
directions), the resultant vector can be determined by the sum of every vector
present. Using Figure 2.1, the resultant vector, RR = AA + BB. If the second vector is
in the opposite direction, RR = AA ă BB.
For non-parallel vector quantities, the resultant vector can be determined using
the triangle of forces or the parallelogram of forces.
A single vector can be resolved into two components. This is known as the
resolution of vectors.
Figure 2.2 shows a single vector FF resolved into its two perpendicular
components, FFx and FFy.
Figure 2.2: Resolution of vectors
46.
X TOPIC 2 FORCES AND MOTION46
The horizontal component is Fx = F Cos ș
and the vertical component is Fy = F Sin ș
Example 2.3:
A man pulls a sack of fruits with a force of 140N at an angle of 35À with the floor.
Determine the horizontal and vertical component of the force.
Solution:
Calculate the horizontal component of the force that causes the sack to be pulled
forward. Thus, cos 35À is considered.
Horizontal component, Fx = 140 cos 35À
Calculate the vertical component of the force that causes the sack to be pulled
forward. Thus, sin 35À is considered.
Vertical component, Fy = 140 sin 35À
KINEMATICS
In this subtopic, we will look at displacement, speed, velocity and acceleration.
This is followed by linear motion, graphs of motion and equation of motion.
2.2
To test your understanding, consider the following quantities listed below.
Categorise each quantity as being either a vector or scalar quantity:
(a) 5 m
(b) 30 ms-1 to the East
(c) 20 degrees Celcius
(d) 256 pound
(e) 5 miles North
ACTIVITY 2.1
47.
TOPIC 2 FORCES AND MOTION W 47
2.2.1 Displacement, Speed, Velocity and Acceleration
Imagine you are visiting a friend who lives several kilometres away from your
home. Whichever route you choose, the starting point and finishing point remain
unchanged (Figure 2.3).
Figure 2.3: Displacement versus distance travelled along a path
Your ddisplacement is the distance directly from the starting point, A directly to
the finishing point, B. So whatever route you take, your displacement from A to
B remains unchanged.
Thus displacement can be defined as the cchange in position of the object.
Displacement is a quantity that has both magnitude and direction, so it is a vvector
quantity.
Distance refers to the length of the path taken. It scalar quantity.
(a) Speed
Speed is a sscalar quantity. It describes the magnitude of how fast or how
slow an object is moving. Speed is defined as the rrate of change of distance
travelled with time.
Distance travelled
Speed =
Time
A car moving along a winding road or a circular track at 80km h-1 is said to
have a speed of 80 kmh-1. Speed is a quantity that has no direction but only
magnitude.
48.
X TOPIC 2 FORCES AND MOTION48
The standard unit for speed is metre per second or m s-1. Conversion of
units to kilometre per hour (km h-1) and centimetres per second (cm s-1) are
also commonly used.
(b) Velocity
Velocity is a vvector quantity. Thus it involves both the magnitude and
direction of the moving object. Velocity is derived from displacement of an
object rather than its distance. It is defined as the rrate of change of
displacement or
Displacement
Speed =
Time
The car in Figure 2.4 has a constant speed of 80km hr-1 as it moves along
the circular track. At every point of the track, such as P and Q, the speed is
the same but velocity v1 and v2 are different. This is because the directions
of the car at P and Q are different as the arrow points at different
directions.
Figure 2.4: Velocity and speed
Velocity can also be measured in the units metre per second (m s-1),
kilometre per hour (km h-1) or centimetres per second (cm s-1).
49.
TOPIC 2 FORCES AND MOTION W 49
(c) AAcceleration
When you reach a highway when driving, you will hit the gas so that the
car will move at a higher velocity. The rate of change of velocity is called
acceleration.
Velocity change
Acceleration =
Time taken
Acceleration is a vvector. The direction of acceleration is the direction of the
velocity change. The unit for acceleration is metre per second per second or
ms-2.
If a car accelerates from 15 ms-1 to 35 ms-1 in 5 s, then the acceleration
1
2
(35 15) ms
a =
5s
= 4 ms
On the other hand, if the car breaks, the velocity may decrease from 30 ms-1
to 20 ms-1 in 5 s. It has a retardation or deceleration of
1
2
(30 20) ms
a =
5 s
= 2m s
The value -2 ms-2 is a negative acceleration or deceleration.
2.2.2 Linear Motion
Linear motion means the movement of an oobject in a straight line. Examples of
linear motions are, a car moving in a straight line, a train moving on a straight
track, a falling coconut and a moving bullet. In linear motion, vector quantities
are treated much like scalar quantity since the direction remain unchanged.
Examples of non-linear motions would be a snake crawling and a roller coaster
ride.
An object moves from rest with a uniform acceleration of 2 ms-2. Find the
velocity of the object after 30 s.
ACTIVITY 2.2
50.
X TOPIC 2 FORCES AND MOTION50
It can be uniform, that is, with constant velocity or non-uniform, that is, with a
variable velocity. Non-uniform motion are further divided into other types of
motions such as constant acceleration motion.
2.2.3 Graphs of Motion
The motion of an object could be represented in a graph to aid understanding.
These would be the displacement-time graph and the velocity-time graph. From
the graphs for linear motion, we can determine:
x The displacement of an object at a specific time;
x The velocity and acceleration of an object; and
x Changes in velocity and displacement at a certain time.
(a) DDisplacement-Time Graph
A displacement against time graph allows us to interpret movement from
the shape of the graph. Figure 2.5 shows displacement-time graphs that
describe several movements of an object. Consider the gradient of the
graphs as the velocity of the object.
Figure 2.5: Examples of displacement-time graphs
51.
TOPIC 2 FORCES AND MOTION W 51
The following describes further the meaning of these graphs:
(i) Figure 2.5(a): As time increases, distance is always the same. Object
is not moving. Gradient of the graph is zero.
(ii) Figure 2.5(b): The distance increases as time increases. Object is
moving with a constant velocity because the gradient
is constant.
(iii) Figure 2.5(c): The distance increases as time increases, gradient of
the graph also increasing. Object is moving with
increasing velocity.
(iv) Figure 2.5(d): The distance increases as time increases, gradient of
the graph decreases. Object is moving with a
decreasing velocity.
(b) VVelocity-Time Graph
A velocity-time graph shows how the velocity of an object changes with
time. TThe gradient of a velocity-time graph represents the acceleration of an
object. We can also calculate the distance travelled by the object by
calculating the area under the velocity-time graph.
Figure 2.6: Examples of velocity-time graphs
52.
X TOPIC 2 FORCES AND MOTION52
The following describes these graphs further:
(i) Figure 2.6(a): As time increases, velocity is always the same. Object
is moving with a constant velocity. Gradient of the
graph is zero.
(ii) Figure 2.6(b): The velocity increases as time increases. Object is
moving with a constantly increasing velocity, or
constant acceleration. The gradient of the graph, that
is, the acceleration is constant.
(iii) Figure 2.6(c): The velocity increases as time increases, gradient of
the graph also increases. Object is moving with
increasing acceleration.
(iv) Figure 2.6(d): The distance increases as time increases, gradient of
the graph decreases. Object is moving with a
decreasing acceleration.
Example 2.4:
A car is moving along a straight road. Its movement is shown in Figure 2.7.
Figure 2.7: A velocity-time graph of a car
(a) Describe the movement of the car along the straight road.
(b) Find the acceleration of the car at OA, AB and BC.
(c) Find the total distance travelled.
53.
TOPIC 2 FORCES AND MOTION W 53
Solution:
(a) Along OA, the car is moving with an increasing velocity. The acceleration is
constant as the gradient along OA is constant.
Along AB, the car is moving with a constant velocity. The acceleration is
zero as the gradient at AB is zero.
Along BC, the car is moving with a decreasing velocity. The acceleration is
constant but has a negative value. The car is decelerating.
(b) The acceleration of the car in a velocity-time graph is the gradient.
The mathematical formula for gradient is
2 2
2 2
=
y y
m
x x
OA
1
2
OA
(15 0)m s
m = = 0.75m s
(20 0)s
The car is accelerating at 0.75m s-2.
AB
1
3
AB
(15 15)m s
m = = 0
(50 0)s
The car is not accelerating. It is moving with a constant velocity.
BC
1
2
5
BC
(0 15)m s
m = = 1.5
(60 0)s
m s
The car is decelerating at 1.5m s-2.
(c) To find the distance travelled in a velocity-time graph, find the area under
the graph. This total distance travelled by the car is:
Total area under the graph = ó(15 u 20) + (50 ă 30)15 + ó(60 ă 50)15
= 675m
54.
X TOPIC 2 FORCES AND MOTION54
2.2.4 Equation of Motion
Imagine a Formula 1 race car driving with an initial velocity, uu, accelerates with a
constant acceleration, a, and achieves a final velocity, v. The displacement of the
race car is ss. The four variables (u, vv, aa, ss) are different but related. The
relationship of these four variables with one another can be shown in the
equations of linear motion.
From the definition of acceleration
=
v u
a
t
Where a = acceleration, u = initial velocity, v = final velocity, t = time.
Hence v = u + at (1)
Displacement, s = Average velocity u Time
=
u
2
u v
t
Substituting Equation (1),
at
t
u
( )
=
2
u u
s
Hence s = ut + 1/2 at2 (2)
Also,
55.
2
2
1
2
1
2
=
v at at
s v at
s
(3)
From Equation (1),
v u
a
t
u=
2
u v v u
s
a
56.
TOPIC 2 FORCES AND MOTION W 55
Hence
2 2
( )
2
v u
a
s
2as = v2 ă u2
Hence v2 = u2 + 2as (4)
From these equations, we can derive:
v = u + at
s = ut + 1/2 at2
v2 = u2 + 2as
Example 2.5:
The driver enters a car which is parked beside the road. The driver starts the
engine and then accelerates with an acceleration of 5.0m s-2. Calculate the
velocity and distance travelled by the car after 7s.
Solution:
Initial velocity, u = 0m s-1
Acceleration, a = 5.0m s-2
Time, t = 7s
Using equation
v = u + at
= 0 + (5.0 ¯ 7)
= 35m s-1
S = ut + 1/2 at2
= (0 ¯5) + 1/2 (5.0 ¯ 72)
= 122.5m
Example 2.6:
In the long jump event, Razak was running at a velocity of 3m s-1 towards the
long jump pit. He needed to achieve a velocity of 6m s-1 after covering a distance
of 5m before lifting himself off the ground from the jumping board. Calculate the
required acceleration for Razak to be able to do so.
57.
X TOPIC 2 FORCES AND MOTION56
Solution:
u = 3 m s-1, v = 6 m s-1; s = 5m
Using equation
v2 = u2 + 2as
62 = 32 + 2a(5)
10a = 36 ă 9
= 27
a = 27/10 = 2.7m s-2
Free fall is an example of linear motion under constant acceleration. In this
special case, a = g which is the constant accelaration due to gravity. g on earth, g
ia approximately 9.8 ms-2 .
DYNAMICS
In this subtopic, we will look at three types of Newton's Laws of Motion;
Newton's First Law, Newton's Second Law and Newton's Third Law.
2.3.1 Newton’s Laws of Motion
Newton's First Law states that when an object is stationary or moving with a
constant velocity, it will remain as such unless an external force acts on it. This
law is also commonly known as the llaw of inertia.
Thus from NewtonÊs First Law:
(a) An object which is at rest will remain stationary;
(b) An object which is moving with constant velocity will continue moving,
unless acted upon by external forces; and
NewtonÊs Second Law states that the rate of change of momentum of an object is
proportional to the resultant force F which acts on the object. The change in
momentum is at the same direction as the resultant force.
2.3
58.
TOPIC 2 FORCES AND MOTION W 57
( )
d
F p
dt
where is p = momentum
( )
d
F mv
d
If mess is constant,
dv
F m
dt
F ma
NewtonÊs Second Law produces the equation
F = ma
where F = resultant force in Newton
m = mass in kg
a = acceleration
Example 2.7:
It is easier to pull a small rock compared with a big rock when you use the same
force to pull the rocks (see Figure 2.8).
Figure 2.8: Example of NewtonÊs Second Law
59.
X TOPIC 2 FORCES AND MOTION58
From F = ma,
(a) When the mass of the rock is big, bigger force is needed to move or stop the
object.
(b) When the mass of the rock is increased for the same force, its acceleration
decreases.
NewtonÊs Third Law states that when two objects interact, they exert equal and
opposite forces on each other.
If you release the air from a balloon, you will notice that the balloon will move in
the opposite direction of the air that rushes out of it. The action of the air rushing
out of the balloon produces an equal but opposite reaction of the balloon, thus
the balloon moves up (see Figure 2.9)! This force is known as Thrust.
Figure 2.9: Example of NewtonÊs Third Law
2.3.2 Mass and Inertia
All objects have mass. The mass of an object is the quantity of matter contained in
the body. A bigger mass will have a bigger inertia. A smaller mass will have a
smaller inertia. What is inertia? LetÊs look at the following phenomenon:
John is a boxer. One day, he tried to push a big punching bag which was
hanging stationary. John noticed that it was difficult to get the punching bag
to move. When the bag finally started swinging, John then tried to stop the
motion of the swinging punching bag. He noticed that it was difficult to stop
the punching bag when it was in motion.
60.
TOPIC 2 FORCES AND MOTION W 59
The above phenomenon can be explained by the concept of iinertia. The swinging
punching bag will continue to maintain its swing, hence the boxer feels that it is
difficult to stop it. This property of matter that causes it to resist any change in its
motion is known as inertia. A force is required to overcome the inertia of an
object or body.
The concept of inertia is related to NewtonÊs First Law of Motion. Consider the
two examples shown in Figure 2.10.
Figure 2.10: Examples of inertia in our daily life
Figure 2.10(i) shows the driver of a car thrown out of the car when the car hits the
wall. He was moving with the same speed of the car before the collision, so when
the car hit the wall, his inertia kept his body moving at the same speed. Thus, if
he fails to fasten his seat belt, he will fall forward.
Figure 2.10(ii) shows a coin placed on the surface of a card on a glass. When the
card is flicked, the coin falls into the glass. The inertia of the coin kept it in a
stationary position, so when the card moves, it falls downwards due to gravity.
2.3.3 Momentum
The product of mass and velocity is known as mmomentum.
Momentum = Mass u Velocity
p = mv
61.
X TOPIC 2 FORCES AND MOTION60
Momentum is a vvector quantity (has both direction and magnitude). The
direction of the momentum follows the direction of the velocity. The right
direction is denoted by the „+‰ sign while the „-„sign denotes the left direction.
The SI unit of momentum is kgm s-1 or Ns. Momentum increases when:
(a) The mass increases;
(b) The velocity increases; and
(c) Both of the mass and velocity increase.
The study of the concept of momentum is important for predicting the motion of
an object after the occurrence of a collision.
This means that the total momentum before the collision is equal to the total
momentum after the collision (this means that it has been conserved) if there are
no external forces acting on the system.
Momentum = Mass u Velocity
P = mv
2.3.4 Collision
There are two types of collisions: eelastic collision and iinelastic collision.
Collisions are often classified based on what happens to the kinetic energy of the
colliding objects. A collision in which the total kinetic energy is the same before
and after is called eelastic.
When the final kinetic energy is less than the initial kinetic energy, the collision is
said to be inelastic. A stick-together collision is a perfectly inelastic collision.
Collisions in one dimension are collisions that occur in a straight line. Suppose a
car of mass, m1 is travelling along a road at speed u1 towards a second car of
mass m2 that is moving with an initial velocity u2. What will happen when the
first car hits the second car?
The PPrinciple of Conservation of Momentum states that the total linear
momentum of a closed system of bodies is cconstant.
62.
TOPIC 2 FORCES AND MOTION W 61
The principle of conservation of momentum states that the total momentum in a
closed system is constant or that is, total momentum before the collision is equal
to the total momentum after the collision.
m1u1 + m2u2 = m1v1 + m2v2
If the collision is an elastic collision, then:
2 2 2 2
1 1 1 2 1 1 2 2
1 1 1 1
2 2 2 2
M U M U M V M V
2.3.5 Projectile Motion
If you throw a ball into the air at any angle, the ball will follow a curved path
(Figure 2.11a). The exact path of the ball is determined by its initial speed and
angle but gravity acts on the ball to pull it downwards. This kind of motion is
called the pprojectile motion, where we study the motion of an object in two
dimensions.
If the effects of air resistance are neglected, the path traced by the projectile will
be a parabola. The shape of the curve can easily be seen by looking at water
projected from a hose (Figure 2.11b).
Figure 2.11: Examples of projectile motion
There are three vector parameters: displacement, velocity and acceleration, which
are used to describe and analyse the motion of the object. As no vector can have
any effect in a direction perpendicular to itself, the horizontal and vertical
components of the parameters of the motion are completely independent of each
other. Thus, to solve any problem regarding projectile motion, it is considered as
two separate, independent motions in the horizontal and vertical components as
if they are one-dimensional motion. We can use the equation of motion to solve
problems in projectile motion.
63.
X TOPIC 2 FORCES AND MOTION62
For aany projectile motion, its vvertical component is at constant acceleration,
g while its horizontal component is at constant speed.
Figure 2.12 shows two balls dropped from the height, one vertically downwards
and the other ball projected horizontally outwards.
Figure 2.12: Multiple exposure photograph showing two balls falling
Source: http://www.chsdarkmatter.com
Observe that the vertical distance are the same for both balls. This distance
represents the time taken for the ball to fall, indicating that an object whether
projected vertically downwards or horizontally will reach the ground at the same
time.
Figure 2.13: A ball rolls down a table
Source: http://francesa.phy.cmich.edu
64.
TOPIC 2 FORCES AND MOTION W 63
The ball in Figure 2.13 rolls down the table of 0.8m height with an initial velocity
of 10m s-1 in the horizontal direction. It will continue to move with the constant
10m s-1 horizontal velocity (ux and vx) until it reaches the ground. As the ball was
rolling on the table initially, there is no initial vertical velocity, uy.
We can categorise the information given according to the two components as
given in Table 2.1.
Table 2.1: Two Components of Figure 2.13
Element VVertical Component HHorizontal Component
Initial velocity, u
Final velocity
Acceleration, a
Displacement, s
Time to reach the ground, t
uy = 0
vy
gravity, g = - 10m s-2
- 0.8m (downwards)
t
ux = 10m s-1
vx = 10m s-1
Constant velocity, a = 0
x m from the edge of the table
t
Using the equations of motion, consider the vertical motion. Use negative signs
for downward movements.
Using the equation sy = uyt + óat2
- 0.8 = (0 u t) + (ó x ă 10 u t2)
5t2 = 0.8
t = 0.4s
For the horizontal motion, we can use t = 0.4s to calculate the horizontal
displacements
Using the equation sx = uxt + óat2
= (0.8 u 0.4) + (ó u 0 u 0.42)
= 0.32m
65.
X TOPIC 2 FORCES AND MOTION64
x Scalar quantity means that the physical quantity only has magnitude.
x A physical quantity that has both magnitude and direction is called a vector
quantity.
x The force obtained from the addition of two or more forces is called the
resultant force.
x A single vector can be resolved into two components which is known as the
resolution of vectors.
x Displacement can be defined as the change in position of the object. It is a
quantity that has both magnitude and direction; a vector quantity.
Try solving this problem:
A stone thrown horizontally at a speed of 24m s-1 from the top of the cliff
takes 4.0s to hit tho the sea. Calculate the height of the clifftop above the
sea, and the distance from the base of the cliff to the point of impact.
ACTIVITY 2.3
1. Which image in Figure 2.6, represents a free fall?
2. Friction is on important force in our daily live. Give two examples
where fiction is important?
3. A 40 kg boy on a roller skate is standing still when he catches a 0.5
kg ball thrown at him. If the speed of the ball is 30 ms-1, how fast
does he move backward?
Explain why he moves backward?
4. A football kicked by a player leaves the ground at 10 ms-1 at angle
30q above the ground. Find the range at the flight time of the ball.
SELF-CHECK 2.1
66.
TOPIC 2 FORCES AND MOTION W 65
x Speed is defined as the rate of change of distance travelled with time; a scalar
quantity.
x Velocity is defined as the rate of change of displacement; a vector quantity.
x Acceleration is the rate of change of velocity; a vector quantity.
x Linear motion means that the motion occurs in a straight line.
x Motion graphs are used to describe the motion of object.
x The gradient of the displacement-time graph represents the velocity of the
object.
x If the displacement-time graph is a curve graph, an increasing gradient will
mean increasing velocity.
x A velocity-time graph will tell how the velocity of an object will change with
time.
x The gradient of the velocity-time graph represents the acceleration of the
object.
x The area under the velocity-time graph represents the distance travelled by
the object.
x The four basic linear motion equations are:
(a) v = vo + at
(b) s = ut + ó at2
(c) v2 = vo
2 + 2as
(d) s = ó (vo + v) t
where v = final velocity; vo = initial velocity; a = acceleration; t = time; and
s = displacement.
x NewtonÊs Laws of Motion consist of three laws.
x Newton's First Law states that when an object is stationary or moving with a
constant velocity, it will remain as such unless an external force acts on it.
67.
X TOPIC 2 FORCES AND MOTION66
x NewtonÊs Second Law states that the rate of change of momentum of an
object is proportional to the resultant force which acts on the object.
x NewtonÊs Third Law states that when two objects interact, they exert equal
and opposite forces on each other.
x All objects have mass. A bigger mass will have a bigger inertia. A smaller
mass will have a smaller inertia.
x The momentum of an object is defined as a vector quantity such that:
Momentum, p = Mass, m ¯Velocity, v.
x There are two types of collisions: elastic collision and inelastic collision,
which are often classified based on what happens to the kinetic energy of the
colliding objects.
x A projectile is any object that has been projected at some angle into the air
where the subsequent motion of the object is a curved path.
x For any projectile motion, its vertical component is at constant acceleration, g
while its horizontal component is at constant speed.
Acceleration
Displacement
Elastic collision
Equation of motion
Force
Graphs of motion
Horizontal components
Inelastic collision
Kinematics
Momentum
NewtonÊs laws of motion
Projectile motion
Range
Resultant and resolution of vectors
Scalar quantity
Speed
Vector quantity
Velocity
Vertical components
68.
TOPIC 2 FORCES AND MOTION W 67
Breithaupt, J. (2000). Understanding physics for advanced level. Cheltenham:
Nelson Thornes.
Cutnell, J. D., Johnson, K. W. (1998). Physics (4th ed.). New York: John Wiley
Sons.
Giambattista, A., Richardson, B. M., Richardson, R. C. (2004). College physics.
New York: McGraw Hill.
Giancoli, D. C. (1998). Physics: Principles with applications. New Jersey: Prentice
Hall.
Hartman, H. J. (2002). Tips for the science teacher. Thousand Oaks: Corwin Press.
Hewitt, P. G. (1998). Conceptual physics (8th ed.). Reading: Addison-Wesley.
Young, H. D., Freedman, R. A. (2000). University physics with modern physics
(10th ed.). USA: Addison-Wesley Longman.
69.
X INTRODUCTION
We have discussed motion in terms of velocity and acceleration. But why do
objects move? What makes an object which is at rest move? What causes a car to
accelerate or decelerate? Each case mentioned involves force. We experience
force in most of the things that we do. Any push or pull on an object requires
force, like pushing a trolley at the supermarket or pulling your luggage bag at the
airport.
Force is also involved when a motor lifts an elevator or a hammer hits a nail or
even when the leaves of a tree move when the wind blows. An object falls to the
ground due to a certain force called the force of gravity. Force, however, does not
always give rise to motion. You may have experienced pushing a car very hard
and it still does not move!
By the end of this topic, you should be able to:
1. Define force and its types;
2. Describe six effects of force;
3. State the relationship between force, mass and acceleration (F = ma);
4. Describe gravity;
5. Relate work to power;
6. Differentiate between potential energy, kinetic energy and energy
conservation; and
7. Discuss simple and compound machines.
LEARNING OUTCOMES
TTooppiicc
33
X Force and
Energy
70.
TOPIC 3 FORCE AND ENERGY W 69
In order to understand force, let us look at two important elements associated
with it ă pushing and pulling.
Whenever there is iinteraction between two objects, there is a force upon each of
the objects. When the interaction ceases, the two objects no longer experience the
force. Forces only exist as a result of an interaction.
Do you know that there are many forces acting on you all of the time? One
example is the force of gravity. You might not be aware of this but this force
exists with you all the time. This can be felt if you are falling ă you feel and sense
that something is pulling you down. On the other hand, if you are standing
perfectly still on the floor, the floor is pushing up on you just as hard as gravity is
pulling you down!
TYPES OF FORCES
Now, let us get to know how many types of forces there are. There are many
types of forces around us. However, in this module, we will only discuss four ă
frictional, mmagnetic, ggravitational and eelectrostatic. Let us look at them one by
one.
3.1.1 Frictional Force
What can you say about friction? Do you know what it stands for? Friction acts
when there is contact between two surfaces. Friction is the resistance between
two surfaces that are in contact with each other. Friction is greater when an object
is on a rough surface rather than on a smooth surface.
How about frictional force? Do you know what it is?
Can you give some examples of friction? Let us look at Figure 3.1 for two
examples of friction.
Frictional force is a force that opposes the direction of motion and acts in the
opposite direction of the motion.
3.1
A force is a ppush or pull upon an object as a result of the object's interaction
with another object.
71.
X TOPIC 3 FORCE AND ENERGY70
Figure 3.1: Examples of friction
Below are explanations for the examples in Figure 3.1:
(a) If we skid a book across the surface of a desk, then the desk exerts a friction
force in the opposite direction of its motion. This stops the movement of the
book after a while.
(b) When we want to slow a bicycle quickly, we need to have a lot of friction
between the brake blocks and the wheels as they touch.
3.1.2 Magnetic Force
I am sure you know what a magnet is. How about magnetic force?
A magnet also exerts force on another magnet. The force that exists between two
magnets can be a force of attraction or repulsion. Figure 3.2 shows a simple
experiment to study the force that magnets exert on each other.
72.
TOPIC 3 FORCE AND ENERGY W 71
Figure 3.2: Two magnets exerting force on each other
3.1.3 Gravitational Force
Another type of force is gravitational force. Gravity holds objects in place on the
EarthÊs surface. As we ascend from the EarthÊs surface, the pull of gravity
decreases. It is gravity which causes all objects to have weight. Thus, the weight
of an object is the force of gravity pulling that object down. Can you think of any
example?
One example is when you kick a ball into the air; it will fall back to the ground.
This shows that gravitational force has pulled the ball back to the EarthÊs surface.
3.1.4 Electrostatic Force
The last type of force for you to learn is electrostatic force. Let us look at its
definition. The attractive and repulsive interaction between any two charged
objects is called an eelectric force. One simple example of this force is the plastic
comb. After running a plastic comb through your hair, you will find that the
comb attracts bits of paper (see Figure 3.3).
Figure 3.3: Bits of papers get attracted to a comb
73.
X TOPIC 3 FORCE AND ENERGY72
The attractive force is often strong enough to suspend the paper from the comb.
Try this out.
The same effect occurs with other rubbed materials, such as glass and hard
rubber. When materials behave this way, they are said to have become
electrically charged and the force is called eelectrostatic force.
Effects of Forces
As we know, we cannot see force. However, we can see and sometimes feel the
effects of forces. Do you know that there are six effects of forces? Let us look at
these effects as explained in Table 3.1.
3.2
Why does a parachutist fall more slowly to the ground when
he uses a larger parachute? Explain.
ACTIVITY 3.1
For each situation listed, name the type of force at work.
(a) A magnet pulls a nail out of a box.
(b) A test tube, after being rubbed with wool, attracts small pieces of
cork particles.
(c) A man pushes a stone up a hill.
(d) A ball stops rolling.
(e) A satellite is held in orbit above the Earth.
SELF-CHECK 3.1
74.
TOPIC 3 FORCE AND ENERGY W 73
Table 3.1: Six Effects of Forces
Effect EExample
Move a
stationary
object
You can kick a ball to start off a football game.
Slow down or
stop a moving
object
A parachute can make an object slow down
because of air resistance.
Change the
speed of a
moving object
When you hit a tennis ball, it speeds up.
Change the
direction of a
moving object
You can make a cricket ball change direction by
hitting it with a bat.
Change the
shape of an
object
If you squeeze or kick a football, it will be
compressed. This change may be permanent or
temporary.
Change the
size of an
object
When you squeeze a sponge, its size changes.
75.
X TOPIC 3 FORCE AND ENERGY74
Now, let us get to know interesting facts about force! Here they are:
FORCE FACTS!
(a) Measured in Newton (N).
(b) Usually acts in pairs.
(c) Acts in a particular direction.
(d) Usually cannot be seen but the effects can be felt.
Label the force in each picture as a push or pull. Then, describe whether
the force is causing a change in speed or direction or both.
ACTIVITY 3.2
1. Define force.
2. Give an example when a force:
(a) Changes the shape of an object.
(b) Changes the direction of a moving object.
(c) Changes the speed of a moving object.
3. Explain four effects of forces.
SELF-CHECK 3.2
76.
TOPIC 3 FORCE AND ENERGY W 75
3.2.1 Force Can Change Shape and Movement of
Objects
Force can change the shape of an object. A simple activity to manifest this is by
throwing a brick into the mud in a basin. The mud is splashed out from the basin
due to the impact of the force from the brick. Another example is about various
materials that require more or less pulling force so that the material can be torn
apart. A tissue paper will need less pulling force while a cardboard will need
more force to be torn apart.
When force is exerted on a soft object, the object becomes squeezed, stretched,
bent, twisted or squashed. When force is exerted on a fragile object, the object
will be broken. For example, a glass bottle will disintegrate if it falls on
the floor.
By understanding the nature of a force, people can prevent their belongings from
colliding. For example, letÊs say a small boy is riding a bicycle. He avoids
colliding with trees because if the bicycle collides, it will experience a change in
shape (Figure 3.4).
Figure 3.4: Crushed bicycle
Source: http://www.wizardsofaz.com
It is the same if you throw plasticine onto a wall. The plasticine will also
experience a change in shape. In order to understand the reason behind those
two situations, think about when pushing certain objects, they will push back to
you. So does the bicycle. When the bicycle hits the tree, the tree will „hit‰ back at
the bicycle. As a consequence, the bicycle will experience some changes in shape
(crushed). The same principle also applies to the plasticine. Once it hits the wall,
the wall will „hit‰ back at the plasticine. As a result, the plasticine experiences
change in shape.
77.
X TOPIC 3 FORCE AND ENERGY76
When you play badminton, you will probably smash the shuttlecock to make it
move faster so that you may defeat your opponent in the game. This activity
shows that force can speed up the motion of an object.
When you go on a shopping spree at the supermarket, you will use a trolley to
bring the groceries around (Figure 3.5).
Figure 3.5: Pushing a trolley
Source: http://www.bbc.co.uk
Sometimes, you will stop the trolley at certain sections in the supermarket to
observe things you are interested in buying. Then, you start to push again to
move to other sections. When you hold the moving trolley, force is applied to the
trolley to make it stop. When you push it back, force is applied to the trolley so
that it starts moving. Sometimes, you push it harder so that it can move faster. By
doing this activity, you are actually putting more force on the trolley.
Table 3.2 shows the different types of forces on objects.
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Table 3.2: Six Types of Forces
Force Explanation
Propulsion This can be any driving force, it may be a push or pull, but it could be
an engine which forces an object forward
Water
resistance
This is a force which acts in water; it can slow objects down, reducing
the effect of gravity.
Air
resistance
This is a force which acts in the air, it can slow objects down when they
are moving against it or if harnessed could be used to move an object
along.
Friction This force acts on objects when they are in contact with a surface, such
as the ground. It can be reduced by ensuring both surfaces are smooth.
Gravity This force affects every object on Earth. It is a force which pulls
everything to the centre of the Earth.
Upthrust This is an upward force which acts in water; it acts on an object against
gravity and it is the reason why certain objects float.
3.2.2 Friction
Let us do this activity to learn more about friction:
It is all about friction. Friction is a force that opposes the movement of an object.
In other words, the direction of a frictional force is always against its motion. For
example, if the direction of a moving object is towards the left, the direction of
the frictional force is towards the right.
Friction occurs when two surfaces rub against each other. For example, when a
marble rolls on the floor, friction occurs when the surface of the marble rubs
against the surface of the floor. Eventually, the marble will stop rolling because
the frictional force longer that the force of the moving marble.
Effects of Friction Force on Movement of Object
Let your students do the following activities to experience and observe the effects
of friction on the movement of an object.
(a) Rub your palms together. What do you feel? Do you feel warm? You can
do this when you feel cold.
Roll a marble on two types of surfaces: smooth and rough. Can you predict
which marble will roll a longer distance? Can you explain why a marble rolls
a longer distance on a smooth surface than a rough surface?
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(b) Got an eraser? Rub it on a piece of paper as much as you can. Observe what
happens to the size and shape of the eraser. Make a conclusion based on
this observation. Relate it to the concept of friction.
(c) Ride a bicycle on a smooth road and then on a field full of grass. Which
place needs more energy for you to ride the bicycle?
The condition of the surfaces that rub against each other is a factor that
contributes to friction. A small friction occurs when the surfaces are smooth
whereas there will be greater friction when the surfaces are rough. This is why it
is harder to ride a bicycle in a field full of grass than a smooth road.
The type of surface also affects the distance moved by the object. If a child rolls a
toy car on different surfaces, the car will move the furthest on the smoothest
surface and the slowest on the roughest surface. At home, have you ever noticed
how easy it is to move a small table compared with a big refrigerator? The reason
is friction also depends on the weight of an object. A heavier object exerts a
greater frictional force.
Students should be taught about friction as a force that slows moving
objects and may prevent objects from starting to move. For that, you may
discuss the following:
(a) Air resistance: Investigating parachutes.
(b) Water resistance: Why is it hard work to walk through water?
(c) Why are fish the shape they are?
(d) Why are boats and ships the shape they are?
(e) Investigating different surfaces: Smooth and rough.
Students also should be taught that when objects are pushed or pulled, an
opposing pull or push can be felt. For that, you may do and discuss the
following exercise:
x Practical: Stretching a spring balance. When they pull harder that is
using a bigger force, the spring balance records a higher reading in
Newton.
ACTIVITY 3.3
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Remember that friction is both an advantage and a disadvantage. Friction allows
us to walk without falling over and to pull a thread with a needle. Smooth car
tyres have less friction on the road than tyres with tread. Which tyre is safer?
Friction is also the cause of wear of the moving parts of engines so you have to
reduce friction with lubricants such as motor oil.
The simplest method of reducing friction is to place rollers between the two
surfaces. This method is used when boats are launched, or when heavy wooden
crates have to be moved. Here linear friction is replaced by rolling friction. Ball
bearings are used to reduce friction for revolving shafts. The axle of a bicycle is
mounted in ball bearings. The ball race is similar to the ball race used in a bicycle.
Friction is thus reduced by:
(a) Replacing linear friction with rolling friction; and
(b) By using hard surfaces, as hard surfaces have less friction than softer
surfaces.
Lubrication is the most common method of reducing friction. On a bicycle all
moving parts have small holes through which oil is squirted so that the parts that
move in contact with one another are covered in oil. How does friction help in
increasing or decreasing the speeds of athletes at sports events?
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Fill in the crossword puzzle.
7 4
1 2
6 5
9
8
3
Hints:
1. Friction allows us to walk or run without _ __________ .
2. Friction enables us to hold things because it __________ the object
from moving.
3. The brake system in vehicles makes use of friction to ________ the
vehicles.
4. If there is no friction, you will not be able to _______ properly on
the ground.
5. Friction enables us to ______ a knife and other instruments.
6. Friction produces _______ which can damage some parts of
machines.
7. Friction causes surfaces which are rubbing ________ each other to
wear out.
8. Friction also causes wasting of ___________.
9. Worn-out tyres are ________ because they can slide and skid
easily, causing accidents to occur.
SELF-CHECK 3.3
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3.2.3 Applications of Frictional Force
Before we go to the applications of frictional force, let us recall what it is. Can you
give the meaning of frictional force?
Frictional forces are present everywhere in our daily life. Friction is useful in
many instances. Without friction, we would not be able to walk or run and cars
will not move. Friction also prevents our feet from slipping. It is simply
impossible to reduce frictional forces completely. Frictional forces are useful in
some situations but can be an obstruction in others.
As stated in its definition, frictional forces exist between surfaces of two objects
being in contact. Their directions are always parallel to that surface and opposite
of the direction of the intended motion of an object (see Figure 3.6).
Figure 3.6: Frictional force
There are many ways to reduce friction. Find out how to reduce friction
using:
(a) Aerodynamic shape.
(b) Rollers or ball bearings.
(c) Lubricants such as oil, wax or grease.
(d) Talcum powder or air cushion.
(e) Smoothening surfaces in contact.
ACTIVITY 3.4
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Let us turn on our time machine to discover the early applications of this force.
The first practical application of friction occurred nearly a million years ago,
when it was discovered that heat from friction could be used to light a fire. The
use of liquid lubricants to minimise the work needed to transport heavy objects
was discovered more than 4,000 years ago. IsnÊt that interesting?
However, friction has its disadvantages. Friction opposes motion. Thus, you have
to add more energy to move an object. This reduces efficiency and leads to
wastage of energy. Friction also causes wear and tear of moving parts in
machines such as cars. That is why we need to replace certain parts of our cars
after some time. When you use a saw to cut up something, be careful with its
blade. It tends to heat up when a lot of sawing is done. This causes the metal to
snap when it becomes very hot. This sounds scary, doesnÊt it? But with proper
equipment and precautions, I am sure this kind of incident can be avoided.
Let us try a simple activity.
By the end of this experiment, can you describe the characteristics of materials
which provide good grip? Is it rubbery, soft, grippy, bendy, smooth or rough?
What conclusion can you make of this experiment? Well, next time you want to
buy a new pair of shoes, you might want to think about having one with
increased frictional forces rather than grip!
How about the objects in or on water? Do you know that water resistance or
friction does exist? Well, being in water, ships, boats, submarines and fish all
have to face the similar effects of water resistance or friction. Let us take a fish as
an example. Have you ever thought how fish reduce the frictional forces on their
bodies as they move through water? The answer is having a streamlined shape,
slippery surface and few protrusions (see Figure 3.7)!
Experiment 3.1
Objective: To identify the characteristics of materials with good grip.
Procedure:
(a) Place different items of footwear on a tray or other flat surface.
(b) Carefully tip the tray. You will notice that the shoes with more grip
(greater frictional forces) will be the last to move. Try this with different
shoes. Predict which will be the best.
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Figure 3.7: A fish has a streamlined shape, slippery surface and
few protrusions to reduce frictional force in water
So, how does a submarine copy the fishÊs characteristics in order to face the
effects of water resistance? By studying the characteristics of a ship, we humans
do the best we can in designing our submarines, ships and boats. This is done by
choosing shapes that will glide through the water and materials which are as
smooth as we can economically make them.
As mentioned before, frictional force can be our friend and also our enemy. One
simple example of being our friend is that friction helps us to walk (Figure 3.8).
Figure 3.8: Friction helps us to walk
Source: http://www.csicop.org
Have you ever tried to walk on ice? Try walking around the room you are in. If
you walk slowly and concentrate hard you may be able to feel each foot as it
pushes down and slightly backwards with each step. Without this friction
allowing you to push back against the floor, you would get nowhere.
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How about Olympic swimmers? Olympic swimmers reduce the frictional forces
of water resistance by using these techniques:
(a) Smooth swimsuits;
(b) Bald heads;
(c) Swimming caps; and
(d) Removal of body hair.
Interesting isnÊt it? How about the aeroplane? How do aeroplane manufacturers
reduce the frictional forces of air resistance in their planes? The planes are made
with:
(a) Smooth materials;
(b) Aerodynamic shape; and
(c) Few protrusions.
Let us do a thought experiment. Imagine you are trying to drive away from a
muddy field. But you are having difficulty because the wheels of your car are
spinning on the mud. This is happening because there is not enough friction
between your tyres and the ground. The mud is acting as a lubricant (rather like
oil) and reducing the friction. So, how could you get out of this sticky mess?
You need to increase the frictional force to make the car move. How? You could
put sand or stones beneath the wheels to reduce the lubricating effect of the mud.
The wheel could „get a grip‰ and you can get drive away in no time!
Can you think of some daily activities that can be associated with friction? Check
out the answers in Figure 3.9.
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Figure 3.9: Friction in daily activities
Find and observe one way that friction affects you in your daily life. After
you have chosen one friction event from your daily life, answer the
following questions and combine them into one paragraph.
(a) What are the two things which rub each other?
(b) How is friction helpful or hurtful in this case?
(c) If the friction is harmful, how can you reduce it? If it is helpful,
what can be done to increase the friction?
(d) Can you think of a similar case in which friction will have the same
effect?
ACTIVITY 3.5
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MEASUREMENT OF FORCE
In this subtopic, we will learn about unit of forces and the principle of spring
balance.
3.3.1 Unit of Forces
As with all physical quantities, force also has a method of measurement. Force
has a certain magnitude or size and acts in one direction. We measure force in
Newton. How do we measure this? We measure force by using an instrument
called a spring balance or Newton balance (Figure 3.10). The spring scale can also
be called a Newton meter because it is used to measure Newton (Figure 3.11).
Figure 3.10: Spring balance
Figure 3.11: Different types of spring balance
3.3
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