Physics Form One Notes – Measurement
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Concepts of Measurement
‘The Concepts of Measurement
Explain the concepts of measurement
Measurement is the process of assigning numbers to observations or event.
Importance of Measurement in Real Life
‘State the importance of measurement in real life
Measurements are so often taken for granted, we sometimes do not appreciate the grand
importance measurements play in our lives. On a baseline level, measurements fall into the
categories of weight, area, volume, length and even temperature. While we look at these various
categories as stoic forms of mathematical measurements, a closer examination of things we do in
everyday life reveals their clear importance.
‘Taking proper medicine. If you are ill (whether a serious or minor illness) you need to take
your medicine and take it in the proper amount. If you take too little or too much then you are
not going to get the proper benefit from it
Cooking properly. Cooking of all forms is based on proper attention to measurement. Can you
bake a chicken at 600 degrees? Well, you can but the results would be pretty catastrophic! Could
you may a cup of tea by dipping a tea bag into a teaspoon of warm water?
Purchasing clothes. Now, how important could measurements be when selecting clothes? After
all, to look good in clothing the main thing you need to pay attention to is style, right? Well, if
you weigh 200Ibs you aren’t going to look stylish in an extra small shit. Clothing is all based on
size and proper fitting which are, of course, variants of measurement,
Playing sports. The importance of measurements may not necessarily reveal itself when you
play sports but itis there in a big way. If you want to throw a runner out at first or make @ 30
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yard touchdown pass then you really need to be accurate and comes from a clear sense of depth
and distance.
Making estimations. If you have to be at school at 9am what time would you have to leave in
the morning if you are at your friend’s house. Often we do not have an exact answer so we need
to make an estimation which is essentially a guess of measurement.
Keeping yourself warm or cool. If the temperature outside dips or inereases you have to make
an adjustment on your thermostat in order to remain at a safe and healthy temperature
Understanding the measurement seale of a thermostat is critical in this regard or else you may
find yourself feeling rather uncomfortable.
Understanding weight. Is that object too heavy to pick up by yourself or do you need to use
something to lift if? Some may think this is not important but itis pretty easy to hurt yourself if
you lift objects that are too heavy.
Proper use of capacity. Just how many clothes can you fit in a dresser or closet without it
becoming too crammed? Without a clear concept of capacity you might find yourself pouring an
entire half gallon of orange juice into a small glass!
Telling time. The ability to tell time is all based on measurement principles. Whether you are
using a digital clock or an hourglass these devices measure the passage of time. Now, imagine
how chaotic the world would be if if was impossible to measure the passage of time.
‘Transportation. How much weight is too much for a plane to take off or a car to move
efficiently? How much fuel is needed to reach a certain point and how long will it take to get
somewhere? Yes, measurements play a significant part in transportation,
Structure. This was saved for last because it is the common theme that is found in all the
multitude of reasons for the importance of measurements. Measurements provide structure and.
remove the chaos that would result without any congruent method of understanding weight,
mass, temperature, ete.
Basic Fundamental Quantities
A Fundamental Quantity
ry
Define a fundamental quantity
Physical quantity:Is any character which can be measured by an instrument.
‘A Unitis the standard which is used to explain measurement of a body-Eg; kilogram, metre,
second ete
Fundamental quantities are numbers that we need to describe the world around us, which we
cannot express in terms of “simpler,” more basicquantities. Here is an example: My weight is
not afundamental quantity, because it depends on how much stuff makes up my body.
Three Basic Fundamental Quantities of Measurement
Mention three basic fundamental quantities of measurement
Basic fundamental quantities are physical quantities from which other physical quantities are
derived from. This includes three quantities namely mass, length and time
‘The S$. Unit of Fundamental Quantity
‘State the S.1 unit of fundamental quantities
SI unit (International system of units): Is the system of units which is used intemationally to
measure three basic physical quantities.
‘ST units of fundamental quantities
Basic physical quantity Stunit
Mass Kilogram (ke)
Length Meter (en)
Time Seconds
Metric system
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1s an international system which is a decimal based system, consequently, conversions from one
Unit to another within the metric system can accomplished by multiplying or dividing by ten or
power often
Note: With the exception of temperature, amount of substance and luminous intensity
international other units of measurement that are smaller or larger than the most commonly used
Units are expressed by attaching a prefix to the most commonly used units,
More than 1 unit
+ Giga(G)= 1,000,000,000 (10°9)
+ Mega(M) = 1,000,000 (10°6)
+ Kilo(K) = 1,000(10°3)
+ Hector (h) = 100(10°2)
+ Decea(da) = 10(10°1)1
Less than 1 unit
+ Deci (d) = 1/10 (10-1)
+ Cent (¢) = 1/100(10″-2)
+ Mill (m) = 1/1000 (10°-3)
+ Micro() = 1/1,000,000(10″-6)
Appropriate Instruments for Measuring Fundamental Quantities
Use appropriate instruments for measuring fundamental quantities
Length, |
Length is the distance between two points, objects or space.The SI unit of length is meter(m).
Other commonly used units are kilometer(km) and centimeter(cm).
km = 1000m
Im=100em
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The instrument used to measure length is the metre rule.
How to read the metre rule:Owing to the thickness of the wood,the eye must always be placed
vertically above the mark being read, in order to avoid errors due to parallax.
Measuring of length (diameter) of small objects
The diameter of small objects is measured by using two instruments:
a. Vemnier caliper
b. Micrometer screw gauge
A venier caliper is the instrument used to measure length to the accuracy of 0,0lem.It is used to
measure lengths to the range of 1.0cm to about 12.0em.The figure below describe the structure of
vernier caliper.
inside
jaws main scale
. th probe
vernier scale cept pr
outside jaws
The main scale is graduated in centimeter (em) while the vernier scale is graduated in millimeter
(mm)-The vernier scale is a short scale 9mm long divided into 10 equal parts, so that the
difference in length between a vernier division and the main scale division is 0.1mm or 0.01em.
The inside jaws are used to measure the inside diameter while the outside jaws are used to
measure outside diameter The vernier slides over the main scale
How to read
+ ‘The main scale reading is recorded. This is the reading which precedes the zero mark of
the vernier scale.
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+ The vemier scale reading is recorded by reading the mark on it which coincide with a
mark on the main scale (i.e. vernier scale reading x 0,01em).
‘+The summation of these two readings is the length of the object measured.
‘A micrometer screw gauge:ls an instrument used to measure length to the accuracy
‘of 0.001em(0.01mm).t is used to measure the diameters of wires and ball bearings. It can
‘measure small lengths up to about 2.Scm.The diagram below describes the micrometer screw
gauge
Anvil Spindle Sleeve Thimble Ratchet
\
NN lps |
— FREER
Sleeve reads 0.55 cm
f Thimble reads
\ 2 divisions © = 0.012 cm
Frame Total reading = 0.562 cm
Fig. 1.6. Micrometer screw gauge
It consists ofa spindle which is fitted with a graduated thimble. The serewed portion ofa spindle
is totally enclosed to protect it from damage, The pitch ofthe screw is 0.5mm, so thatthe spindle
moves through o,0Sem foreach complete tum
The anvil and the spindle grip the measured object between them. The ratchet prevents the user
from using undue pressure. The sleeve is graduated in mm, each graduation represent one
complete tur of the screw.
How to read a micrometer screw gauge:
+ Sleeve reading is recorded. This gives the units and the first two decimal places in mm.
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+ Thimble reading is then recorded. This gives the third decimal place (thimble reading x
0.001mm).
+ The summation of these two readings gives the diameter of the object under
measurement.
Precautions when using a micrometer screw gauge.
1, Before use.the faces of anvil and spindle should be wiped clean to remove any dirty
particle which would give false readings.
2. Cheek and record for zero error then + or ~the correction to the final answer.
Mass
Mass of a body is the amount of matter it contains. The SI unit of mass is kilogram(kg). Other
commonly used units are gram(g) and tones(t),
tkg = 1000
1t= 1000kg
The mass of a body doesn’t change from place to place. The instrument used to measure mass is
called abeam balance.
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Difference between mass and weight
Mass Weight
1s the amount of mater contained [Is the force by which the earth pl body to its centre
Slunitis kilogram Sl units Newton
Doesn’t vary fom place to place on the earth’s surface Varies from place o place on the earth’s surface
“Measured by beam balance “Measured by a spring balance
Time
Is the gap between two occasions or events.The SI unit of time second(s). Other units used are
minutes (min), hour(h) day ete.
Imin = 605
th= 3600s
day = 86400;
The instruments for measuring time are clocks and watches.
@
Derived quantities
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Derived Quantities
Explain derived quantities
Derived quantities are units which are derived from the fundamental quantities. Examples are
volume, density, power, work, energy, weight, frequency etc
‘The S.1 Units of Derived Quantities
State the S1 units of derived quantities
Sl units of Derived quantities
Volume Cubic meter (m3)
Density Koln’
Power Was (W)
Work Joules)
Fneray Soules 0)
Weight Newton (N)
Frequency Hert (Hi)
Basic Apparatus/equipment’s and their uses
Basic Apparatus/Equipments Used for Measurement
Describe basic apparatus/equipments used for measurement
Volume
Volume is the amount of space occupied by a substance. The SI unit is cubic meter (m3) Other
units used are cubic centimetre (cm*3) and litre(1).
Instruments used to measure the volume of liquids:
Measuring cylinder-used for measuring or pouring out various liquids
n
A B
Measuring flask and pipette are used for getting fixed pre-determined volume.
Flask
2
Pipette
Burette-used to deliver any required volume up to its total capacity,
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1.26 Burette
Z
ZI] stopcock
How to read volume measuring instrument (precautions)
Readings are always taken at the level of the boom of the meniscus or curved surface ofthe
liquid. Mercury is an exception as its meniscus curves downwards.
a
Care should be taken to place the eye correctly to avoid parallax errors. When taking readings,
the pipette and burette must be upright and the cylinder and flask must stand on a horizontal
bench otherwise errors may arise from tilting,
Measuring volume of irregular objects.
The volume of an irregular solid can be determined by measuring the volume of water displaced
in a measuring cylinder directly or with the aid of an overflow eureka can.
ee
Experiment
Aim: To measure the volume of an irregular object.
Methods
By using a measuring cylinder directly
Materials and apparatus: Irregular object eg; stone, thread, measuring cylinder, eureka can and
water.
Procedures
+ Poora known volume of water in a burette(V1)
+ Tie atone with a thread.
+ Immerse the tied stone in water holding the thread and record the volume (V2)
+ Make sure the stone is totally immersed in water.
Results
+ Volume before introducing solid = V1
+ Volume after introducing solid = V2
+ Volume of irregular solid(V3) = V2~ V1
By using the eureka can
2s
Procedure to follow
+ Poor water into eureka can up to its spout
+ Immerse a well tied stone in water completely
+ Collect the overflowed water in the water.
+ Use a measuring cylinder to determine the volume of water collected
Observation
+ When a stone was introduced in an overflow can, water overflowed to the measuring
cylinder.
+ The volume of water collected is equal to the volume of irregular object(stone)
Sources of Errors in Measurement
Identify sources of errors in measurement
Error is the difference between the measured value and the real or actual value (The difference in
reading is known as the error).
There are two types of errors, namely:
a. Systematic errors
b. Random errors
Systematic errors
‘Systematic errors results in the measurement or reading being consistently over the actual value
OR consistently smaller than the actual value.
Sources of systematic errors,
a. Zero error: Zero Error is caused if the reading shown is Not zero when the true value is
actually zero. This is most probably caused by a flaw in the instrument for example when using a
ruler that has lost its zero scale due to wear and tear hence causing an error in the measurement
of length.
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b. Wrong assumptions: For example if you assume that water boils at 100 degree Celsius
but actually its boiling point is higher if there are impurities in it. (Pure water boils at 100 degree
Celsius),
© Lag of reaction time: For example in a sports day, when measuring a 100 m running
time using a stopwatch. The observer may not press the stop button exactly when the foot of the
runner touches the finishing line
4. Calibration errors: Instruments that are not properly calibrated could also cause error
and this has to be put in consideration when writing a report or when there is an anomaly in
reading.
Random errors
Random error is caused by the observer who reads the measuring instrument. Just like the
systematic error, there is also positive or negative error. Positive error is when the reading is
bigger than the real value and negative error is when the reading is smaller than the real value.
Ways of reducing errors
1 Taking several readings and then find the average.
2. Avoiding parallax error by positioning the instrument (meter rule) properly on the table
with the eyes perpendicular to the scale
3. Some instruments can be adjusted to eliminate zero error. For example when using an
ammeter, there is an adjuster to set the indicator to zero before making any measurement
4, Inthe case of a ruler, measurement can be carried out starting from the next clear scale
for example if scale 0.0cm is blurted, we can start measuring the length from 2.0cm, of course
taking the difference of value in consideration when recording the final reading.
Density and Relative Density
The Concept of Density of a Substance and its S.1 Unit
Explain the concept of density of a substance and its S.1 unit
‘The Density ofa substance is its mass per unit volume,
az
‘The unit of density is kg/m”3. Other unit used is g/cm’3.Density of regular solid object can easily
be found by direct and easy measurements-It involves measuring the mass and calculating the
volume as described in the experiment below.
‘The Density of Regular and Irregular Solids
Determine the density of regular and irregular solids
Experiment
‘Aim; To measure the density of rectangular block.
Material and Apparatus ‘Ruler, beam balance and rectangular block.
Procedures‘Using a beam balance measure mass of the block, m.Measure its length, width and
height
Results
+ The mass of the rectangular block is m
+ The volume of the rectangular block will be calculated by multiplying the obtained
length, | height, h and width, w.
+ Volume, V = 1x hx w, But; Density = mass/volume
+ The volume of a material can be obtained by using various methods depending on the
shape of the material
Experiment.
‘Aim; To determine density of iregular solid
Materials and apparatus:Irregular soli like stone, measuring cylinder, beam balance and water.
Procedures
+ Obtain the mass ofthe given object using the beam balance.
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+ Fill water tothe measuring cylinder to the volume V,
+ Immerse the well tied irregular object totaly inthe cylinder containing water.
+ Record the new volume Vz
Results
+ Volume of irregular object = V2 -Va
+ Mass obtained = M
Density = SE =
‘The Density of a Liquid
Determine the density ofa liquid
Density of liquids can be determined by using a burrete ora density.
|
Experiment
‘Aim: To determine density of liquids using a burette.
Materials and apparatus: Burette, beaker, beam balance and kerosene.
Procedures
+ Record the mass ofthe empty beaker m; using a beam balance
+ Pour the known volume of kerosene into the beaker by using bur rete, V.
+ Record the mass ofthe beaker and kerosene mz
Results
The mass of the kerosene =m; -mz
Density of kerosene = eseet reser = usm)
2
Definition of the Relative Density of a Substance
Define the relative density ofa substance
‘The Relative density of a substance isthe rato of its density to the density of water.The density
of water has the density of approximately 1.Og/cm* or 1000kg/m.
RD of a substance = Demat ofa substance
Deneity of water
c_imau of substance __eolume
= ase of wearer
= ass of any volume of the substance
mass of equal volume of water
Note:Since the density of pure water is 1g/em?, the RD of a substance will be represented by the
same number as its density in g/em*.RD has no units as its ratio of same quantities
Applications of Density and Relative Density in Real Life
Interpret applications of density and relative density in real life
Application of RD in real life.
1, It is the key factor which is considered during the design of various structures and
equipment. Eg. ships and planes.
2. Density is considered during the selection of materials,
3. Density is also considered during the design of equipment used in swimming
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