Transcript PPT Measuring Length, Area & Volume

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Objectives
• To identify mm, cm as sub-multiples of the
metre and km as a multiple of the metre
• To state the SI units of length, area and
volume
• To use the metre rule and measuring tape
correctly to take measurements
• To use the vernier calipers correctly to take
measurements and read the measurements
from diagrams, to take into account zero
error if any
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Objectives
• To identify the use of the micrometer screw
gauge (workings & readings taken by
instruments are not required)
• To choose the appropriate instruments
(measuring tape, metre rule, micrometer
screw gauge or vernier calipers) for
measuring length, diameter or thickness
• To measure the area of irregular figures
using squared paper
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Objectives
• To identify the different apparatus for
measuring the volumes of liquids, e.g.
volumetric flask, measuring cylinder, pipette,
burette and know their degree of accuracy
• To use the measuring cylinder and Eureka
can to find the volume of irregular objects
• To state the precautions to take when using
the metre rule and vernier calipers and when
taking readings from measuring cylinder
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Science is based on empiricism
- a search for knowledge based on
experimentation and observation.
Observations can be either qualitative or
quantitative.
Qualitative observations describe while
quantitative observations measure.
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In science, quantitative observations are
preferred because they can be clearly
communicated.
They are normally measured according to
standard procedures.
Measuring allows us to make accurate
observations that are required in scientific
work as well as in everyday uses.
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Instruments have been invented to make more
accurate measurements.
Some instruments which you will use to
measure with are the
- metre rule
- vernier calipers
- burette
- pipette
- measuring cylinder.
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Physical Quantities, SI Units and
Prefixes
A physical quantity is a quantity which can be
measured.
Examples of some of them are length, volume,
mass, time, temperature, etc.
A non-physical quantity is one which cannot be
measured.
Examples of some of them are beauty,
kindness, humour, sadness, untidiness, etc. 8
Since 1960, scientists from different parts of
the world have agreed to adopt a single
system of units called the SI Units (SI stands
for Système International d’Unités in
French). This system is an adaptation of the
metric system.
There are altogether seven basic quantities:
length, mass, time, electric current,
thermodynamic temperature, luminous
intensity and amount of substance.
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All the other physical quantities are derived
from the seven basic quantities.
For example, area, volume, speed.
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The International System of Units (SI units)
Out of these seven basic quantities, only five
will be covered at your level.
They are length, mass, time, electric current
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and temperature.
Prefixes are used to change them by factors of
ten into smaller or bigger units.
Prefix
Symbol
micro
milli
centi
deci
kilo
mega

m
c
d
k
M
Factor
10-6 one millionth
10-3 one thousandth
10-2 one hundredth
10-1 one tenth
103 one thousand times
106 one million times
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Class Work:
Convert the following to SI unit:
(a)
(b)
(c)
(d)
(e)
(f)
24 km
55 cm
56 MJ
9.8 g
35 mg
77 s
=
=
=
=
=
=
24000
_________
m
0.55
_________
m
56000000 J
_________
0.0098
_________
kg
0.000035
_________
kg
_________
s
0.000077
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Measurement of Length
Length is the distance between two points.
SI unit: metre, m
1 m = 100 cm
1 cm = 10 mm
Short distance - cm or mm
Long distance - km
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Metre rule
This instrument is commonly used in the
laboratory to measure the lengths of objects
such as wires or distance between two points.
Metre rules are graduated in millimetres
therefore readings taken from a metre rule
should be given to the nearest millimetre.
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If a metre rule is thick, it should be placed so
that the scale is as near to the object as
possible so that readings can be taken without
parallax error.
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When taking readings from the metre rule,
make sure that the line of vision is
perpendicular to the scale so as to avoid
parallax error.
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Parallax error
For accurate measurements using the metre
rule, the eye must be placed vertically above
the markings of the metre rule to avoid
parallax error.
Parallax errors are errors due to the incorrect
positioning of the eye and the object not
touching the markings of the scale.
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Parallax errors can be avoided by
- placing the eye vertically above the
marking on the scale to be read.
- placing the metre rule on its edge beside
the object to be measured so that the scale
is touching it.
- using a thin rule so that the scale is
touching the object to be measured.
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Calipers
External Caliper
- accuracy of 0.1 cm
Internal Caliper
- accuracy of 0.1 cm
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External Calipers
Measuring the external
diameter.
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Internal Calipers
Measuring the internal
diameter.
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Vernier Calipers
The vernier calipers is most commonly used
for accurate measurement of up to ±0.1 mm
or ±0.01 cm.
By means of a vernier scale, the second
decimal place in cm can be obtained without
having to estimate fractions of a division
using the eye.
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Vernier calipers have a set of inside jaws,
outside jaws and a tail.
The inside jaws are used for measuring
internal diameters, the outside jaws is for
measuring external
diameter while the tail is
for measuring depth.
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Step 1: Grip the object using the outside or
inside jaws of the calipers.
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Step 2: Read the last division on the main
scale that has passed the zero line of
the vernier scale.
Step 3: Look for a line on the vernier scale
which is exactly opposite to any line
on the main scale, count this line,
starting from the zero-line (of the
vernier scale). This number is the
next decimal place in your answer.
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Step 2 (3.1 cm)
Step 3 (3.18 cm)
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4
5
0
5
_______ cm
10
8
9
0
5
10
_______ cm
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To Java Applet
Zero error
Before using the vernier calipers, the jaws
must be closed to check if there is zero error.
When the zero marking on the vernier scale is
not in line with the zero marking on the main
scale, the distance between the two markings
is the zero error.
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If the zero marking of the vernier scale is to
the right of the zero marking on the main
scale when the jaws are closed, the zero error
is positive.
0
1
0
5
10
Zero error
= 0.09 cm
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If the zero marking of the vernier scale is to
the left of the zero marking on the main scale
when the jaws are closed, the zero error is
negative.
0
1
0
5
10
Zero error
= -0.01 cm
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0
1
0
5
10
4
5
0
5
10
Zero error
= 0.09 cm
Observed reading
= 4.03 cm
Accurate reading
= 4.03 - 0.09 cm
= 3.94 cm
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0
1
0
5
Zero error
= -0.01 cm
10
4
5
0
5
10
Observed reading
= 4.03 cm
Accurate reading
= 4.03 - (-0.01) cm
= 4.04 cm
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Micrometer Screw Gauge
The micrometer screw gauge is used to give
very accurate measurements of length up to
25 mm. It has an accuracy of ±0.01 mm (or
±0.001 cm).
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Measurement of Area
Area is a measure of the extent of a surface.
SI unit: square metre, m2
1 km2 = 1000000 m2
1 cm2 = 0.0001 m2
1 mm2 = 0.000001 m2
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The area of regular surfaces can be calculated
using formulae.
l
a
l
l
b
h
b
Area of a Square = l2
Area of a Rectangle = l  b
Area of a Trapezium = ½ (a + b) h
Area of a Circle =  r2
r
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For irregular surfaces, their areas can be
estimated by first dividing them into small
unit squares and counting them.
An incomplete square is counted as one if its
area is more than or equal to half of the area
of a unit square.
If areas of the incomplete square are less than
half, they are not counted.
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Area of 1 square = 1 cm2
No. of squares counted = 15
Total area estimated
= 15  1
= 15 cm2
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Measurement of Volume
Volume is a measure of the space occupied by
a substance.
SI unit: cubic metre, m3
1 km3 = 100000000 m3
1 cm3 = 0.000001 m3
1 mm3 = 0.00000001 m3
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Some objects have regular shapes, for
example, books, basketballs, pyramids and
soft-drink cans. The volume of regular-shaped
objects can be calculated using formulae.
r
l
r
h
l
l
b
l
Volume of a cube = l3
Volume of a rectangular block = l  b  h
Volume of a sphere = 4/3  r3
Volume of a cylinder =  r2 h
h
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Instruments commonly used in the laboratory
for measuring volume of liquids include the
measuring cylinder, burette, pipette and
volumetric flask.
Liquids are drawn into a pipette
by means of a pipette filter up to
|a mark showing the exact volume
of a liquid in the pipette. Sucking
by mouth is not recommended
due to safety and hygiene reasons.
pipette
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burette
When using a measuring cylinder,
readings are taken to the nearest
half-division.
When reading, the measuring cylinder
must not be held in hand. It must be
placed on a horizontal bench.
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Meniscus reading
When you pour water into a measuring
cylinder and place it on the bench or any flat
surface, you will observe that the water
surface is curved.
The meniscus of most liquids curves
downwards. The correct way to read the
meniscus is to position the eye at the same
level as the meniscus.
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The mark corresponding to the bottom of the
meniscus is taken as the reading.
The meniscus of mercury curves upwards. The
correct reading is the mark that corresponds to
the top of the meniscus.
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When taking readings from the measuring
cylinder, the bottom of the water meniscus
was read horizontally at the eye level to avoid
parallax error.
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Measuring the volume of a small irregularshaped object
1.
Partly fill a measuring cylinder with
water. Observe and record the initial
water level, V0, in the measuring cylinder.
2.
Tie the irregular-shaped object with a
piece of string. Lower it gently into the
measuring cylinder so that it is completely
covered with water. Observe and record
the final water level, V1.
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3.
The volume of the irregular-shaped object,
V, is the difference between the two water
level readings and
is given V = V1 - V0.
V1
V0
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Measuring the volume of a small irregularshaped object that floats on water
-
use a sinker
(an object that sinks)
V = V1 - V0
V0 = Level of weight
V1 = Level of weight
and sinker
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Measuring the volume of a large irregularshaped object
1.
Fill the
displacement can
with water until
excess water flows
out of its spout into
a beaker. Remove
the beaker when water stops flowing into
it.
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2.
Place an empty measuring cylinder below
the spout of the displacement can. Tie the
irregular-shaped
object with a piece
of string. Lower it
gently into the can
until it is
completely
immersed in the
water.
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3.
When the water stops flowing into the
measuring cylinder, observe and record
the volume of water displaced by the
object and collected in the measuring
cylinder. The volume
of the water in the
measuring cylinder
is equal to the volume
of the irregular-shaped
object.
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References
Tho Lai Hong, Ho Peck Leng, Goh Ngoh Khang,
(2001), Interactive Science 1, Pan Pacific
Publications.
Chan Kim Fatt, Eric Y K Lam, Lam Peng Kwan, Loo
Poh Lim, (2000), Science Adventure, Federal
Publications.
Chuen Wee Hong, Lee Khee Boon, Hilda Tan, Ruth
Chellappah, Koh Thiam Seng, Yap Kueh Chin,
(2000), EPB.
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