 Measuring Length, Area & Volume.

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Measuring Length, Area & Volume

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

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

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

Science is based on empiricism -. a search for knowledge based on
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.

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.

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.

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.

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.

All the other physical quantities are derived from the seven basic quantities. For example, area, volume, speed.

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 and temperature.

Prefixes are used to change them by factors of ten into smaller or bigger units.
Prefix Symbol Factor micro  one millionth milli m one thousandth centi c one hundredth deci d one tenth kilo k one thousand times mega M one million times

Class Work: Convert the following to SI unit:
(a) 24 km = _________ m (b) 55 cm = _________ m (c) 56 MJ = _________ J (d) 9.8 g = _________ kg (e) 35 mg = _________ kg (f) 77 s = _________ s 24000 0.55 0.0098

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

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.

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.

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.

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.

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.

Calipers External Caliper - accuracy of 0.1 cm Internal Caliper - accuracy of 0.1 cm

External Calipers Measuring the external diameter.

Internal Calipers Measuring the internal diameter.

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.

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.

Step 1:. Grip the object using the outside or
Step 1: Grip the object using the outside or inside jaws of the calipers.

Step 2:. Read the last division on the main
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.

Step 2 (3.1 cm) Step 3 (3.18 cm)

_______ cm 4 5 0 5 10 _______ cm 8 9 0 5 10 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.

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

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 = cm

Accurate reading = 4.03 - 0.09 cm = 3.94 cm
0 1 0 5 10 Zero error = 0.09 cm Observed reading = 4.03 cm Accurate reading = cm = 3.94 cm 4 5 0 5 10

Accurate reading = 4.03 - (-0.01) cm = 4.04 cm
0 1 0 5 10 Zero error = cm Observed reading = 4.03 cm Accurate reading = (-0.01) cm = 4.04 cm 4 5 0 5 10

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).

Measurement of Area Area is a measure of the extent of a surface.
SI unit: square metre, m2 1 km2 = m2 1 cm2 = m2 1 mm2 = m2

The area of regular surfaces can be calculated using formulae.
Area of a Square = l2 Area of a Rectangle = l  b Area of a Trapezium = ½ (a + b) h Area of a Circle =  r2 l a l h l b b r

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.

Area of 1 square = 1 cm2 No. of squares counted = 15 Total area estimated = 15  1 = 15 cm2

Measurement of Volume Volume is a measure of the space occupied by a substance. SI unit: cubic metre, m3 1 km3 = m3 1 cm3 = m3 1 mm3 = m3

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. 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 r h r l l h b

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. burette pipette

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.

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.

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.

When taking readings from the measuring cylinder, the bottom of the water meniscus was read horizontally at the eye level to avoid parallax error.

Measuring the volume of a small irregular-shaped 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.

3. The volume of the irregular-shaped object,
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

Measuring the volume of a small irregular-shaped 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

Measuring the volume of a large irregular-shaped 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.

2. Place an empty measuring cylinder below
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.

3. When the water stops flowing into the
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.

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.