dbs1012 chapter 1 physical quantities and measurement

PHYSICAL QUANTITIES AND MEASUREMENT DBS1012- ENGINEERING SCIENCE

UNIT SAINS JMSK PUO/JUN 2014

1.0: PHYSICAL QUANTITIES AND MEASUREMENT 1.1 : Understand the Physical Quantities.

Physical Quantities

Physical Quantities are measurable and have physical (feel, see…) meaning. A physical quantity is a quantity that can be measured.

Numerical values and units give quantities meaning. There are many units for each quantities

Example - Length: metres, centimetres, kilometres, feet, inches, miles, nautical miles,

light year Only one of the many is an SI unit

Quantity SI Unit Symbol

Length Metre m

Mass Kilogram kg

Time Second s

Temperature Kelvin K

At the end of this lesson, students should be able to: Describe physical quantities, base quantities, derived quantities and the

International System (SI) of units.

Define scalar and vector quantities.

Solve problems of unit conversion.



SI units for some other quantities.

Quantites Unit

speed m/s

area m2

volume m3

density kg/m 3

Only quantities that have the same units can be added or subtracted. Example

400 cm3 of water is added to 1 litre of water. How much water is there? Incorrect: 400 + 1 = 401cm3 Correct: 1 litre = 1000cm3 400 + 1000 = 1400 cm3

Prefixes

Prefixes may be added to very small quantities. Very small numbers may have prefixes to make writing them easier.

Example: 2 000 000 000 Byte = 2 GByte

0.000045 m = 45 m Prefixes are the preceding factor used to represent very small and very large physical

quantities in SI units.

Prefix Abbreviation Power

Tera T x 1012

Giga G x 109

Mega M x 106

Kilo K x 103

deci d x 10-1

centi c x 10-2

milli m x 10-3

micro µ x 10-6

nano n x 10-9



Base Quantities

1. A base quantity is a physical quantity that cannot be derived from other physical quantities. Example: length, mass, time.

2. The base quantities and their respective units as well as the symbols used to represent them are shown in Table 1.

Table 1 Derived Quantities Derived quantities are physical quantities that are derived from the combinations of base quantities through multiplication or division or both these operations. Examples

(Speed is derived from dividing distance by time.) Example: Which of following is a derived quantity? Length / Mass / Weight /Temperature/Density/Heat

Base Quantities SI Unit Symbol of Unit

Length, l meter m

Mass, m kilogram kg

Time, t second s

electric current, Q ampere A

Temperature, T kelvin K

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Example: State the physical quantity that can be measured by the following equipments:

a) voltmeter b) thermometer c) ammeter d) balance.

Derived Unit The derived unit is a combination of base units through multiplying and/or dividing them.

Example 1 Find the derived unit of density. Answer

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Scalar and Vector Quantity

A scalar quantity is a quantity that has magnitude, but no direction.

A vector quantity is a quantity that has both magnitude and direction.

Scalars Vectors

distance displacement

speed velocity

mass weight

time acceleration

pressure force

energy momentum

Conversion of units Area and Volume

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Example 1 Convert the unit of length, area and volume below to the units given. a) 7.2 m = ____________cm b) 0.32 m2 = ____________cm2 c) 0.0012 m3 = ____________cm3 d) 5.6 cm = ____________m e) 350 cm2 = ____________m2 f) 45000 cm3 = ____________m3 Answer a) 7.2 m = 7.2 x 102 cm b) 0.32 m2 = 0.32 x 104 cm2 = 3.2 x 103 cm2 c) 0.0012 m3 = 0.0012 x 106 cm3 = 1.2 x 103 cm3 d) 5.6 cm = 5.6 x 10-2 m e) 350 cm2 = 350 x 10-4 m2 = 3.5 x 10-2 m2 f) 45000 cm3 = 45000 x 10-6 m3 = 4.5 x 10-2 m3 Example 2 Change the following quantities to the units shown. a) 1 cm3 = ……… m3 , b) 13.6 g cm-3 = …….kg m-3 c) 72 km h-1 = ….m s-1 d) 15 ms-1 = …….kmh-1 Solution a) 1 cm3 = 1 cm x 1 cm x 1cm = 10-2 m x 10-2 m x 10-2 m = 10-6 m3 b) 13.6 gcm3 = 13.6g/1cm3 = (13.6 g x 10-3 kg)/( 10-6m3 ) =13.6 x 103 kg m-3 = 1.36 x 104 kg m-3 c) 72 km h-1 = 72 km/1h = (72 x 1000 m)/(60 x 60 s) = 20 m s-1 d) 15 ms-1 = …….kmh-1 = (15 x 10-3) / (1/3600) = 54kmh-1

Practices: Convert the following quantities to the units shown: a) 29 km to mm b) 600mm to cm c) 800 cm3 to m3

d) 60kmh-1 to ms-1

e) 10ms-1 to kmh-1

f) 3000kgm-3 to gcm-3

g) 2.84 gcm-3 to kgm-3



1.2 : Analyse Data Of Measurement

Measuring Instruments Metre rule The smallest division on a metre rule is 0.1 cm. A metre rule can therefore measure length accurately up to 0.1 cm only.

Figure 1: Meter Ruler Example calculation: Figure 2 shows the measurement of the length of a wooden block with ruler. a) State the accuracy of the ruler. b) Why the zero mark on the ruler not used as the origin of the measurement? c) State the category of error that must be avoided when reading the scale. d) What is the length of the wooden block?

Figure 2 Answer:

At the end of this lesson, students should be able to: How to read and use Micrometer screw gauge, Vernier Calliper and meter rule .

Describe inaccuracy and errors in measurement.



The Vernier Caliper

This instrument may be used to measure outer dimensions of objects (using the main jaws), inside dimensions (using the smaller jaws at the top), and depths (using the stem).

How to read and use the Vernier Caliper?

The reading here is 3.7 mm or 0.37 cm.



In figure above, the first significant figures are taken as the main scale reading to the left of the vernier zero, i.e. 3.4 cm. The remaining digit is taken from the vernier scale reading that lines up with any main scale reading, (i.e. 0.60 mm or 0.060 cm) on the vernier scale. Therefore the reading is 3.460 cm. EXERCISE:

Answer: 3.090 cm



Answer: 0.810 cm MICROMETER A micrometer allows a measurement of the size of a body. It is one of the most accurate mechanical devices in common use. The micrometer screw gauge can be used to measure very small lengths such as the diameter of a wire or the thickness of a piece of paper as it can measure length accurately up to 0.01 mm.

Figure 5: Micrometer Screw Gauge



7.5+0.000 = 7.500 mm

8.000 mm + 0.120 mm = 8.120 mm



Depending on your eyes and screen resolution, you might be fairly confident that the

reading is less than, say, 8.627 mm and similarly confident that it is greater than 8.621 mm. Thus you might assign a Reading Error to this measurement of 0.003 mm

So, we would report the distance as 8.624 ± 0.003 mm. EXERCISE:

Answer: 7.880 mm

Answer: 3.090 mm

8.500 mm + 0.124 mm = 8.624

mm



Answer: 5.801 ± 0.003 mm Inaccuracy and errors in measurement. Consistency

The consistency of a measuring instrument is its ability to register the same reading when a measurement is repeated.

A set of measurements are consistent if all the values are close to the mean value.

The consistency of a measuring instrument can be improved by a) eliminating parallax errors during measurement. b) exercising greater care and effort when taking readings. c) using an instrument which is not defective.

Accuracy

Accuracy is the degree of how close a measured value is to the actual (true) value. Precision is how close the measured values are to each other. Ways to improve the accuracy of a measurement: a) Repeated readings are taken and the average value is calculated. b) Avoid parallax errors. c) Avoid zero errors. d) Use measuring instruments with a higher accuracy.

Examples of Precision and Accuracy:

Low Accuracy High Precision

High Accuracy Low Precision

High Accuracy High Precision



Sensitivity The sensitivity of a measuring instrument is its ability to respond quickly to a

small change in the value of a measurement. A measuring instrument that has a scale with smaller division is more

sensitive.

ERROR An error is defined as: "The difference between the measured value and the actual value."

If two persons use the same instrument for measurement for finding the same

measurement, it is not essential that they may get the same results. There may arise a

difference between their measurements.

This difference is referred to as an "ERROR".

Types Of Error

Errors can be divided into three categories: (1) Personal Error (2) Systematic Error (3) Random Error Personal Error

An error comes into play because of faulty procedure adopted by the observer is called

"PERSONAL ERROR".

Personal error comes into existence due to making an error in reading a scale. It is due to

faulty procedure adopted by the person making measurement.

A parallax error is an error in reading an instrument due to the eye of the observer and

pointer are not in a line perpendicular to the plane of the scale. Parallax errors are

considered systematic errors. (*Systematic errors are those you can improve on. A

parallax error can be corrected by you).

Systematic Error

The type of error arises due to defect in the measuring device is known as

"SYSTEMATIC ERROR"

Generally it is called "ZERO ERROR". it may be positive or negative error.

Systematic error can be removed by correcting measurement device.

Random Error

The error produced due to sudden change in experimental conditions is called "RANDOM

ERROR".

For example:

During sudden change in temperature, change in humidity, fluctuation in potential

difference(voltage).

It is an accidental error and is beyond the control of the person making measurement.



Minimum requirement assessment task for this topic: 1 Quiz & 1 Lab work Specification of quiz: CLO1- C3 , Specification of theoretical exercise: CLO3- C3, Specification of lab work: CLO2 – (P2,A2) ************************************************************************************************************** COURSE LEARNING OUTCOME (CLO) Upon completion of this topic, students should be able to:

1. solve the basic engineering science problems by using related concept. (C3)

2. organize appropriate experiments to prove related physic principles (P2),(A2)

3. apply related physic principles in various situations to enhance knowledge (C3)

AKTIVITI PELAJAR (JIGSAW METHOD) TUJUAN (OBJECTIVE): By the end of this lesson, the students should be able to:

Define physical quantities, base quantities and derived quantities.

List base quantities and their unit.

List derived quantities and their unit.

Convert the quantities unit.

BAHAN AKTIVITI: SKIL 1 : Physical Quantities, SI unit and Prefixes. SKIL 2 : Base Quantities, SI unit and symbol. SKIL 3 : Derived Quantities and unit conversion. (Bahan boleh dirujuk dari nota atau rujukan lain) LANGKAH-LANGKAH: 1. Pelajar dibahagikan kepada 3 orang dalam satu kumpulan. Kumpulan ini dipanggil

‘Original Group’

2. Setiap pelajar dalam satu kumpulan akan mendapat bahan aktiviti dari skil yang

berbeza.

3. Pelajar diberi masa untuk mencari bahan dan berbincang. (Agihan akan diberi

sebelum aktiviti sebenar yang akan dijalankan pada kelas berikutnya).

4. Pada hari aktiviti, pelajar duduk dalam kumpulan ‘Original Group’ masing-masing.

5. Kemudiannya pelajar yang mempunyai bahan pada skill yang sama akan

digabungkan dalam satu kumpulan. Maka terbentuk tiga kumpulan yang dikenali

sebagai ‘Expert Group’. Beri masa yang sesuai untuk perbincangan. Pensyarah boleh

memberi input tambahan dan menjawab pertanyaan atau membuat pertanyaan.

6. Setelah selesai, pelajar akan kembali ke kumpulan masing-masing. Pelajar dari setiap

skil yang akan mengajarkan apa yang diperbincangkan tadi kepada pelajar lain di

dalam kumpulannya. Berikan masa yang sesuai.

7. Setelah selesai perbincangan tersebut, setiap pelajar akan menjawab satu soalan

penilaian. Penilaian ini perlu untuk mengenalpasti semua pelajar telah mencapai

objektif P&P pada hari tersebut. Soalan penilaian adalah berbentuk soalan pendek.

Setiap pensyarah bebas menyediakan soalan masing-masing yang dapat menguji

pelajar untuk mencapai objektif diatas.

dbs1012 chapter 1 physical quantities and measurement

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