bb101 chapter 1 physical quantities and measurement

PHYSICAL QUANTITIES AND MEASUREMENT BB101- ENGINEERING SCIENCE

UNIT SAINS JMSK PUO/DISEMBER2012

1.0 : PHYSICAL QUANTITIES AND MEASUREMENT

1.1 : Quantities and Units

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

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.



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 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

Prefix Value Symbol

Giga One billion G

Mega One million M

Kilo One thousand K

Deci One tenth d

Centi One hundredth c

Milli One thousandth m

Micro One millionth µ

nano One billionth n

Prefixes are the preceding factor used to represent very small and very large physical quantities in SI units.



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 A derived quantity is a Physics quantity that is not a base quantity. It is the quantities which derived from the base quantities through multiplying and/or dividing them. Example

(Speed is derived from dividing distance by time.)

Example: Which of following is a derived quantity? Length / Mass / Weight /Temperature/Density/Heat

http://3.bp.blogspot.com/_PyvjcvYfRLk/SWD5jbDv2fI/AAAAAAAAAU4/yrjfWmPQz1I/s1600-h/base+quantity.png

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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.

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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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http://2.bp.blogspot.com/_PyvjcvYfRLk/SWGFg6JnP7I/AAAAAAAAAVo/VGcZDqBYJVw/s1600-h/derived+unit+2.png



Unit Conversion Area and Volume

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 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

http://2.bp.blogspot.com/_PyvjcvYfRLk/SWGHLTLBS_I/AAAAAAAAAVw/6DxW_s2M5y8/s1600-h/unit+of+area.png



1.2 : Analyse Data Of Measurement

Measuring Instruments Metre rule The smallest division on a metre rue is 0.1 cm. A metre ruler 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:

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

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



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

Answer: 5.801 ± 0.003 mm



Inaccuracy and errors in measurement.

Consistensy The consistency of a measuring instrument is its ability to register the same

reading when a measurement is repeated. 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 how close a measured value is to the actual (true) value. Precision is how close the measured values are to each other.

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 arises 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 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- C1 , Specification of lab work: CLO2 – (C2,P1) ***************************************************************************************** COURSE LEARNING OUTCOME (CLO)

Upon completion of this topic, students should be able to: 1. Identify the basic concept of physical quantities, measurement, (C1)

2. Apply concept of physical quantities and measurement to prove related

physics principles. (C2,P1)

Compliance to PLO : PLO1 , LD1 (Knowledge) – Quiz 1,PLO2, LD2 (Practical Skill) Exp.1

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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.

bb101 chapter 1 physical quantities and measurement

Documents

faulty procedure adopted

micrometer screw gauge

list base quantities

define physical quantities

measure length accurately

list derived quantities

person making measurement

main scale reading