3 e physcial quantities and units_pure_upload

Specific Instructional ObjectivesAt the end of the lesson, you should be able to: show understanding that all physical quantities consists of a numerical magnitude

and a unit. Recall the following base quantities and their units mass (kg), length (m), time (s),

current (A), temperature (K) use the following prefixes and their symbols to indicate decimal sub-multiples and

multiples of the SI units: nano (n), micro (μ), milli (m), centi (c), deci (d), kilo (k), mega (M)

show an understanding of the orders of magnitude of the sizes of common objects ranging from a typical atom to the Earth

state what is meant by scalar and vector quantities and give common examples of each

add two vectors to determine a resultant by a graphical method describe how to measure a variety of lengths with appropriate accuracy by means

of tapes, rules, micrometers and calipers, using a vernier scale as necessary describe how to measure a short interval of time including the period of a simple

pendulum with appropriate accuracy using stopwatches or appropriate instruments

amount of substance (mol)

Unit 1: Physical Quantities and Units

Specific Instructional Objectives

At the end of the lesson, you should be able to:

1. show understanding that all physical quantities consists of a numerical magnitude and a unit.

2. Recall the following base quantities and their units mass (kg), length (m), time (s), current (A), temperature (K), amount of substance (mol)

Quantitative vs Qualitative (Measurements vs Descriptions)

•Scientists do not use descriptions to make observations as these would most likely cause disagreements.

•“How large is large?” or “How small is small?”

•Instead, sizes are specified using a number and a standard unit such as the metre.

1.1 Physical Quantities

What is a Physical Quantity???

Definition:Definition: A physical quantity is one that can be

measured and that consist of a numerical magnitude and a unit.

Examples include length, volume, time and temperature.

What other physical

quantities can you think of?

Magnitude and Unit

All physical quantities consists of a numerical magnitude (size) and a unit.

E.g. My height = 1.76 m

E.g. The temperature today is 29 oC

Base Quantity There are 7 base quantities. All the other quantities (derived quantities)

can be worked out from the 7 base quantities.

Base Quantities

1. Length

2. Mass

3. Time

4. Temperature

5. Electric current

6. Luminous intensity

7. Amount of substance

Why are these quantities called base quantities?

SI units

French ‘Le Systeme International d’ Unites’ English translation: ‘International System of

units’ This set of units is internationally

accepted/agreed by scientist Imperial Units versus Metric Units

7 Base Quantities and their SI Units

Base Quantities SI units

1. Length (l) metre (m)

2. Mass (m) kilogram (kg)

3. Time (t) second (s)

4. Temperature (T) kelvin (K)

5. Electric current (I) ampere (A)

6. Luminous intensity (Iv) candela (cd)

7. Amount of substance (n) mole (mol)

http://physics.nist.gov/cuu/Units/index.html

SI Units of derived quantities

Example

breadth length

2mm m area ofunit SI

Area(a)

density (b)

m m

volume

mass kg

m3

)-33 kgm(or kg/m density ofunit SI

1.2 SI Units1.2 SI UnitsDerived Quantities

Derived quantities

Symbol for unit

Special name

area m2

volume m3

density kg m3

speed m s—1

acceleration m s—2

force kg m s—2 (N) newton (N)pressure kg m1 s2(N m2) pascal (Pa)work kg m2 s2 (N m) joule (J)power Kg m2 s3 (J s1) watt (W)

Quick Check

1. Name the base quantities and identify their SI units.

Theory Workbook

Exercise 1.1 (page 1)

Q1 and Q2



1. use the following prefixes and their symbols to indicate decimal sub-multiples and multiples of the SI units: nano (n), micro (μ), milli (m), centi (c), deci (d), kilo (k), mega (M)

2. show an understanding of the orders of magnitude of the sizes of common objects ranging from a typical atom to the Earth

gram

Understanding prefixes

kilo

prefix

kilo = 103 = 1000

Therefore 1 kilogram = 1000 gram

1 km = ________m 1 kJ = ________J

metre

Understanding prefixes

centi

prefix

centi = 10-2 = 0.01

Therefore 1 centimetre = 0.01 metre

Common Prefixes

Factor Name

109 Giga (G)

106 mega (M)

103 kilo (k)

10-1 deci (d)

10-2 centi (c)

10-3 milli (m)

10-6 micro ()

10-9 nano (n)

Example

Write

(a) 50 megawatts (MW) in watts (W)

(b) 250 nanoseconds (ns) in seconds (s)

MWa 50)( W61050W 50000000

nsb 250)( s910250 s 00000025.0

Why do we need prefixes?

Approximate length of some objects

Distance from Earth to Sun 1.5 x 1011 m

Radius of the Earth 6 x 106 m

Height of Mount Everest 1 x 104 m

Length of a football field 1 x 102 m

height of a 4 year-old child 1 m

length of a bee 6 x 10-3 m

diameter of a strand of hair 1 x 10-4 m

diameter of a hydrogen atom

6 x 10-10 m

Quick Check

1. Rewrite the following quantities using suitable prefixes.

(a) 5 000 000 J

(b) 48 000 g

(c) 0.0009 s

MJ 5

kg 48

s 900 ms .9or 0

Theory Workbook


Q3

The Standard Form

Many measurements in modern scientific fields involve very large and very small numbers.

E.g.

Speed of light = 300 000 000 m/s

wavelength of violet light = 0.00000038 m

It is troublesome to write many zeroes for very large and very small numbers.

The Standard Form

Hence mathematicians/scientists decided to use a more convenient known as the standard form: E.g

3 00 000 000 can be written as

3.0 × 100 000 000

= 3.0 × 108 m/s (standard form)

The standard form is always written as

A × 10n,

Where 1 < A < 10 and n is an integer

Which of these figures in standard form?

0.5 × 106

105 × 1082.6 × 103

1.002 × 105

9.9 × 10-8

The Standard Form

Example: Express the following as standard form:

(i)4 0 0 0 0 0 .

= 4.0 × 105

(ii) 3 4 5 0 0 0 0.

= 3.45 × 106

The Standard Form


(i)2 2 2 0 .

= 2.22 × 103

(ii) 1 0 1.

= 1.01 × 102

The Standard Form

Very small numbers can also be written as standard form: For example

0.038 can be written as

3.8 × 10-2

A × 10n

The Standard Form


(i) 0. 0 0 0 0 1 2 5.

= 1.25 × 10-5

(ii) 0. 0 0 0 3 4.= 3.4 × 10-4

The Standard Form


(i) 0. 0 0 0 0 0 2 2 3.

= 2.23 × 10-6

(ii) 0. 0 1.

= 1.0 × 10-2

The Standard Form

Example: Express the following in ordinary notation:

(a) 1.25 × 103

(b) 4.3 × 106

(c) 2.6 × 10-3

(d) 8.7 × 10-5

Theory Workbook


Q4

Prefix and standard form

50,000,000 W

= 50MW (prefix)

= 5 x 107 W (standard form)

Both prefixes and use of standard form reduces the need to write many zeros. Which is better?



1. describe how to measure a variety of lengths with appropriate accuracy by means of tapes, rules, micrometers and calipers, using a vernier scale as necessary.

Measurement of lengths

Which instrument would you use to measure the length of a pencil?

A 15-cm or 30-cm rule


Which instrument would you use to measure the length of your desk?

A metre rule


Which instrument would you use to measure the length of a room?

A measuring tape


Which instrument would you use to measure the length of a school field?


Which instrument(s) would you use to measure the thickness of a pencil?

0.9 cm 0.92 cm

0.922 cm

ruler Vernier calipersMicrometer screw gauge

Measurement of Length

Measuring Instrument Range Precision

Measuring tape 0 – 5 m 0.1 cm

Metre rule 0 – 1 m 0.1 cm

Vernier calipers 0 – 15 cm 0.01 cm

Micrometer

screw gauge0 – 2.5 cm 0.001 cm

Quick Check

Which instruments would you use to measure the lengths of the following?

Diameter of a strand of hair

Internal diameter of a mug

Length of your textbook

Vernier Calipers

Vernier Calipers

Measured value is between 23 and 24 mm

= 23. __ mm

23 6

6

mm

Vernier Calipers

0 5 10

3 cm 4 cm0 cm

2.9_ cm4

Main scale

Vernier scale

Theory Workbook


Q4

(a) 3.43 cm

(b) 1.39 cm

Parts of a vernier calipers

Depth bar

Outer jaws

inner jaws

• Two main types of errors

1.5 Measurement of Length and Time1.5 Measurement of Length and Time

Random errors Systematic errorsRandom errors because they are unpredictable

Not random but constant

They arise when observers estimate the last figure of a reading on an instrument.

Due to the equipment being used – e.g. a ruler with zero error

Minimized by averaging a large number of readings

Cannot be reduced by averaging, but they can be eliminated if the sources of the errors are known

Accurate Measurement

Zero Error on a Vernier Scale

What isZero Error???

What isZero Error???

Definition:Definition:If the zero marks on the main scale and vernier scale do not coincide when the jaws are closed, there is a zero error.

Zero Error Subtracted from Reading

4th line after zero on vernier scale coincides with line on main scale: zero error = 0.04 cm

Zero error is subtracted from the reading

Zero Error Added to Reading

7th line after zero on vernier scale coincides with line on main scale:

Zero error = 0.1 – 0.07

= 0.03 cm


0.07 cm


7th line after zero on vernier scale coincides with line on main scale:

Zero error = 0.1 – 0.07

= 0.03 cm Zero error is ‘added’ to the reading

Note: By convention, ‘under-read’ zero error is negative, i.e. the zero error in this case is – 0.03 cm.

Textbook

Read TB pg 13

Example

Reading when jaws are closed

Reading when jaws are used to measure the thickness of a coin

Zero error

= +0.08 cm

Reading on scale

= 0.64 cm

Thickness of coin= 0.64 – 0.08 = 0.56 cm

Example

0 5 10

1 cm 2 cm

0 5 10

0 cm

1

Reading when jaws are closed

Reading when jaws are used to measure the thickness of a coin

Zero error

= - 0.02 cm

Reading on scale

= 0.84 cm

Thickness of coin= 0.84 – (- 0.02) = 0.86 cm

The micrometer screw gauge

http://members.shaw.ca/ron.blond/Micrometer.APPLET/


Reading

= main scale R + thimble scale R

5.5 mm

mm 0.14 mm

= 5.5 + 0.14 = 5.64 mm


5.14 mm

mm


25

30

35

7.29 mm

mm


25

30

35

3.79 mm


35

40

45

4.39 mm


35

40

45

6.89 mm

Theory Workbook


Q5

(a) 4.13 mm

(b) 2.79 mm

Precautions when using a micrometer

Avoid over-tightening use the ratchet for fine adjustment

Clean the ends of anvil and spindle before measuring.

Check for zero-error (read TB page 14)

Zero-error

Theory Workbook


Q6

Zero error = -0.02 mm

Reading on scale = 1.19 mm

Thickness of the coin = 1.19 – (-0.02)

= 1.21 mm



1. describe how to measure a short interval of time including the period of a simple pendulum with appropriate accuracy using stopwatches or appropriate instruments

How to measure time?

A simple pendulumPendulum.mht

A BO

1 oscillation

= A – O – B – O – A Or: 1 oscillation

= O – B – O – A - O

The Period (T) of a pendulum is the time taken for 1 complete oscillation.

http://www.fearofphysics.com/Pendulums/pendhl.html

http://www.phy.ntnu.edu.tw/oldjava/pendulum30/pendulum.html

Pendulum Lab

Stop Watches

Human Reaction Time: 0.3 s

Theory Workbook

Exercise 1.3 (page 3-4)Q1Q9Q10Q111 (a) Metre rule; (b) vernier calipers; (c) micrometer screw

gauge; (d) zero error; (e) period9 28.4 s; 2 min 25.6 s; 2 min 55.6 s10 34.26 s; 1 min 23.48 s11 (a) 0.64 s; (b) 0.16 s; (c) The period of oscillatoin

increases

Ticker-Tape Timer

Frequency:

50 dots per second

S 50

1

Class Practice/ Homework

Self-Management (TB page 23)

Misconception Analysis Q1 – 10

Practice (TB page 23 – 25)

Q3 and 4

Q1 on unit conversion is a bit challenging (optional)

Documents

3 e physcial quantities and units_pure_upload