as chapter 1 physical quantities and units

8/18/2019 As Chapter 1 Physical Quantities and Units

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Chapter 1Physical Quantities

andUnits

Mr. Chong Kwai Kun


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Learning Outcomes

Candidates should be able to:

(e) show an understanding of and use the con"entions for labeling

graph a!es and table columns as set out in the AS# publication

Signs, Symbols and Systematic ($he AS# Companion to %&'%

Science, ***)

(f) use the following prefi!es and their symbols to indicate decimal

submultiples or multiples of both base and deri"ed units: pico (p),nano (n), micro (+), milli (m), centi (c), deci (d), kilo (k), mega (),

giga (-), tera ($)

(g) make reasonable estimates of physical quantities included within the

syllabus

(.) distinguish between scalar and "ector quantities and gi"e e!amplesof each

(k) add and subtract coplanar vectors

(l) represent a vector as two perpendicular components.


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CHAPTER 1.1

Physical

Quantities


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Physical Quantities

- a quantity that can be measured/0hysical 1uantity

Notes:

%/ has a numerical magnitude and a unit/

/ can be subdi"ided into: 2undamental 3 4ase 1uantity 5eri"ed 1uantity


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Base Quantities

- 1uantity that cannot be e!pressed in

terms of other quantities/

4ase 1uantity

Notes:

%/ $here are se"en base quantities/

Base Quantity SI Units symbol

ass kilogram kg

6ength meter m

$ime second s

$emperature el"in

#lectric current Ampere A

6ight intensity candela cd

Amount of substance mole mol


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Derived Quantities

- 1uantity that is a combination of

two or more base quantities by meantof multiplication, di"ision or both/

5eri"ed 1uantity

Notes:

%/ #!amples of deri"ed quantities/

eri!ed Quantity Relation "ith #ase Quantity

Area Length x width

Volume Length x width x Height

Density Mass / Volume

!eed Distance / "imeAcceleration Distance / #"ime x "ime$

%orce Mass x Acceleration

Moment o& &orce %orce x Per!endicular Distance

Pressure %orce / Area


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n erna ona ys em oUnits (&%)

7 A unit is a particular physical quantity, defined

and adopted by con"ention, with which otherparticular quantities of the same kind are

compared to e!press their "alue/

7 $he SI is founded on se"en SI base units for

se"en base quantities assumed to be mutually

independent/

7 $he SI derived units for these deri"ed quantities

are obtained from these equations and the

se"en SI base units/


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eri!ed &% Units

eri!ed *uantity &% deri!ed unit&ym+o

larea s'uare meter m(

volume cu)ic meter m*

s!eed+ velocity meter !er second m/s

acceleration meter !er seconds'uared

m/s(

wave num)er reci!rocal meter m-

mass density.ilogram !er cu)ic

meter.g/m*

s!ecic volumecu)ic meter !er

.ilogramm*/.g

current densityam!ere !er s'uare

meter

A/m(

ma netic eld


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%mportant eri!ed Units7 2or ease of understanding and con"enience, *8 SI

deri"ed units ha"e been gi"en special names andsymbols

eri!ed *uantity ,ame&ym+

ol

Epression

in terms

o'other &%

units

Epression

in terms

o' &% +aseunits

!lane angle radian rad - m0m- 1

&re'uency hert2 H2 - s-

&orce newton 3 - m0.g0s-( !ressure+ stress !ascal Pa 3/m( m-0.g0s-(

energy+ wor.+'uantityo& heat

4oule 5 30m m(0.g0s-(

!ower+ radiant 6ux watt 7 5/s m(

0.g0s-*

electric charge+


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%mportant eri!ed Units

eri!ed *uantity ,ame&ym+ol

Epression

in termso'

other &%units

Epression

in termso'

&% +aseunits

electric !otentialdi9erence+

electromotive&orce

volt V 7/A m(0.g0s-*0A-

ca!acitance &arad % 8/V m-(0.g-0s:0A(

electric resistance ohm V/A m(0.g0s-*0A-(

magnetic 6ux we)er 7) V0s m(0.g0s-(0A-

magnetic 6ux

densitytesla " 7)/m( .g0s-(0A-

inductance henry H 7)/A m(0.g0s-(0A-(


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&% Pre/es7 0refi!es are the preceding factor used to represent "ery

small and "ery large physical quantities in SI units/Prefix Decimal Multiplier Symbol

mto 10

15

f

pico 10

12

p

nano 10

9

n

micro 10

6

milli 10

3

m

c nti 10

2

c

d ci 10

1

d

kilo 10

3

k

M ga 10

6

M

Giga 10

9

G

T ra 10

12

T


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Dimensions ;


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%undamental Dimensions

1)Length 0 L

$)ass 0

2)Time 0 T

3)Electric Current 0 %4)Temperature 0

θ

5)Amount o' atter 0 ,

6)Light %ntensity 0 7


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Physical Quantities Dimensions

1)8elocity9 :!; < LT=1

$)Acceleration9 :a; < LT=$

2)>orce9 :>; < LT=$

3)ensity9 :ρ; < L=24)Pressure9 :P; < L=1T=$

5)Energy9 :E; < L$T=$

ny Physical Quantity; < aL+Tc%d


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Dimensions =ules

Rule 2

7 5imensions obey rules of multiplication anddi"ision

L][

][L

[M]

[L]

][T

][T

[M]

2

2

2

=

==C

AB D


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Rule 3

7 In scientific equations, the arguments of9transcendental functions must be

dimensionless/

x must )edimensionless

ranscen!ental "unction - Cannot be gi"en by algebraic e!pressions consisting

only of the argument and constants/ ;equires an infinite series

Dimensions =ules

x D x B

xC x A3 )exp(

)sin( )ln(====

...!3!2

132

++++= x x

xe x


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imensions and dimensional analysis

$he dimension of an equation is said to be #omo$eneous

if all the terms in it ha"e the same dimensions or units/

6(63$)$


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Question

Check the equation for dimensional consistency:

=ere, m is a mass, g is an acceleration,

c is a "elocity, h is a length

2

2

2

)/(1mc

cv

mcmgh −

−=


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6> ?% $?

Consider the equation:

@here m and M are masses, r is a radius andv is a "elocity/

@hat are the dimensions of G

Question (

mv2

r = G

Mm

r 2


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-i"en 9! has dimensions of distance, 9u has

dimensions of "elocity, 9m has dimensions of massand 9g has dimensions of acceleration/

Is this equation dimensionally "alid

Bes

Is this equation dimensionally "alid

o

Question *

x = (4 / 3)ut

1− (2gt 2 / x)

x = vt

1− mgt 2


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CHAPTER 1.3

Scalars andVectors


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Scalars 1uantities

1uantities that ha"e magnitude only/

Dectors 1uantities

1uantities that ha"e both magnitude

and direction/

calars ; Vectors


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Question


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Answer:

Question (

Answer:


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Answer>

Answer>

Question *


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Adding &calars

added or subtracted by using simple arithmetic/

#!ample: E kg plus & kg gi"es the answer %* kg

8 <

E kg& kg

%* kg


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Adding 8ectors

&!!ition of 2 'ectors in t#e same !irection

E Resultant force

( E 8 < & ) *


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Adding 8ectors

&!!ition of 2 'ectors in t#e opposite

!irections

E

Resultant force

< E 8 (− )

< E −

<

Adding Vectors


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0oints to note:

7 All gi"en "ectors must be +oine! #ea! to tail in order tofind the resultant "ector

7 $he order of the "ectors to be added !oes not matter

7 $he magnitude and direction of the resultant "ector is

measured after t#e scale !ra,in$ is finis#e!/

Adding Vectors


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@raphical ethod#!ample %: Add these "ectors using the tip?to?tail

method/

8

8 <

A B

C

A B C

A ng 8ectors


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A ng 8ectors@raphically

@hen you ha"e many"ectors, .ust keep

repeating the process

until all are included

$he resultant is still

drawn from the origin

of the first "ector to

the end of the last"ector

B A+

B A+

C B A ++


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8ector &u+traction

Special case of "ectoraddition Add the negati"e of the

subtracted "ector

Continue with standard"ector addition procedure

( )− = + −A B A Br r r r

A

B

B A−

B−

ultiplying or i!iding a


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ultiplying or i!iding a8ector

The magnitude of the vector is multiplied or divided

by the scalar If the scalar is positive, the direction of the result is

the same as of the original vector If the scalar is negative, the direction of the result is

opposite that of the original vector

A3−

A3 A


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Adding Dectors:

7 5iagram shows two forces 2% < E and 2 < & actingon a body with an angle of EFo between them/ @hat is

the resultant force ;

@xam!le

EFG

E

& Solution (%)

Hsing a suitable scale, for e!ample, % cm : %

%/JG

R

&

E

$he resultant force is /> and makes an angle of %/JG

with the & "ector/


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>

Solution () Again, using a suitable scale, for e!ample, % cm : %

E

&

R

%/JG

$he resultant force is /> and makes an angleof %/JG with the & "ector/


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=esultant &orce o& * %orces in ( Dimensions

(a) Hnbalanced forces

–@hen we apply > forces to a point ob.ect, the

resultant force acting on the ob.ect can be obtained

by adding the force "ectors/

A

BC

R


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=esultant %orce o& * %orces in ( Dimensions

(b) 4alanced forces

• @hen > forces acting on an

ob.ect are balanced, the ob.ect will not accelerate/

• @hen we draw the "ector diagram the > "ectors form

a closed triangle/

• ;esultant is Kero/

Q ti :


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Answer> 8

Question :

Q ti


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Answer> A

Question


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Resolution o' !ectorsIt is often con"enient to split a single "ector

into two perpendicular components/

Consider force 2 being split into "ertical and

horiKontal components, 2D and 2=/

In rectangle A4C5 opposite:

sin L < 4C 3 54 < 5A 3 54 < 2D 3 2

$herefore: 2D < 2 sin L

cos L < 5C 3 54 < 2= 3 2

$herefore: 2= < 2 cos L

""%

".

/

B&

D

"% ( " sin .

" ( " cos .

The ‘cos’ component is always

the one next to the angle

Q ti


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Answer>

Question

Q ti C


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nswer>

Question C

Question


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Answer> 8

Question

Question G


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omments> 7hen the o)4ect is in e'uili)rium state+ the resultant vector is EF

Question G


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as chapter 1 physical quantities and units

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