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KOLEJ MATRIKULASI PERAK
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1.1 Physical Quantities
and Units
1.2 Scalars and Vectors
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State basic quantities and their respective SI units: length(m), time (s), mass (kg), electrical current (A), temperature(K), amount of substance (mol) and luminosity (cd).
State derived quantities and their respective units andsymbols: velocity (m s-1), acceleration (m s-2), work (J),force (N), pressure (Pa), energy (J), power (W) andfrequency (Hz).
State and convert units with common SI prefixes.
1.1 Physical Quantities and Units (1 hours)
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How fast does light travel ? How much do you weigh ?What is the radius of the Earth?What temperature does ice melt at?
We can find the answers to all of thesequestions by measurement.Speed, mass, length and temperature are
all examples of physical quantities.
Measurement of physical quantities is an essential part of Physics.
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1.1 Physical Quantities and Units
Physical Quantities- Quantities that are measurable with instruments in laboratory or can be
derived from these measured quantities.
- consists of a precise numerical value & a unit.
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- categorized into 2:
1. Base Quantities
2. Derived Quantities
- are standards for measurement of physical quantities that need cleardefinitions to be useful.
Physical Unit
- ex: metre (m) unit for lengthsecond (s) unit for timeKelvin (K) unit for temperature
SI Unit- International System of Units
- has been agreed internationally.
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Base Quantities & units
- fundamental quantity that can not be derived in terms of other physicsquantities.
candela
mole
kelvin
ampere
second
kilogram
meter
Name of SI unit
KTemperature, T
mLength , l
kgMass, m
sTime, t
cdLuminous intensity
molAmount of substance, n
AElectric current, I
Unit symbolBase
Quantity
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Derived Quantities & units- Are the physical quantities other than the base quantities.
- Are derived from base quantities according to a defining equation.
Q = It
W = Fs
P = F / A
F = ma
f = 1 / T
= m / Vv = s / t
Defining equation
A s
kg m2 s2
kg m1 s2
kg m s2
s1
kg m3
m s1
SI unit
Pa (Pascal)Pressure
--Velocity
--Density
Hz (Hertz)Frequency
C (Coulomb)Charge
J (Joule)Work
N (Newton)Force
Special
name
Physical Quantity
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Unit is defined as a standard size ofmeasurement of physical quantities.
Examples : 1 second is defined as the time required for
9,192,631,770 vibrations of radiation emitted bya caesium-133 atom.
1 kilogram is defined as the mass of a platinum-iridium cylinder kept at International Bureau ofWeights and Measures Paris.
1 meter is defined as the length of the pathtravelled by light in vacuum during a timeinterval of
s,, 458792299
1
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Prefixes- can be added to SI base & derived units to
make larger or smaller units
- Some physical quantities have no units.- Example:refractive index, strain
MultiplePrefix ( &
symbol)
1012 tera- (T)
109 giga- (G)
106 mega- (M)
103 kilo- (k)
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102 hecto- (h)
101 deci- (d)
102 centi- (c)
103 milli- (m)
106 micro- ()
109 nano- (n)
1012 pico- (p)
1015 femto- (f)
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Unit Conversions
- SI unit system is predominant throughout the world.
- another metric system that has been used:(a) cgs system ( centimeter gram second )(b) British Engineering system ( foot slug second )
- Units in different systems or differentunits in the same system can
express the same quantity.
- Is necessary to change from oneset of units to another.
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Solve the following problems of unit conversion.
a. 30 mm2 = ? m2 b. 865 km h-1 = ? m s-1
c. 300 g cm-3 = ? kg m-3 d. 17 cm = ? in
e. 24 mi h-1 = ? km s-1
Solution :
a. 30 mm2 = ? m2
b. 865 km h-1 = ? m s-1
1st method :
h1m10865hkm8653
1
Example 1 :
s3600
m10865hkm865
31
11 sm240hkm865
232 m10mm1 262 m10mm1
25262m103.0orm1030mm30
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2nd method :
c. 300 g cm-3 = ? kg m-3
s3600
h1
km1
m1000
h1
km865hkm865 1
s3600
h1
km1
m1000
h1
km865hkm865 1
11 sm240hkm865
33
2-
33-
3
3-
m10
cm1
g1
kg10
cm1
g300cmg300
-353 mkg103.0cmg300
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d. 17 cm = ? in
e. 24 mi h-1 = ? km s-1
cm1
incm17cm17 2.54
1
in6.69cm17
s3600
h1
mi1
km1.609
h1
mi24hmi24 1-
-1-21 skm101.07hmi24
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1.2 Scalars and Vectors (2 hours)
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1.2 Scalars and Vectors (2 hours)
ABBABA coscos
ABBABA sinsin
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Scalar Quantity
- Quantity which has only magnitude.
- Example: mass, distance, speed, work.
Vector Quantity
- Quantity which has both magnitude and direction.
- Example: displacement, velocity, force, momentum
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- Magnitude of the vector is written as |A|A
- Symbols for vectors : A or A
- A vector can be represented by an arrow. The length of the arrowindicatesits magnitude & arrow head shows the direction.
A
Representing vectors
Head of vector
Tail ofvector
A
magnitude
direction
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Equality of two vectors
- 2 vectors & are equal if they have the same magnitude and point inthe same direction.
A
B
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Negative Vector- Negative vector is a vector with the same magnitude as
but points in opposite direction.A
A
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Vector Addition & SubtractionAddition
- The addition of 2 vector, and result in a third vector called
resultant vector.
A
B
R
- Resultant vector is a single vector that will have the same effect as 2 ormore vectors.
- 2 methods of vector addition:
(1) Drawing / Graphical method - tail to head & Parallelogram
(2) Mathematic Calculation unit vector & trigonometry
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(1) vectors in the same directions
(2) vectors in the opposite directions
The direction ofresultant vector R is inthe direction of thebigger vector
Adding Parallel Vectors
NA 3
NB 7
NR 10Resultant,
NA 3
NB 7
NR 4Resultant,
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Resultant = 9 N East
Resultant = 40 N East
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(a) Tail to head method
Two equivalent ways to add vectors graphically: the tail-to-head method and
the parallelogram method.
Placing the tail of Bso that it meets the head of A
The Resultant, R=( A + B), is the vector from the tail of A to the head of B
A
B
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Placing the tail of each successive arrow at the head of theprevious one. The resultant vector is the arrow drawn from the tailof the first vector to the head of the last vector.
A
B C
D
+ + += ?
How to add vector A, B, C and D ?
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DCBAR
A
B
C
D
R
Tail of firstvector
Head of last vector
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(b) Parallelogram method
Resultant vector, : diagonal of a parallelogram formed with & as
two of its 4 sides.
R
A
B
A
B
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Resolving vector into 2 perpendicular compoments (2D)
A vector may be expressed in terms of its components.
A
Ax
Ay
x
y
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with the aid of trigonometry:
22|| yx AAA
A
Ax
cos cosAAx
A
Aysin sinAAy
Magnitude of vector A :
Direction of vector A :
x
y
A
Atan
* is alwaysmeasured from +x
axis.
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Unit vectors
A unit vector is a vector that has a magnitude of 1 with no units.
Are use to specify a given direction in space.
, & is used to represent unit vectorspointing in the positive x, y & z directions.
i j k
| | = | | = | | = 1i j k
http://d/Physics_SF017/Chap1/unitvector.swfhttp://d/Physics_SF017/Chap1/unitvector.swfhttp://d/Physics_SF017/Chap1/unitvector.swf -
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jAiAA yx
The vector can also written in unit vector form:A
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Example
A force of 800 N is exerted on a bolt A as shown in Fig. below. Determine thehorizontal and vertical components of the force.
x
y
yF
xF
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Solution
with the aid of trigonometry:
cosFFx
35cos800
NFx
655
sinFFy
35sin800
NFy 459
We may write in the unit vector formF
jNiNF )459()655(
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Example
The magnitudes of the 3 displacement vectors shown in drawing. Determine theresultant value when these vectors are added together.
By= 5 sin 30
Bx = 5 cos 30Ax=10 sin 45
Ay = 10 cos 45
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1.572.74Resultant
R
80C
5 sin 30 = 2.505 cos 30 =4.33B
10 cos 45 = 7.0710 sin 45 = 7.07A
Component yComponent xVector
22yx RRR
m16.3
)57.1()74.2(22
Magnitude of resultant vector
74.2x
R
57.1yR
R
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x
y
RRtan 573.0
74.257.1
xabove81.29
Direction of resultant vector
Or can write in unit vector form
jmimR )57.1()74.2(
Resultant vector , R = 3.16 m at 29.81 above +x
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Example
Let :
jib
jia
35
52
Find : (a)
(b)
(c)
ba
ba
32 |2| a
Solution
)
3
5()
5
2( jijiba
(a)
ji 27
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To find the magnitude of , 1st we have to calculate
(b) )35(3)52(232 jijiba
jiji 915104
ji
19
11
(c) |2| a
a
2
)52(22 jia
)104 ji
22 104|2| a
77.10
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Multiplying a vector by a vector
Dot Product ( )BA
cos|||| BABA
where |A| : magnitude of vector|B|: magnitude of vector
: angle between &
A
B
A
B
0 180
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is the magnitude of multiplied bythe component of parallel to .
BA
A
B
A
B cos
cos|||| BABA
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= zero when = 90 because cos 90 = 0BA
= maximum value when = 0because cos 0 = 1BA
Commutative law applied to dot product :
ABBA
Example of physical quantity : sFW
Dot product Calculation
Given 2 vector :
kBjBiBB
kAjAiAA
zyx
zyx
How to perform ? BA
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zzyyxx BABABABA
Remember :
090cos)1)(1(
10cos)1)(1(
kjkiji
kkjjii
)()( kBjBiBkAjAiABA zyxzyx
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Example
Given 2 vectors :
)285(
)423(
kjiB
kjiA
Calculate(a) the value of(b) the angle between 2 vectors
BA
Solution
)285()423( kjikjiBA
)2)(4()8)(2()5)(3(
9BA
(a)
produces a scalar
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(b)
||||cos
BA
BA
)64.9)(39.5(
9
cos:from BABA
03.80
222
)()()(|| zyx AAAA
222 )()()(|| zyx BBBB
39.5)4()2()3( 222
64.9)2()8()5( 222
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Example
Find the scalar product of the two vectors in figure. Themagnitude of the vectors are A = 4.0 N and B = 5.0 m
BA
A
B
130
53
Answer : 4.50
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Cross Product ( )BA
sin|||||| BABA
- produce a third vector, which is perpendicular to both of theoriginal vectors.
- The magnitude of the cross product is given by:
0 180
- Also called vector product.
A
B
BA
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is equals the magnitude of multiplied by thecomponent of perpendicular to .
|| BA
A
B
A
AB
sinB
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-- if is parallel @ anti parallel ( =0 @ 180 ) BA
& 0|| BA
-- if is 90 max|| BA
BA
&
Example of physical quantity :
BvqFm
Force acting on a charge moving in magnetic field
00sin|||||| BABA
ABBABA
90sin||||||
1
0
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BA
- the direction of new vector ( ) is normal to the plane that contain vector
& given by Right Hand RuleBA
A
B
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A
B
BA
Directed
upwards
A
B
AB
Directeddownwards
)( ABBA
C d t C l l ti
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Cross product Calculation
zyx
zyx
BBBAAA
kji
BA
jABBAiABBA zxzxzyzy ][][ kABBA yxyx ][
Keep In mind (RHR) :
0 kkjjii
kBB
AA
jBB
AA
iBB
AA
yx
yx
zx
zx
zy
zy
jkijik
kijkji
ijkikj
http://d/Physics_SF017/Chap1/unitvector.swf -
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Fig. (a) Fig. (b)
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Example
Given 2 vector :
Calculate : (a)(b)
)085(
)423(
kjiB
kjiA
Solution
)085()423( kjikjiBA
(a)
BA
|| BA
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222 342032|| BA
085
423
kji
BA
i)]4(8)0(2[
kjiBA 342032
79.50
j)]4)(5()0(3[
k
)]2)(5()8(3[
(b)
produce a vector