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Fisika Dasar Introduction and Vector 1

Jun 01, 2018

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    Basic Physics

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    Introduction

    1. What is Physics?

    2. Give a few relations between physics

    and daily living experience

    3. eview of !easure!ent and units "I#

    $%&I'# %(G)I"*

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    +%'&, -( "'-)-

    Scalar  is a /uantity which only signifies its!agnitude without its direction. 0 4

    %x. 15g of apple# 263 degreescentigrade# etc.

    Vector  is a /uantity with !agnitude and

    direction. 0 4%x. +elocity of a !oving ob7ect 8 a carwith a velocity of 199 5!hr due to (orth

    West# etc.

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    +%'&, -( "'-)-

    Writing conformity

    F  Bold fontF  Italic font signifying its magnitude

    :  (or!al :ont with an arrowhead on top of it (Use this)

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    +%'&, -( "'-)-

    efining a +ector by;

    1. 'artesian +ector 

    Ex. F = 59i + 59j + 29k N

    the magnitude i F = !592

     + 592

     + 292

    "  F = ##.$$ N

    %ue to &hich i the 'ector ((

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    +%'&, -( "'-)-

    X (i)

    Z(k)

     Y(j)

    F =

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    +%'&, -( "'-)-

    efining a +ector by;2. >nit +ector 

    Ex. F = F u !ue the )re'iou exam)le"

      =

    F for magnitude !F2 = Fx2 + Fy

    2 + F*2"

    u for direction !dimenionle and unity"

    u::

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    +%'&, -( "'-)-

    agnitude F = !592 + 592 + 292"

    F = ##.$$ N

    %irection = 

    9.@6i 9.@67 9.335

    α cos1 9.@6 A6.= 9 0angle fro! xaxis4

    β cos1 9.@6 A6.= 9 0angle fro! yaxis4

    γ  cos1 9.33 69.6 9 0angle fro! Baxis4

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    +%'&, -( "'-)-

    D 0i 4

    E 0k 4

    F 0 j 4

    F CC.33 (

    U

    FU 9.@6i 9.@67 9.335 

    α

    γ 

    β

    α  A6.= 9 

    β  A6.= 9 

    γ   69.6 9O

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    +%'&, -( "'-)-

    efining a +ector by;

    3. Position +ector 

    "i!ilar to unit vector# it differs on how tolocate the vectors direction which isusing the point coordinate.

    %x. : = :  u !ee next exam)le"

     r  0position vector4r 0position vector !agnitude4

    u

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    +%'&, -( "'-)-

    U

    @ !

    A !     2

         !

    Given;

    F 1

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    +%'&, -( "'-)-

    "olution;

      r r 

    u

    : = :  u

    2i A7 @5

    6.AC

    9.26i 9.

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    +%'&, -( "'-)-

    ,perations of +ector 

    1. -ddition

    2. "ubtraction3. ot Product

    A. 'ross Product

     

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    +%'&, -( "'-)-

    1. -ddition

    :1

    :2

      = :1 :2

      = 0:1x :2x4 i   0:1y :2y4 j   0:1B:2B4 k 

    θ

    θ   =y

    x

    &an 1

    ,

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    +%'&, -( "'-)-

    1. -ddition

    :1

    :2

      = :1 :2

      = 0:1x :2x4 i   0:1y :2y4 j   0:1B:2B4 k 

    θ

    θ   =y

    x

    &an 1

    ,

    esultant is directed

    fro! initial tail towards

    final arrow head

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    +%'&, -( "'-)-

    2. "ubtraction

      :1

    :2

      = :1 :2

      = 0:1x :2x4 i   0:1y :2y4 j   0:1B :2B4 k 

    θ

    θ   = y

    x

    &an 1

    ,

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    +%'&, -( "'-)-

    2. "ubtraction

      :1

    :2

      = :1 :2

      = 0:1x :2x4 i   0:1y :2y4 j   0:1B :2B4 k 

    θθ   =

    y

    x

    &an 1,

    &a5e note and watch

    out HHH

    0the sense is

    opposite to the givendiagra!4

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    +%'&, -( "'-)-

    3. ot Product

     

    :

    d  

    θ

    D 0i 4

    E 0k 4

    F 0 j 4

    :

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    +%'&, -( "'-)-

    - . B   - cos θ 0General :or!ula4           { {

    Vector Magnitude

              {

    The angle between

    vectors (between their

    tails)

    'artesian >nit vector  dot )roduct

    i . i =

    i . j = / i . k = / k . j = /

     j . j = k . k =

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    +%'&, -( "'-)-

    :ro! %xa!ple;

    J F . d  :d cos θ 0>sing +ectors !agnitude4

    0:xi :y 7 :B54 . 0dxi dy 7 dB54

    :x dx :y dy :B dB 0>sing 'o!ponent +ector4

    &he dot product of two vectors is called scalar product

    since the result is a scalar and not a vector 

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    0he dot )roduct is used to deter !ine;

    1. &he angle between the tails of the vectors.

    +%'&, -( "'-)-

    θ cos1

    - . B

     -

    2. &he pro7ected co!ponent of a vector 1 onto an axis

    defined by its unit vector u

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      W e  l c

     o m e  t o  t  h e 

      J u n g  l e 

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    +%'&, -( "'-)-

    D 0i 4

    E 0k 4

    F 0 j 4

    B

    -

    3

    : 199

    (

    θ

    Given ; :igure 1

    e/uired;

    1. θ

    2. :- 0$agnitude4

    :ig.1

    %xa!ple;

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    +%'&, -( "'-)-

    "olution ;

    1. Angle θ 

    :ind position vectors fro! to - and to 'r - 299i 8 2997 1995

    r '  9i 8 3997 1995 8 3997 1995

    cos θ r - . r 'r - r '

    9 @9999 19999

    [email protected]

    69999

    =AC@= 9.63C

    θ  'os 1 9.63C A2.A< o 0answer4

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    +%'&, -( "'-)-

    "olution ;

    r -u-

    r -

    2. F BA

    299i 8 2997 1995

    399 9.@@6i 8 9.@@67 9.335

    r 'u'

    r '

    9i 8 3997 1995

    [email protected] 8 9.=A=7 9.31@5

    :'  :' . u' 199 . 08 9.=A=7 9.31@54 =A.=7 31.@5

    :-  :' . u- 0=A.=i 31.@74 . 09.@@6i 8 9.@@67 9.3354

    @3.3 19.< 63.C ( 0answer4

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    +%'&, -( "'-)-

    "olution ;

     Alternative Solution

    :-  0199 (4 0cos A2.A<o4

    63.6= (

    :- :- u-  63.6= 09.@@6i 9.@@67 9.3354

    A=.2i 8 A=.27 2A.3

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    +%'&, -( "'-)-

    A. 'ross Product 

    B

    -

    F

    D 0i 4

    E 0k 4

    F 0 j 4

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    +%'&, -( "'-)-

     - x '  A is eual to B cross ! 

     -pply the right hand rule

     j k 

    i x 7 5

     7 x 5 i

    5 x i 7

     7 x i 5

    5 x 7 i

    i x 5 7

    i x i 9

     7 x 7 9

    5 x 5 9

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    +%'&, -( "'-)-

    Right Hand Rule

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    +%'&, -( "'-)-

    Right Hand Rule

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    +%'&, -( "'-)-

    Right Hand Rule

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    +%'&, -( "'-)-

    Right Hand Rule

    44. (answer for

    yourself)

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    +%'&, -( "'-)-

     - x '

    0x i   y j   B k 4 x 0'x i   'y j 'B k 4

    i j k 

    x y B

    'x 'y 'B

    0y 'B 8 B 'y4i   0B 'y 8 x 'B4 j   0x 'y 8 y 'x4"  -

    i j k 

    x y B

    'x 'y 'B

    i j 

    x y

    'x 'y

    0y 'B 8 B 'y4i  8 0x 'B 8 B 'x4 j   0x 'y 8 y 'x4" 

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    +%'&, -( "'-)-

     - x '

    0x i   y j   B k 4 x 0'x i   'y j 'B k 4

    i j k 

    x y B

    'x 'y 'B

    0y 'B 8 B 'y4i   0B 'y 8 x 'B4 j   0x 'y 8 y 'x4"  -

    i j k 

    x y B

    'x 'y 'B

    i j 

    x y

    'x 'y

    0y 'B 8 B 'y4i   8 0x 'B 8 B 'x4 j   0x 'y 8 y 'x4" 

    Full cautionfor the +6 ign

    and

    u,cri)t

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    +%'&, -( "'-)-

    %xa!ple; Given ; :igure 2

    e/uired ;

    1. $o 0$o!ent at

    point ,4

    2. $y 0$o!ent

    about y axis4

    B

    -

    F = //N

    D 0i 4

    E 0k 4

    F 0 j 4

    o

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    +%'&, -( "'-)-

    "olution;:inding the vectors needed

    : : u

    199A99i 8 2

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    +%'&, -( "'-)-

    B

    -

    F = // N

    D 0i 4

    E 0k 4

    F 0 j 4

    o

    7// j

    7//i + 5/j 8 2//k

    F = #./i 8 7#.9j 8 $9./7k

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    +%'&, -( "'-)-

    $o

    $o 1

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    +%'&, -( "'-)-

    $o

    $o 1