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					TECHNOLOGY AND ENGINERRING




SKILL DEPARTEMEN PROGRAM : BUILDING TECHNOLOGY
 SKILL COMPETENCE : DRAWING BUILDING TECHNOLOGY
Implementing Statistics and Energy

                         Objectives :

 The students are able to explain the meaning of mechanical
  technique and building statistics

 The student are able to explain the meaning of energy,
  resultant vector and energy moment

 The students are able to explain arranging and decomposition
  process graphically and analytically

 The students are able to arrange and to decompose energy
  graphically and analytically


                                              Technology and
                                              Reenginering
     Implementing Statistics and Energy

 The students are able to decompose energy to some
  energies graphically well

 The students count energy resultant

 The students are able to count energy moment

 The students are able to explain mean and kinds of
  burden on construction counting of building statistics




                                         Technology and
                                         Reenginering
   Implementing Statistics and Energy

 The students are able to know the working
 principal of energy action reaction

 The students are able to explain the working
 pricipal of torque coupling

 The stdents are able to explain the working
 principal of energy balance


                                  Technology and
                                  Reenginering
Term of Technical Mechanic and building
                  static




                    OR




                               Technology and
                               Reenginering
Term of Technical Mechanic and building
                  static




     a scientific science learning about energy
   balance of statics constructions even though
   there are several working energies.




                                     Technology and
                                     Reenginering
Term of Technical Mechanic and building
                  static




   A scientific science learning about
   action of an abject without learning the
   cause of that action




                                Technology and
                                Reenginering
Term of Technical Mechanic and building
                  static




  A science studying about moves and
    cause of that move itself




                                Technology and
                                Reenginering
Term of Technical Mechanic and building
                  static




  A scientific science learning about
   stability and power of a building
   construction or parts of those building
   itself


                                  Technology and
                                  Reenginering
Term of Technical Mechanic and building
                  static



   Including




                               Technology and
                               Reenginering
Term of Technical Mechanic and building
                  static




  A calculation held to make building to be strong.
  In this case, a checking must be held concerning
  of building position together with foundation and
  land texture as the foundation.




                                     Technology and
                                     Reenginering
Term of Technical Mechanic and building
                  static




  is a calculation deciding the size of material
  texture needed to support power/energy working
  on the construction by considering security
  factors.




                                       Technology and
                                       Reenginering
Term of Technical Mechanic and building
                  static




  This kinds of calculation is very important to
  guarantying power and to make material ussage
  efficient




                                         Technology and
                                         Reenginering
Term of Technical Mechanic and building
                  static




  Is a calculation to check whether there are a
  change in shape, over limit transitioning or not.




                                       Technology and
                                       Reenginering
Term of Technical Mechanic and building
                  static




 a calculation to check whether the building be built
   strong enough to the load planned




                                      Technology and
                                      Reenginering
  Term of energy, vector, resultante dan
            energy moment
 Term of Energy

  If we are going to know what is energy, see and
  observe these experiences below.




  A ball is kicked so it will rotate, or there is a change of
  place of the ball.

                                           Technology and
                                           Reenginerring
Term of energy, vector, resultante dan
          energy moment




A rolling ball is kicked again, this will rotate a bit
faster. It means there is a chage to the ball.




                                          Technology and
                                          Reenginerring
Term of energy, vector, resultante dan
          energy moment




A quite ball is placed in the corner of the wall.
Having kicked, this ball doesn’t move at all. But, a
fiew seconds there is change with ball.


                                      Technology and
                                      Reenginerring
  Term of energy, vector, resultante dan
            energy moment




From the three experiences above that :

“Energy is whatever things that may cause
 change of a place, movement or shape.”




                                 Technology and
                                 Reenginerring
Term of energy, vector, resultante dan
          energy moment




            P=mxa

           P = energy
           m = weight
           a = speed



                               Technology and
                               Reenginerring
Term of energy, vector, resultante dan
          energy moment




                               Technology and
                               Reenginerring
Term of energy, vector, resultante dan
          energy moment




For example 100 kgs, 1000 Newtons and 50
Tons
               = 100 kgs


                            = 1000 N




                               Technology and
                               Reenginerring
Term of energy, vector, resultante dan
          energy moment




   A target for the energy working




    The box is pushed on spot A, so
    the box will move to the right.

                                Technology and
                                Reenginerring
Term of energy, vector, resultante dan
          energy moment




    The box is pushed on spot B, so it
    won’t move othetwise it plunges




                                Technology and
                                Reenginerring
Term of energy, vector, resultante dan
          energy moment



    Both experiment pictures show
    that energy has a work spot




                               Technology and
                               Reenginerring
Pengertian gaya, vektor, resultante dan
            momen gaya




    Work line is a stright line scratching
    with that energy itself.




                                   Technology and
                                   Reenginerring
Term of energy, vector, resultante dan
          energy moment

               Work                   Work
                line                  line




  An energy can be moved straight or

  Reverse as long as staying on its work line

                           primary



               reverse     straight


                                             Technology and
                                             Reenginerring
Term of energy, vector, resultante dan
          energy moment




Energy has a direction to the left, right,
upper side, under etc.

Energy is a vector that is range that has
direction.



                                  Technology and
                                  Reenginerring
Term of energy, vector, resultante dan
          energy moment

We can’t see energy but sense it. So,

To describe energy in finishing building
static problem, we need symbols.

Symbol is scaling and direction line called

Vector.



                                Technology and
                                Reenginerring
Term of energy, vector, resultante dan
          energy moment


For instance energy (P) = 100 kgs

Energy scale 1 cm = 20 kgs so,

vector length =
                  100
                       5 cms
                   20


Energy scale 1 cm = 20 kgs shows that 1
cm works for 20 kgs energy.



                                 Technology and
                                 Reenginerring
Term of energy, vector, resultante dan
          energy moment




       TO FINISH BUILDING STATIC PROBLEMS
        BY USING PAINTING OR GRAPHICS


                                     Technology and
                                     Reenginerring
Term of energy, vector, resultante dan
          energy moment




Organizing or adjoining energy or if two
energies or more could be linked to be a
resulting one called RESULTANTE.




                                Technology and
                                Reenginerring
 Term of energy, vector, resultante dan
           energy moment

Resultante symbolized R
See this picture:

                          Having combined to R,
                          It has a different height and
                          direction.




P1 = Energy 1
P2 = ENERGY 2
R = Resultante
                                    Technology and
                                    Reenginerring
 Term of energy, vector, resultante dan
           energy moment




Moment is a situation in which action and
reaction is not in the same work line.
                    Energy moment is the Moment multiplied by
                    Length.

                    M=Pxl
                    M = Moment
                    P = Energy
                    L = Length

                                         Technology and
                                         Reenginerring
   Term of energy, vector, resultante dan
             energy moment
Rules of moment :
1. If it rolls as straight as clock pointer, it’s called
    positive moment (+).
2. If it rolls inconventional, it’s called negative moment
    (-).

SEE THIS PICTURES :




                                         Technology and
                                         Reenginerring
Setting and dividing energy graphically and
                 analitically




Arranging or adjoining energy is to determine
resultante (R), it means two or more energies can
be joined to be one called resultante (R).




                                         Technology and
                                         Reenginerring
Setting and dividing energy graphically and
                 analitically




                      Achieved by two ways




       Image method        Calculation method




                                       Technology and
                                       Reenginerring
 Setting and dividing energy graphically and
                  analitically




This method must involve energy scales and draw it
properly. An error in imaging will effect the result.




                                             Technology and
                                             Reenginerring
 Setting and dividing energy graphically and
                  analitically



Is on the same straightly work line

Example:
Set energy P1 = 50 kgs and P2 = 80 kgs on one track
To be resultante (R).


Conclussion :
Decide energy scale for instance 1cm = 20 kgs
a. Vector image P1
b. Relate vector P2 from the bottom side of P1


                                                 Technology and
                                                 Reenginerring
Setting and dividing energy graphically and
                 analitically




           Work line                    P2          Work line

                       P1


            2,5 cm               4 cm   R




       R = (2,5 + 4) cm x 20
         = 130 kg (to the right side)



                                             Technology and
                                             Reenginerring
 Setting and dividing energy graphically and
                  analitically



Is on an inconventional work line

example:
Set two energies P1 = 150 kgs to the left and P2 = 50 kgs (to the right)
   to be a single resultante (R).


Conclussions :
Decide energy scale for instance1cm = 25 kgs




                                                    Technology and
                                                    Reenginerring
Setting and dividing energy graphically and
                 analitically



          Work line                               Work line

                   P1                 P2
                                            50
                                            25
          2,5 cm

                        6 cm



                               4 cm




                                           Technology and
                                           Reenginerring
Setting and dividing energy graphically and
                 analitically




                             150
   a. Illustrate vectur P1 =     = 6 cm
                              25
   b. Illustrate vector P1 =        = 2 cm
                               50
                               25

   So R = ( 6 – 2 ) cm x 25
          = 100 kg ( left side )




                                             Technology and
                                             Reenginerring
Setting and dividing energy graphically and
                 analitically




                                  Single work spot/

     Different work line          Different work spot




                                    Technology and
                                    Reenginerring
  Setting and dividing energy graphically and
                   analitically


Arranging energy with Paralelogram
 Arranging energy with paralelogram is so
 easy to do, but for one that is different
 direction and spot, may cause a
 complicated image.




                                     Technology and
                                     Reenginerring
  Setting and dividing energy graphically and
                   analitically

Example:




Decide energy resultante of
P1 = 100 kg
P2 = 100 kg
P3 = 125 kg
With angles above
                                     Technology and
                                     Reenginerring
   Setting and dividing energy graphically and
                    analitically



Conclussion :

1. Decide energy scales for instance 1 cm = 25 kg.

2. Illustrate energy position with scaling. Make
   parallelogram with P1 and P2 as the side.

3. Pull the diagonal (made from P1 and P2 and R1)




                                        Technology and
                                        Reenginerring
  Setting and dividing energy graphically and
                   analitically



5. Make a paralelogram with R1 and P3 as its side.

6. Pull diagonally from the angle R1 and P3 and to be
  R

7. Decide R length then multiplied with energy scale
  and that’s R




                                       Technology and
                                       Reenginerring
  Setting and dividing energy graphically and
                   analitically

See this picture :




   R = 10,2 cm x 25 = 280 kg
   If there are many energies, so the way used is the
   The same with above.
                                       Technology and
                                       Reenginerring
  Setting and dividing energy graphically and
                   analitically

Arranging energy with poligon
  Deciding resultante with poligon, we only connect

 one energy with the other, then the connector

 of the first work line with the last one, then we called
 it resultante (R). Otherwise, it move to the last
 energy.




                                         Technology and
                                         Reenginerring
    Setting and dividing energy graphically and
                     analitically

Example: Decide energy resultante P1, P2, P3
          and P4
For instance energy scale1 cm = 30 kgs
                                   Solving steps :
                                   1. Ilustrate the enrgy position
                                      with scaling.
                                   2. Connect P2 from the bottom P1.
                                   3. Connect P3 from the bottom P2.
                                   4. Connect P4 from the bottom P3.
                                   5. Connect the work line P1 to the
                                      bottom P4 that’s R.
                                   6. Decide the length of R then
                                      multiplied with energy scale,
                                      that’s R total
                                                 Technology and
                                                 Reenginerring
 Setting and dividing energy graphically and
                  analitically




1. Arrange energies scraching in single work line

  By inserting digit of energy where it must be
  positive if go to the right (+) and be negative (-) if
  go to the left or both.




                                         Technology and
                                         Reenginerring
  Setting and dividing energy graphically and
                   analitically

Case1 :



R = 60 + 50 + 40 = 150 kgs (to the right)


Case 2 :



R = -120 + 40 + 30 = -50kgs (to the left)

                                     Technology and
                                     Reenginerring
   Setting and dividing energy graphically and
                    analitically


2. Arranging two single work line energies but not in
   a single work line.




  The second Resultante of the energy P1 and P2

  creating  angle can be found with a formula :
              R  P  P2  2P P2 cos
                   1         1
                                              Technology and
                                              Reenginerring
  Setting and dividing energy graphically and
                   analitically


Otherwise R position can be found with sinus formula




              P1           R
                  
            sin  sin (180   )
                    P1. sin(180   )
            sin  
                            R
                                        Technology and
                                        Reenginerring
Setting and dividing energy graphically and
                 analitically




Decide the resultante P1 and P2 that create 45
degree angle, also  angle formed R



Conclussion ….
                                      Technology and
                                      Reenginerring
   Setting and dividing energy graphically and
                    analitically

Conclussion :


                R  P  P2  2 P P2 cos
                      2    2
                     1          1

                  502  702  2.50.70 cos 45o
                  2500  4900  7000.0,707
                  7400  4949
                  12349
                 111kg

                                           Technology and
                                           Reenginerring
Setting and dividing energy graphically and
                 analitically


                     P . sin(180   )
           sin      1
                             R
                     50. sin 45o
                
                          111
                     35,35
                
                      111
                    0,3184
               a sin 0,3184
                 18,57 o


                                         Technology and
                                         Reenginerring
   Calculating Energy moment

If we wish to know moment, check this
experiment




                              Technology and
                              Reenginerring
     Calculating Energy moment




The three images are pieces of wood connected to

Angle. Then, we hold from the vertical and we give

Slight load (P) from upper side

                                      Technology and
                                      Reenginerring
    Calculating Energy moment

, so it sense slight by our hands. We move the slight
load (P) a litle bit to the right on the horizantal
(image 2) so it will sense heavier otherwise the load
is still the same. Then, we move untill the bottom
horizontal wood then our hands are to weak to hold
this load other wise this load is still slight.




                                            Technology and
                                            Reenginerring
    Calculating Energy moment

From the experiment above, we can coclude on
the first situation the load sense slight bacause the
load scraches on the line with the reaction (there’s
no moment)



In the second experiment, the load sense heavier
because it no more in the same work line with
reaction (the moment is works).

                                       Technology and
                                       Reenginerring
  Calculating Energy moment


In the third experiment, our hand are too weak to
hold because the distance of action and reaction
work line getting bigger (the moment get higher)




So ……                       next slide




                                    Technology and
                                    Reenginerring
       Calculating Energy moment

SO :

1. Moment is an event where an action and reaction
   isn’t in the single work line.

2. The total of moment is energy multiplied by
   distance

3. Unit of moment is unit of energy multiplied by unit
   of distance (kg.cm, kg.m, ton.cm, ton.m)



                                        Technology and
                                        Reenginerring
   Calculating Energy moment

Case1 :

A cube clipped vertically on a wall. The bottom
of the cube is loaded P = 100 kgs.

How big the moment in A?



Conclussion …


                                     Technology and
                                     Reenginerring
       Calculating Energy moment

Conclussion :




   A            P = 100 kg


       L=2m
                        Moment on A is :
                        MA = P.L
                             = 100.2
                             = 200 kg.m

                                          Technology and
                                          Reenginerring
      Calculating Energy moment

Case 2 :                    Known :

                            P1 = 150 kg

A          P1               P2 = 50 kg
                       P2
                            Searched MA ?
                            Coclussion :
    L=2m        L=2m
                            MA = P1.2 – P2.4
                               = 150.2 - 50.4
                               = 300 – 200
                               = 100 kgm

                                      Technology and
                                      Reenginerring
 M Calculating Energy moment
Case 3 :

        A            P1               P2              P3




            L=2m           L=2m              L=2m

    Known : P1 = 100 kg, P2 = 40 kg dan P3 = 80 kg
    Searched    : MA ?
    Conclussion : MA = -P1.2 + P2.4 - P3.6
                      = -100.2 + 40.4 – 80.6
                      = -200 + 160 – 480
                      = -520 kgm
                                                    Technology and
                                                    Reenginerring
    Calculating Energy moment
Case 4
Contoh 4 :        Psin 60
                       P = 1000 kg


A
                          Coclussion:
                          1. Describe P to vertical
     L=3m
                          2. Description Psin60o
Known: P = 1000 kg        MA = Psin 60 x 3
             angle60o         = 1000.0,866.3
Serched: MA?                  = 2598 kgm



                                        Technology and
                                        Reenginerring
Describing kinds of loads on building static
         constraction calculation




                                     Technology and
                                     Reenginerring
Describing kinds of loads on building static
         constraction calculation




Decease Load                  Life load




Wind Load                     Tremor Load

                                     Technology and
                                     Reenginerring
 Describing kinds of loads on building static
          constraction calculation




Centered                               Load is not
                      Edge
 Load                                  divide well
                      Load

                                      Technology and
                                      Reenginerring
Describing kinds of loads on building static
         constraction calculation




  Direct                              Indirect

   Load                                   Load


                                     Technology and
                                     Reenginerring
Describing kinds of loads on building static
         constraction calculation

Loads on building contructios based on its nature are :
1. Decease Load
  is all kinds of load comes from weight of building
  begin from the pondation to the roof
2. Life Load
  is all kinds of load temporarily load loading the
  building itself or its element.



                                          Technology and
                                          Reenginerring
Describing kinds of loads on building static
         constraction calculation

3. Wind Load
  is all kinds of load on the building caused by winds.
4. Tremor Load
  is all kinds of loadon building caused by a
  tremor/earthquake.




                                         Technology and
                                         Reenginerring
   Explaining mean and kinds of load on
         building static calculation
Based on its shape, load of a buildig is divide in to two :
• Centered Load
  Is a load that has a small volume
  Example: pressing to train monorail by the train
  wheel
2. Spreading Load
  is a load that has spreading volume.
  example : Floor plat, concrete beam, and a
  pressuere on cocrete beam wall.

                                           Technology and
                                           Reenginerring
   Explaining mean and kinds of load on
         building static calculation
3. Centered Load
  is a load where the volume is spreading but its load
  isn’t divide widenly.
  Example : Forcing water on bathtube wall or forcing
  water on a eater gate.




                                        Technology and
                                        Reenginerring
 Explaining mean and kinds of load on
       building static calculation
Based on its working of load on construction, on that
load is given two loads they are direct and indirect
loads.




                                      Technology and
                                      Reenginerring
Explaining mean and kinds of load on
      building static calculation

                        P



                    a

  Load (P) direct to cocrete (a)




                                   Technology and
                                   Reenginerring
 Explaining mean and kinds of load on
       building static calculation

                            P
             1/2P                   1/2P


                        a
                    b           b


Load (P) direct to the concrete (a) otherwise indirect
                to the concrete (b).


                                           Technology and
                                           Reenginerring
 Explaining mean and kinds of load on
       building static calculation
Labelling these loads contains :
For centered load :
→ P = 1000 kg, P = 12 ton, etc.
For spread load :
→ q = 400kg/m, q = 2ton/m, etc.
For wind load :
→ q = 20kg/m2, q = 0,02 t/m2, etc.




                                     Technology and
                                     Reenginerring
    Work principal of energy action and
                 reaction

An object A takes pressing energy to the other one B,
so object B takes the same pressing energy to A but it
has different direction received by B.
Pressing energy A on B is called action energy while B
to A is called reaction energy. So, Newton rule III;
Action energy = Reaction energy




                                          Technology and
                                          Reenginerring
   Work principal of energy action and
                reaction
As an exampel, see this :
An object A with weight G is placed on flat floor B:



               N=G      Because the object A is in silent, so
                        Floor B will create reaction energy
                        with amount N kg to the abject A.
                 A      So, N = G kg where direction of
  LANTAI        B       energy N contradicted to C. Those is
  Floor
           G            called Normal energy.



                                           Technology and
                                           Reenginerring
     Work principal of energy action and
                  reaction
If the object A is in the blunt flat side pulled by an energy P1, this is
why moving energy W1 coming between object A and those blunt
flat. Because, moving energy W1 as same sa with P1 but it has
contradiction direction, so the resultant energy is nil, W1 = P1.



                                N=G




                                        A
                     W1                     P1

                     LANTAI             B
                     Floor
                                 G
                                                    Technology and
                                                    Reenginerring
    Work principal of energy action and
                 reaction
If the object A is in a blunt flat floor pulled with P2 energy where
P2>P1 so object A-when it moves to the right, in the same time
power energy W reaches the biggest score (W max).



                         D         N




                                                A

                        Wmaks         P2 > P1   B
                                  G

                                                    Technology and
                                                    Reenginerring
     Work principal of energy action and
                  reaction
When the object A is going to move, the object is still staying. So,
Wmax = P2
Resultant energy from w Max and normal energy (N) is D




                    Wmaks
             tgn 
                     N

 tgn  = f is called energy coeeficient
 angle  is called angle energy


                                                  Technology and
                                                  Reenginerring
   Work principal of energy action and
                reaction
If the energy P2 tobe higher to P3, otherwise Wmax has a
constant score
In addtion P3 is bigger than W Max so object A moving to the
right with acceration :



     P3  Wmaks
  a
         m
    Note :
    a = acceleration
    m = Object Mass A

                                             Technology and
                                             Reenginerring
   Work principal of energy action and
                reaction

Rules of magnetism energy

a. Magnetism energy straightly proportionates to
  normal energy N.
b. Amount of Magnetism energy defends on kinds
  both materials, on its immense.
c. Amount of Magnetism energy doesn’t defend on
  the immense, except if the volume is small and its
  deformation relatively huge.


                                       Technology and
                                       Reenginerring
  Work principal of energy action and
               reaction

d. Magnetism energy is impossibly bigger than the
  energy from the silent object.
e. Static energy between tow objects is tangensial
  energy forcing up one object to another.
e. Magnetism energy is reaction energy contradicted
  to action energy direction.




                                      Technology and
                                      Reenginerring
   Work principal of energy action and
                reaction

If energy P doesn’t work on the wall between
object and floor (see image).


                       N=G


                                 G
                   b
                                     a
              W

                             A
                  G


                                         Technology and
                                         Reenginerring
Work principal of energy action and
             reaction
                            N=G



                   W                 P
                             Z




                                         A
                            G

  Energy P and Magnetism energy W causes kopel +P.a. This is
  called Rooling Kopel and is balance where it is set up by
  normal energy N and weight energy G –Nb (stability
  moment)

                                             Technology and
                                             Reenginerring
Work principal of energy action and
             reaction
So Pa – Nb=0 or momen = 0. then, spot side of
normal energy N moves to B to the right with length b.
if the object will then roll, so the spot side N right to di
A.


Generally in energy term, if the object considered as
material spot, alll kinds action and reaction energy is
tyaken from spot side Z of the object


                                             Technology and
                                             Reenginerring
     Work Principal of EnergyBalances

If the action and reaction energies are working on a
work line concurrent, so the object is in balance with
some rules :
a. Amount of horizontal energy = 0 or H=0
b. Amount vertical energy = 0 or V=0
c. Amount moment=0 or MA=0, with A is a arbiterary
spot on a flat land.



                                        Technology and
                                        Reenginerring
 Work Principal of EnergyBalances
                       N=G



              W                P
                       Z




                                   A
                       G
From the diagram of action and reaction energy, we have
a. P-W=0
b. N-G=0
c. Amount of energy momen to contradicted work line Z=0.



                                       Technology and
                                       Reenginerring
    Work Principal of EnergyBalances

                 W              N




               G              P
These are graphics calculation:
Object is in balance if :
a. Closed Poligon, resultan R=0.
b. Energies through a single spot Z.


                                       Technology and
                                       Reenginerring
   Work Principal of EnergyBalances



Notes :
As a note that eventhough resultant R=0 that quite
situaton not means balance, so we need to
discover whether the object happend




                                    Technology and
                                    Reenginerring
Work Principal of EnergyBalances

                 See the image !
     P           The object isn’t balance R = 0.
                 R=P- P
         r        =0
                 Why isn’t it balance?
             P
                 Because there is kopel on that
                 object.




                                   Technology and
                                   Reenginerring
  Work Pricipal of momen kopel


Kopel are two big, in line, and contradicted
energies.


Kopel is the same with moment where the amount
kopel moment is the result of multiplying one of the
energy with the distance of both energy.



                                      Technology and
                                      Reenginerring
Work Pricipal of momen kopel

                               P
                    a
     P

          Momen Kopel = +P.a


      P
                    a
                               P
          Momen Kopel = -P.a



                               Technology and
                               Reenginerring
  Work Pricipal of momen kopel


Nature of Kopel:
1. A kopel may be placed to the flat field
  where it comes ferom and on a flat field
  parraled to the place where the kopel is
  placed.
  see the image…..


                                Technology and
                                Reenginerring
    Work Pricipal of momen kopel

          B
                    P
                            MO1 = P.01B – P.O1A
                        a       = P(O1B – O1A)
           O   2
P                               = P.a →O1B – O1A = a
           A
                            MO2 = P.O2B + P.O2A
                                = P(O2B + O2A)
                                = P.a →O2B + O2A = a
           O1
    So, whenever spot O is taken kopen will not
    change



                                       Technology and
                                       Reenginerring
  Work Pricipal of momen kopel

2. A kopel has rotating nature on a flat field kopel.



                 a


        P
                                     P
                          M = P.a




                                         Technology and
                                         Reenginerring
  Work Pricipal of momen kopel



  screwdriver will be rotated by a kopel, so the
  moent kopel is M = P.a.




Two kopels laying on a flat field may be added
  numerically



                                     Technology and
                                     Reenginerring
Work Pricipal of momen kopel

 P1


                              P2    M1 = P1.a
      a               b
               P2
                                    M2 = P2.b
                                    MR = M1 + M 2

          P1

If the kopel isn’t in single flat field otherwise on
two flat fields.



                                        Technology and
                                        Reenginerring
             Work Pricipal of momen kopel

         V



              a   P1
    P1
                                    P2
                                b

                           P2       W         MR =   M 1  M 2  2M 1M 2 cos
                                                        2       2


                                         MR
                                               Notes:

                  M2
                                               MR = momen resultante
V
                                         M1
                                               M1 = momen kopel P1
                                              M2 = momen kopel P2
                                         W


                                                            Technology and
                                                            Reenginerring
Work Pricipal of momen kopel
Two parrarel energies.
Place resultante two parrarel energies can be
counted with moment rules.

            A     C              B
                                 B
                 C'
      P1

        R
                         P2

                R = P 1 + P2
                                  Technology and
                                  Reenginerring
     Work Pricipal of momen kopel
R position is closer to bigger energy (P1) and stays on
C.
Based on momen rules :
M R  M1 + M 2
to spot A
R.AC’ = O + P2.AB’
R = P1 + P2
(P1 + P2) – AC’ = P2 .AB’
AC’ = AC cos 
AB’ = AB cos 
                                       Technology and
                                       Reenginerring
     Work Pricipal of momen kopel
so
(P1 + P2) AC cos  = P2 AB cos 
(P1 + P2)AC          = P2AB
P1AC + P2AC          = P2AB
P1AC                = P2AB – P2AC
P1AC                = P2BC
→       AB – AC = BC
              P1 : P2 = BC : AC
                                    conclussion…………..

                                        Technology and
                                        Reenginerring
    Work Pricipal of momen kopel

coclussion :
a. Amount of resultante (R) = amount of energy (P1 +
  P2)
b. Direction resultante (R) takes one way P1 and P2
c. Resultante Position(R) between P1 and P2 and its work
  line (C) is closer to the bigger ones (P1).
Position of work line C is decided by the comparison :

               P1 + P2 = BC : AC

                                          Technology and
                                          Reenginerring
  Work Pricipal of momen kopel

Two parrarel and contradicted energy.
position of resultante (R) two parrarel energies and
contradicted can also be decided with moment
formula :
                                           P2
                 C'

            C             A
                                     B

      R = (P2 - P1)

                      P1

                                     Technology and
                                     Reenginerring
  Work Pricipal of momen kopel
P1DP2 and P1P2 is also contradicted way.
Direction of resultante is the same way with the
biggest ones, in this term P1.
Amount of resultante R = P1 – P2
Based on moment rules :
MR = M1 + M2 (to A position)
R : AC’ = 0 – P2.AB’
(P1 – P2).AC’ = -P2AB’
AC’ = AC.cos 
AB’ = AB. cos 
                                     Technology and
                                     Reenginerring
    Work Pricipal of momen kopel

-(P1 – P2)AC cos  = -P2.AB cos 
(P1 – P2)AC cos  = P2.AB cos 
(P1 – P2)AC       = P2.AB
P1.AC – P2AC      = P2AB
P1.AC             = P2AB + P2AC
P1.AC             = P2(AB+AC)
P1.AC             = P2.BC
AB + AC             = BC
P1 : P2 = BC : AC
                                    Technology and
                                    Reenginerring
    Work Pricipal of momen kopel

Notes :
a. Amont of resultante (R) = deviates of both energies
  (P1-P2).
b. Position of resultante (R) is closer to the bigger ones
  (P1).
c. Direction of resultante (R) is parrareled to the bigger
  energy.
  position of work line C is decided by the comparison
  P1 : P2 = BC : AC
                                          Technology and
                                          Reenginerring
Improve your knowledge by yourself




        Thank you
       Compiled by : Deke Hernadin, S.Pd
        SMK Negeri 2 Kota Tasikmalaya
                                   Technology and
                                   Reenginerring

				
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posted:8/27/2012
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