# menerapkan ilmu statika dan tegangan_english ok by lanyuehua

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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

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

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

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

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

Edge

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

Direct                              Indirect

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

Loads on building contructios based on its nature are :
is all kinds of load comes from weight of building
begin from the pondation to the roof
building itself or its element.

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

is all kinds of load on the building caused by winds.
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 :
Is a load that has a small volume
Example: pressing to train monorail by the train
wheel
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
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

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
→ P = 1000 kg, P = 12 ton, etc.
→ q = 400kg/m, q = 2ton/m, etc.
→ 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

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Reenginerring
Work Pricipal of momen kopel

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

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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 
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-(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
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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