Download - Statics Ch1 Presentation
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Engineering Mechanics 1
Chanat Ratanasumawong (CRW)309 Salab Building
Tel: 022186593
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1/1 MechanicsMechanics is the physical science which deals with the effects of
forces on objects
1. Statics : equilibrium of bodies2. Dynamics : motion of bodies
The subject of mechanics is divided into two parts:
Applications
Strength of machines and structuresVibrations (engine, building, bridge)Fluid mechanics (airplanes, fluid machinery)
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1/2 Basic conceptsSpace : the region occupied by bodies whose positions are
described using coordinate system (meter)
Time : the measure of the succession of events (sec)Used in dynamics
Mass : the bodys resistance to change in velocity (kg)the bodys ability to generate attractive force betweenitself and another
Force : the action of one body to another (N)
Particle : a body of negligible dimensions (dimensions are notsignificant to the description of its position or forcesapplied to it) concentrated mass
Rigid body : a body with negligible deformation
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1/3 Scalars and vectorsScalars : only magnitude is associated
Ex. mass, volume, density, speed, length, angle
Vectors : magnitude and direction are important
Ex. Displacement, velocity, acceleration, force, moment
Vectors can be classified by the importance of their position
1. Free vector2. Sliding vector3. Fixed vector
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1/3 Scalars and vectors
Free vector
Displacement of body moving
without rotation
Sliding vector
Force acting on a rigid body
Fixed vector
The action of force on a deformablebody
Deformable body
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1/3 Scalars and vectors
Free vector
Displacement of body
moving without rotation
Sliding vector
Force acting on a rigid body
Fixed vector
The action of force on adeformable body
Deformable body
Sv
S
v Sv
Sv
F
v
F
v
F v
F v
Rigid body
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Vector basics (1) Representation
Addition (parallelogram law)
2V r
1V r
V r
V r
(same magnitude butopposite direction)V
r
or V
or V | |V r
Magnitude =
Vector =
= Direction
1 2V V V = +r r r
1V r
2V
r
V
r
1V r 2
V rV
r
1 2V V V +
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Vector basics (2) Subtraction
2V r
1V r
1 2 1 2( )V V V V V = = +
r r r r r
2V r
1V r
V r
Basic relations
2 2 21 2 1 22 cos( )V V V VV = +
1V r 2
V rV
r
2
sin( ) sin( )
V V
=
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Example (1)
V 2
V 1
V V 2 V 1= -
Given: V 2 = 12, V 1 = 10 = 30 deg
Find: V and
cosine law )cos(2 212
22
12 V V V V V +=
)30cos()12)(10(21210 222 o+=V
V = 6.013
sine law sinsin
2 V V =o30sin
013.6sin
12 =
oo 74.93,26.86=
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Example (2)Check by cosine law
cosine law )26.86cos()013.6)(10(2013.61012 222 o+=
o26.86=
128144
cosine law )74.93cos()013.6)(10(2013.61012 222 o+=
o74.93=
144144 = OK
o74.93,013.6 == V Ans
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Vector basics (3) Components
xV r
yV r V
r
x
y
22 y x V V V +=
)cos( V V x =)sin( V V y =
) / (tan1
x y V V
=
Rectangular Components
Given V , and , we have1
V r
2V r V
r
1
2
V 1V 2
Sine lawSine law
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Vector basics (4)
V Vn=r
, = unit vector; (magnitude = 1, samedirection as )
nV
r
Unit vector
3D Rectangular component
x
y z
V r
xV i
yV j
zV k
k j
i
z
x
y
cos( ) x xV V =
cos( ) y yV V =
cos( ) z zV V =
2 2 2 2 x y zV V V V = + +
2 2 2
1 cos ( ) cos ( ) cos ( ) x y z = + +
k V jV iV V z y x ++=r
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Newtons Laws (1)Law 1
A particle remains at rest or continues to move in a straightline with a uniform velocity if there is no unbalanced forceacting on it.
0F =r
ar
= 0
Law 2
The acceleration of a particle is proportional to the resultant
force acting on it and is in the direction of this force.
F ma=r r
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Newtons Laws (2)Law 3
The force of action and reaction between interacting bodiesare equal in magnitude, opposite in direction, and collinear.
Action = Reaction
Action and reaction are acting on different bodies.
*
F r
F r
F F