Statics Ch1 Presentation

8/8/2019 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

Statics Ch1 Presentation

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