Engineering Mechanics

What is Mechanics ?

Mechanics is a science that describes or predicts the conditions of rest or motion of bodies under the action of forces.

Mechanics Mechanics of Rigid Bodies Mechanics of Deformable Bodies Mechanics of Fluids Statics Dynamics

History

•

Aristotle ( 384 -322 B.C.)

•

Archimedes ( 287 – 212 B.C.)

•

Isaac Newton ( 1642 – 1727)

•

D’Lambert

•

Lagrange

•

Hamilton

•

Albert Einstein ( Theory of Relativity - 1905)

Basic Concepts

Space : 3 dimensional Position of point A is defined by three lengths measured from the origin in three directions. (coordinates)

Unit of length is meter (m) A o

Basic Concepts

Mass :

•

a fundamental property of a body

•

amount of matter in the body

•

a numerical measure of its inertia

Unit of mass is kilogram (kg)

Force :

•

the action of a body on another body

•

it causes the body to accelerate, that is to change its velocity

•

It can be applied by actual contact or at a distance (gravitational forces, magnetic forces)

Basic Concepts

Force : Force is defined by :

•

its point of application

•

its magnitude

•

its direction

Unit of force is newton (N)

30 ° Defined by a vector

A

Basic Concepts

Resultant Force : The total effect of two or more forces acting on a particle or a body can be represented by a single force which is called

resultant

force. A Q P R

Basic Concepts

Particle : very small amount of matter which may be assumed to occupy a single point in a space Rigid Body : combination of a large number of particles

Basic Concepts

Newton’s Three Fundamental Laws: If the resultant force on a particle is zero, then: a. if it was at rest originally , it remains at rest b. if it was in motion, its velocity doesn’t change

Basic Concepts

Newton’s Three Fundamental Laws: 2. If the resultant force is not zero, then it causes the particle or the body to have an acceleration.

The amount of the acceleration is proportional to the magnitude of the resultant and in the direction of the resultant force F

= m

a F

= resultant force acting on the particle m = mass of the particle

a

= acceleration of the particle

Basic Concepts (Reminder)

Speed

• • • • •

Speed is the rate at which a particle changes its position The distance taken in unit time (meters/second) It refers to how fast a particle is moving It is a scalar quantity. Direction doesn’t matter Velocity

• •

Speed with defined direction Vector quantity

Basic Concepts (Reminder)

Acceleration

•

the rate of change in velocity

•

It refers to how fast a particle changes its velocity

•

amount of change in velocity in unit time (meters/second) / second = meters/ second squared)

m

/

s s

=

m

/

s

2

Basic Concepts

Newton’s Three Fundamental Laws: 3. The forces of action and reaction between bodies in relation have the same magnitude, same line of action but opposite direction.

Basic Concepts

M

F Newton’s Law of Gravitation: -F

m m,M : masses of particles r : distance between particles r Two particles (bodies) attract each other mutually with equal and opposite forces

F

and

–F

of magnitude F

F



G M r

2

m

G : universal constant

Basic Concepts

Newton’s Law of Gravitation: Special Case

Attraction of earth on a particle located on its surface R : the radius of earth, M: mass of earth

F



G M R

2

m F



g m



W

Basic Concepts

Newton’s Law of Gravitation: Special Case

F



g m



W

Weight : W the gravitational force applied on particle by the earth

F



g m F



m a g



a g

 9 .

81

m

/

s

2

Systems Of Units

Time :

second (s) Original definition : 1 / 86400 of mean solar day Official definition : 9,192,631,770 cycles of the radiation corresponding to the transition between two levels of the fundamental state of cesium-133 atom.

Length :

meter (m) Original definition : 1 / 10,000,000 of the distance from equator to either pole Official definition : 1,650,763.73 wavelengths of the orange red light corresponding to a certain transition in a atom of krypton-86

Systems Of Units

Mass :

kilogram (kg) Original definition : mass of 0,001 m3 water Official definition : mass of platinum-iridium standart

Force :

newton (N)

m

/

s

2 to a mass of 1 kg.

m

/

s

2

Systems Of Units

Weight :

Newton (N) the gravitational force applied on a body by the earth

W



g m g

 9 .

81

m

/

s

2 m : the mass of particle ( kg) The weight of a body of mass 1 kg :

W



g m

 ( 9 .

81

m

/

s

2 ) ( 1

kg

)  9 .

81

N

Systems Of Units

Homework Review the other systems of units

•Units of Area •Units of Volume •etc