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.

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)

Unit of length is meter (m) Basic Concepts Space : 3 dimensional Position of point A is defined by three lengths measured from the origin in three directions. (coordinates) o Unit of length is meter (m) A

Basic Concepts Mass : Unit of mass is kilogram (kg) Force : a fundamental property of a body amount of matter in the body a numerical measure of its inertia 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) Unit of mass is kilogram (kg)

Basic Concepts Force : Unit of force is newton (N) Defined by a vector 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. P R A Q

combination of a large number of particles 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

Newton’s Three Fundamental Laws: 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) =

Newton’s Three Fundamental Laws: 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.

Newton’s Law of Gravitation: Basic Concepts Newton’s Law of Gravitation: m -F m,M : masses of particles r : distance between particles F M r Two particles (bodies) attract each other mutually with equal and opposite forces F and –F of magnitude F G : universal constant

Newton’s Law of Gravitation: 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

Newton’s Law of Gravitation: Basic Concepts Newton’s Law of Gravitation: Special Case Weight : W the gravitational force applied on particle by the earth

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) The magnitude of force that gives an acceleration of 1 to a mass of 1 kg. 1 N = (1 kg) ( 1 )

Systems Of Units Weight : Newton (N) the gravitational force applied on a body by the earth m : the mass of particle ( kg) The weight of a body of mass 1 kg :

Review the other systems of units Homework Review the other systems of units Units of Area Units of Volume etc