Mechanics is divided into three parts as shown below:

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2 Mechanics may be defined as the physical science which describes and predicts the conditions of rest or motion of bodies under the action of force systems. In engineering, mechanics is generally based on Newton s Laws and is often called Newtonian (or Classical) Mechanics after the English scientist Sir Isaac Newton ( ).

3 Mechanics is divided into three parts as shown below: Statics Strength of Materials Compressible Fluids Dynamics Theory of Elasticity Incompressible Fluids Theory of Plasticity Theory of Failure As seen, mechanics of rigid bodies are divided into two parts as Statics and Dynamics.

4 Statics deals with the bodies that are acted on by balanced forces. A force system acting on a body is said to be balanced if it has no tendency to change the state of rest or motion of the body in any way. If a body is in equilibrium, the force system acting on it must be balanced. Furthermore, a body in a state of equilibrium must be either at rest or moving along a straight path with a constant velocity. Most problems in Statics concern bodies at rest.

5 FUNDAMENTAL CONCEPTS The basic concepts in mechanics are space, time, mass and force. In Newtonian mechanics, space, time and mass are absolute quantities, which mean that they are independent of each other and cannot be defined in terms of other quantities or in simpler terms (this is not true in Relativistic Mechanics, where the time of an event depends upon its position and the mass of a body varies with its velocity). Force is a derived quantity.

6 Space is the geometric region occupied by bodies whose positions are described by linear or angular measurements relative to a specific coordinate system. For two dimensional problems only two coordinates will be required. For three dimensional problems, three independent coordinates are needed.

7 Time is a concept for measuring the succession and the duration of events. Time is not directly involved in the analysis of problems in Statics.

8 Mass is a measure of the translational inertia of the body, which is its resistance to a change in velocity. Mass can also be thought of as the quantity of matter in a body. Although the mass of a body is an absolute quantity, its weight can change depending on the gravitational force (W=mg).

9 Force: A force represents the action of one body on another. Forces always occur in pairs. This pair of forces is always equal in magnitude and opposite in direction. Force is a vector quantity. The action of a force is characterized by its magnitude, by the direction of its action and by its point of application.

10 Magnitude : F Direction : OO Sense : From O to O Point of application : O O F F O

11 Particle (Parçacık ya da Maddesel Nokta) is a body of negligible dimensions. A particle is a body whose dimensions are considered to be near zero so that we may analyze it as a mass concentrated at a point. A particle has mass but no shape and dimensions. In so doing, the principles of mechanics are reduced to a rather simplified form, since the geometry of the body will not be involved in the analysis of the problem.

12 Since a particle is considered to be concentrated at a single point, all the forces acting on the body will have to pass from this point. The forces will be concurrent.

13 Rigid Body (Rijit ya da Katı Cisim) is an idealized body composed of a large number of particles all of which always remain at fixed distances from each other. In addition to the tendency to move a body in the direction of its application, a force may also tend to rotate a body about an axis. A rigid body is assumed to undergo no deformation under the action of applied forces. Its shape and dimensions remain fixed under all loading conditions and at all times.

14 Some examples of rigid bodies are shown here.

15 NEWTON S LAWS Law I. (Equation of Equilibrium) A particle remains at rest or continues to move with uniform velocity (in a straight line with a constant speed) if there is no unbalanced force acting on it. F 0

16 NEWTON S LAWS Law II. (Equation of Motion) The acceleration of a particle is proportional to the resultant force acting on it and is in the direction of this force. F ma F ma kg m s Newton (N)

17 NEWTON S LAWS Law III. (Principle of Action and Reaction) The forces of action and reaction between interacting bodies are equal in magnitude, opposite in direction, and collinear.

18 GRAVITATION Newton s law of gravitation, which governs the mutual attraction between bodies, is F 1 F G m m 1 r G = a universial constant called the constant of gravitation G m 3 kgs G F r m m 1 N m kgkg kgmm s kgkg m 3 kgs

19 UNITS The International System of metric units (SI) is defined and used in this lecture. Quantity Symbol Unit Mass m kg (kilogram) Time t s (second) Length L m (meter) Force F N (Newton)