Engineering mechanichs - Part two

Engineering mechanichs - Part two

Statics

Static deals with the conditions of equilibrium of bodies acte upon by forces and is one of the oldest branches of science. When several forces of various magnitudes and directions act upon a body, they are said to constitute a system of forces. The general problem of statics consist of finding the conditions that such a system must satisfy in order to have equilibrium of the body. The various methods of solution of this problem are based on several axioms, called the principles of statics, which are given here in brief.

 

Parallelogram law

If two forces, represented by vectors AB and AC, acting under an angle α, are applied to a body at point A, their action is equivalent to the actionof one force represented by the vector AD, obtained as the diagonal of the parallelogram constructed on the vectors AB and AC.

Equilibrium law

Two concurrent forces can be in equilibrium only of their resultant is zero. This will be the case if we have two forces of equal magnitude acting in opposite directions along the same line. We shall now generalize this conclusion as the second principle of statics, usually called the equilibrium law: Two forces can be in direction, and collinear in action.

Law of superposition

When two forces are in equilibrium (equal, opposite, and collinear), their resultant is zero and their combined action on a rigid body is equivalent to that of no force at all. A generalization of this observation gives us the third principle of statics, sometimes called the law of superposition: The action of a given system of forces on a rigid body will in no way be changed if we add to or subtract from them another system of forces in equilibrium.

Law of action and reaction

Very often we have to investigate the conditions of equilibrium of bodies that are not entirely free to move. Restriction to the free motion of a body in any direction is called constraint. A body that is not entirely free to move and is acted upon by some applied force (of forces) will, in general, exert pressures against its supports. These actions of a constrained body against its supports induce reactions from the supports on the body, and as the fourth principle of statics we take the following statement: Any pressure on a support causes an equal and opposite pressure from the support so that action and reaction are two equal opposite forces.

 Kinematics and kinetics

In statics we have considered rigid bodies that are rest. In dynamic we shall consider bodies that are in motion. For convenience, dynamics is comonly divided into two branches called kinematics adn kinetics. In kinematics we are concerned only with the space-time relationship of a given motion of a body and not at all with the forces that cause the motion. If we see that a wheel rolls along a straight level track with uniform speed, the determination of the shape of the path described by a point on its rim and of the position along this path that the chosen point will occupy at any given instant are problems of kinematics.

In kinetics we are concerned with finfing the kind of motion that a given body or system of bodies will have under the action of given forces, or with what forces must be applied to produce a prescribed motion. If a constant horizontal force is to be applied to a given body that reset on a smooth horizontal plane, the prediction of the way in which the body will move is a problem of kinetics.

The whole science of dynamics is based on the natural laws governing the motion of a particle under the action of a given force. Whenever a particle moves through space, it describes a curve that is called the path. The path of a particle may be either a pace curve, called a tortuous path, or a plane curve, called a plane path. In the simplest case the path will be a straight line, and the particle is said to have rectilinear motion. This can be uniform of nonuniform. If the rectilinear motion of a particle is nonuniform, its velocity is changing with time and we have acceleration. In the case of uniform motion, however, the velocity remains constant describes a curved path, it is said to have curvilinear motion.