Lecture 1 The main concepts of theoretical mechanics

Lecture 1 The main concepts of theoretical mechanics. Axioms of statics. Projection of a force onto an axis. The resultant force. Associated professor of the Department of General Construction Gumenyuk Valeriya Vladimirovna

Theoretical mechanics – science concerned with the motion and equilibrium of rigid physical bodies. The course of theoretical mechanics is divided into three branches: Statics – this brunch studies the methods of conversion of the systems of forces into equivalent systems and sets the conditions for the equilibrium of forces applied to the body. Kinematics – the brunch studies motion of bodies in space without regard for the forces causing it. Dynamics – the study of motion of bodies in space and its relation to the forces.

Main concepts Material point – a zero-dimensional body with a nonzero mass that can interact with other point particles. Mechanical system (or system of material points) – collection of point particles in which the position and the motion of each particle depends on the position and the motion of other particles. Absolutely solid body – the body , the distance between any two given points of that remains constant in time under all circumstances.

Force – measurement of mechanical interaction of bodies that characterizes the interaction of one body onto another body. Force is characterized by the quantity (module), direction and the application point; that is, it is a vector quantity. Force is measured with SI units of Newtons (N). A balanced system of forces – system of forces that does not change the mechanical state of absolutely solid body when applied to it.

Resultant force – one force whose action on the body is equivalent to a given system of forces. Equilibrant – a force that is equal in magnitude to the resultant force but opposite in direction. External forces - the forces acting on the mechanical system of the other points, not in the file system. Internal forces - forces of interaction between the points of the system. Balancing force - a force equal in quantity (module) of the resultant and the opposite direction.

Projection of a force onto an axis is a scalar quantity because it does not have a direction and is defined by the direction of the axis. Projection of the force will be positive if the direction of the force vector coincides with the positive direction of the axis. 1) Fx=Fcos 2) Fx=-Fcos

Axioms of statics. Axiom 1 Two forces applied to the free body balance each other when they are equal and directed in a straight line to the opposite side.

Axiom 2. The action of a given system of forces on the absolutely solid body does not change if a balanced system of forces is added to or extracted from a given system of forces. Corollary from axiom 2: A force acting on an absolutely solid body can be shifted along the line of its action without any change in its module and direction.

Axiom 3 (Parallelogram rule). The resultant of two intersecting forces applied at one point and directed angularly to each other attached to point of their intersection and is equal in modulus and direction of the diagonal of the parallelogram formed by these two intersecting forces.

Axiom 4 Forces exerted by the two bodies act on each other, always equal in module and direction in a straight line to the opposite side. This axiom is also known as principle of action and reaction. Axiom 5 (Axiom of connection) Any connection can be discarded and replaced by a reaction - the force or system of forces.