If the body of weight G in Fig. Section 1.

From experience we also know that force has a direction. The box on the smooth surface in Fig. The direction of the force can be described by its line of action and its sense of direction orientation.

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In Fig. The sense of direction is indicated by the arrow. Finally, a single force acts at a certain point of application.

Depending on the location of point A in Fig. In contrast to a free vector, which can be moved arbitrarily in space provided it maintains its direction, a force is tied to its line of action and has a point of application. Therefore, we conclude: The force is a bound vector. According to standard vector notation, a force is denoted by a boldfaced letter, for example by F , and its magnitude by F or simply by F. In Cartesian coordinates see Fig. This principle is illustrated in Fig.

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Displacing force F in a parallel manner causes the body to rotate Fig. It is almost realized when a body is loaded over a thin wire or a needlepoint. In nature, only two kinds of forces exist: volume forces and surface or area forces. Weight is an example of a volume force. The sum of the force elements dG, which are continuously distributed within the volume yields the total weight G.

Other examples of volume forces include magnetic and electrical forces. Area forces occur in the regions where two bodies are in contact. Examples of forces distributed over an area include the water pressure p at a dam Fig.

## Engineering Mechanics 1: Statics (Springer Textbook) (Pt. 1)

A further idealization used in mechanics is the line force, which comprises forces that are continuously distributed along a line. Active forces refer to the physically prescribed forces in a mechanical system, as for example the weight, the pressure of the wind or the snow load on a roof.

Reaction forces are generated if the freedom of movement of a body is constrained. For example, a falling stone is subjected only to an active force due to gravity, i. However, when the stone is held in the hand, its freedom of movement is constrained; the hand exerts a reaction force on the stone.

Reaction forces can be visualized only if the body is separated from its geometrical constraints. This procedure is called freeing or cutting free or isolating the body. Supports A and B prevent the beam from moving: they act on it through reaction forces that, for simplicity, are also denoted by A and B. These reaction forces are made visible in the so-called free-body diagram Fig. It shows the forces acting on the body instead of the geometrical constraints through the supports.

Chapter 5. This procedure is still valid when a mechanical system becomes movable dynamic due to freeing. In this case, the system is regarded as being frozen when the reaction forces are determined. Section 5. An external force acts from the outside on a mechanical system. Active forces as well as reaction forces are external forces. Internal forces act between the parts of a system.

They also can be visualized only by imaginary cutting or sectioning of the body. If the body in Fig. Accordingly, the system initially consists of the complete body at rest.

## Engineering Mechanics 1: Statics (Springer Textbook) (Pt. 1) - PDF Free Download

After the cut, the system consists of two parts that act on each other through area forces in such a way that each part is in equilibrium. This procedure, which enables calculation of the internal forces, is called the method of sections. It is valid for systems in equilibrium as well as for systems in motion. If the entire body in Fig. As stated in Section 1. Consequently, the principle of transmissibility can be used in the analysis of the external forces. However, this principle can generally not be applied to internal forces.

In this case, the body is sectioned by imaginary cuts, therefore it matters whether an external force acts on one or the other part.

The importance of internal forces in engineering sciences is derived from the fact that their magnitude is a measure of the stress in the material. This axiom states that a force always has a counteracting force of the same magnitude but of opposite direction. Therefore, a force can never exist alone. If a hand is pressed against a wall, the hand exerts a force F on the wall Fig. An opposite force of the same magnitude acts from the wall on the hand. These forces can be made visible if the two bodies are separated at the area of contact.

Note that the forces act upon 1. Analogously, a body on earth has a certain weight G due to gravity. In short: The forces that two bodies exert upon each other are of the same magnitude but of opposite directions and they lie on the same line of action. Volume 3.

It is valid for longrange forces as well as for short-range forces, and it is independent of whether the bodies are at rest or in motion. Force is another important element that is considered; however, from a physical point of view, force is a derived quantity.

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All other mechanical quantities, such as velocity, momentum or energy can be expressed by these four quantities. The geometrical space where mechanical processes take place is threedimensional. The magnitude of a physical quantity is completely expressed by a number and the unit. In numerical calculations units are treated in the same way as numbers. In physical equations, each side and each additive term must have the same dimension.

This should always be kept in mind when equations are formulated or checked. Table 1. Customary Unit SI Equivalent 1 ft 0. Customary system of units is still frequently used although the SI system is recommended. As division and multiples of length the inch in , yard yd and mile mi are used. In Table 1.