Statics of Particles

First we will learn how to replace two or more forces acting on a given particle by a single force having the same effect as the original forces. This single equivalent force is the resultantof the original forces acting on the particle. Later the relations which exist among the various forces acting on a particle in a state of equilibrium will be derived and used to determine some of the forces acting on the particle. 

 The use of the word “particle” does not imply that our study will be limited to that of small corpuscles. What it means is that the size and shape of the bodies under consideration will not significantly affect the solution of the problems treated in this chapter and that all the forces acting on a given body will be assumed to be applied at the same point. Since such an assumption is verified in many practical applications, you will be able to solve a number of engineering problems in this chapter. 

The first part of the chapter is devoted to the study of forces contained in a single plane, and the second part to the analysis of forces in three-dimensional space.

FORCE ON A PARTICLE. RESULTANT OF TWO FORCES
A force represents the action of one body on another and is generally characterized by its point of application  ,its magnitude ,and its direction.Forces acting on a given particle, however, have the same point of application. Each force considered in this chapter will thus be completely defined by its magnitude and direction. 

The magnitude of a force is characterized by a certain number of units. As indicated in Chap. 1, the SI units used by engineers to measure the magnitude of a force are the newton (N) and its multiple the kilonewton (kN), equal to 1000 N, while the U.S. customary units used for the same purpose are the pound (lb) and its multiple the kilopound (kip), equal to 1000 lb. The direction of a force is defined by the line of actionand the sense of  the force. The line of action is the infinite straight line along which the force acts; it is characterized by the angle it forms with some fixed axis ( Fig. 2.1 ). The force itself is represented by a segment of

              

that line; through the use of an appropriate scale, the length of this segment may be chosen to represent the magnitude of the force. 

Finally, the sense of the force should be indicated by an arrowhead. It is important in defining a force to indicate its sense. Two forces having the same magnitude and the same line of action but different sense, such as the forces shown in Fig. 2.1  aand b, will have directly opposite effects on a particle. 

            

Experimental evidence shows that two forces P and Q acting on a particle A ( Fig.  2.2  a) can be replaced by a single force R which has the same effect on the particle ( Fig. 2.2  c). This force is called the resultantof the forces P and Q and can be obtained, as shown in Fig. 2.2  b, by constructing a parallelo gram, using Pand Q as two adjacent sides of the parallelogram. The diagonal that passes through A represents the resultant.This method for finding the resultant is known as the parallelogram lawfor the addition of two forces. This law is based on experimental evidence; it cannot be proved or derived mathematically.