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# stat_of_part - 2 STATICS OF PARTICLES 2.1 Concurrent Forces...

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StP-1 2. STATICS OF PARTICLES 2.1 Concurrent Forces . In this chapter we shall study the effect of forces on particles. The use of the word particle does not imply that we shall restrict our study to that of small corpuscles. It means that the size and shape of the bodies under considerations will not affect the solution of problems treated in this chapter and that all the forces acting on given body will be assumed to have the same point of application. Forces whose lines of action intersect at one point are said to be concurrent . A system of concurrent forces acting on a particle A can be replaced by an equivalent force, i.e. by the resultant R (Fig.2.1) The problem of determining the resultant of concurrent forces F 1 , F 2 , …, F n is reduced, according to the 3 rd principle of statics, to the composition of the given forces, i.e. R = F 1 + F 2 + … + F n ( 2 . 1 ) 2.2 Resolution of Forces . As we know from the chapter Elements of Vector Algebra, the problem of resolution of a force, F , into components is indeterminate and can be solved uniquely only if additional conditions are stated. Two cases are of particular interest: 1. One of the two components , P , is known . The second component, Q , is obtained by applying the triangle rule and joining the tip of P to the tip of F (Fig.2.2a). Ones Q has been determined graphically or by trigonometry, both components P and Q should be applied at A ; 2. The line of action of each component is known. Both components are obtained by means of parallelogram law (Fig.2.2b). This process leads to well-defined

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stat_of_part - 2 STATICS OF PARTICLES 2.1 Concurrent Forces...

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