Statics_of_Rigid_Bodies_02_Particles - Section 2.2 2.2 The...

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Solid Mechanics Part I Kelly 12 2.2 The Statics of Particles 2.2.1 Equilibrium of a Particle The statics of particles is the study of particles at rest under the action of forces. Such particles can be analysed using Newton’s first law only. This situation is referred to as equilibrium , which is defined as follows: Equilibrium of a Particle A particle is in equilibrium when the resultant of all the forces acting on that particle is zero In practical problems, one will want to introduce a coordinate system to describe the action of forces on a particle. It is important to note that a force exists independently of any coordinate system one might use to describe it. For example, consider the force F in Fig. 2.2.1. Using the vector polygon law, this force can be decomposed into combinations of any number of different individual forces; these individual forces are referred to as components of F . In particular, shown in Fig 2.2.1 are three cases in which F is decomposed into two rectangular (perpendicular) components, the components of F in “direction x ” and in “direction y ”, x F and y F . Figure 2.2.1: A force F decomposed into components F x and F y using three different coordinate systems Resolving forces into rectangular components, one can obtain analytic solutions to problems, rather than relying on graphical solutions to problems, for example as done in Fig. 2.1.2. In order that the resultant force F on a body be zero, one must have that the resultant force in the x and y directions are zero individually 1 , as illustrated in the following example. 1
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This note was uploaded on 01/20/2012 for the course ENGINEERIN 1 taught by Professor Staff during the Fall '11 term at Auckland.

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Statics_of_Rigid_Bodies_02_Particles - Section 2.2 2.2 The...

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