5.1 Introduction
5.1
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Introduction
In reality, forces are applied over a region of which often its area is negligible. When forces are applied over a region whose dimensions are not negligible compared with other pertinent dimensions, we must account for the actual manner in which the force is distributed by summing up the effects of the distributed force over the region. For this purpose, we need to know the intensity of the force at any location and we will use the integration to determine their total effect. Figure 5.1 are common engineering examples of the distributed forces.
Figure 5.1: Some examples of the distributed forces ([1], pp. 237)
5.2
Center of Mass
In this section, we study the method to determine the location of the center of gravity, the center of mass, and the center of volume. The principle of moment, i.e. “The sum of the moments is equal to the moment of the sum.” is basically employed to determine these locations.
5.2.1
Center of Gravity
The center of gravity (C.G.) is the point where the resultant gravitational force W acts. It is determined from the principle of moment: “Moment of the resultant gravitational force W about any axis is equal to the sum of the moments about the same axis of the gravitational force dW acting on all particles of the body.” Most of the objects subject to the earth gravity can be safely assumed that the intensity of the earth’s force field over the body is uniform. The other reasonable assumption is that the field of force due to the gravitational attraction is parallel. Applying these assumptions to the principle of moment simplifies the derivation of the C.G. because the cross product degenerates to a simple multiplication. Chulalongkorn University
Phongsaen PITAKWATCHARA