Modern Textile Technology by J.B. Rattan
By J.B. Rattan
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Extra resources for Modern Textile Technology
A vector diagram by completing the parallelogram with sides P and Q and diagonal R. In addition, S is equal in magnitude, but opposite in direction, to R, so can be represented by a vector -R on the diagram. Thus, we can use two adjacent sides and a diagonal of the parallelogram, its shown, to represent the three forces in magnitude and direction. It is also evident that the three are arranged in sequence around the triangle and that either triangle of the original parallelogram may be used. This is the rule of the triangle of forces; three non-parallel forces in equilibrium may be represented in magnitude and direction by the three sides of a triangle taken in sequence.
It is obvious, by considering the two foregoing conditions, that U must be equal to the weight of the object, the force W exerted by gravity on its mass, and that it must pass through the centre of gravity, G, since the mass of the object acts there also. This may be achieved in two ways; the suspending string can be attached vertically above G, at A. or vertically below G, at B. A slight displacement from each of these two equilibrium states serves to indicate that the former is a stable one, whereas the latter is unstable, as indicated in the diagram.
Application of a couple may bring about a rotation or may merely balance another couple, and many types of calculation using the principle of moments may be envisaged. Sample ones are given in the following worked examples. Example 9 Find the tension on the specimen when the angle a is (i) Tt/6 rad and (ii) Ttl3 rad. Although the pendulum and pointer are slowly moving as the left-hand grip moves, we can regard the system as being instantaneously in equilibrium at any given position, as indeed is the case if the traverse is stopped at that position.