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Applied Mechanics. Made Simple by George E. Drabble

By George E. Drabble

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Such a situation would be impossible to achieve in practice, for no matter how tight the wire, the central load must cause it to sag a small amount. Even if there is no central load, the dead weight of the rope or wire itself must cause a small amount of sag. ' (4) Resultant and Equilibrant I hope that by now you can see that the triangle of forces enables us not only to evaluate forces in equilibrium, but also to examine systems of forces which are not in equilibrium. If only two forces act at a point, they cannot be in equilibrium (except in the special case where they are exactly equal and act in opposite directions).

Every body continues in a state of rest, or of uniform motion in a straight line, unless or until acted upon by a force. 2. The acceleration of a body is proportional to the force acting upon it, and takes place along the line of action of the said force. 3. Every force induces an equal and opposite reaction. The first law gives us a definition of force: force is something which, by itself, produces an acceleration. This is the definition of force, and is clearly more satisfactory than the 'push or pull' we have had to accept so far.

Force R can be replaced by its components G and C2. Examine the situation shown in Fig. 15. We have a single force R acting at a point. I have drawn a force triangle alongside, in which R is the resultant of a pair of forces C\ and C2, and I have assumed these to be respectively vertical and horizontal. So the single force R can be replaced by its two components Ci and C2. The advantage is that, if we assume them at rightangles, as I have done, we can see from the simple trigonometry of the rightangled triangle that C\ is R cos Θ and C2 is R sin Θ.

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