Engineering Transportation

Applied Mechanics. Made Simple by George E. Drabble

By George E. Drabble

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But it is quite easy to calculate the magnitudes of the reactions by taking moments about some point, although this is not a case where actual turning takes place. Let us call the two unknown forces Fx and F2. p U k-1m- -1m- \e -1m- + le ■1m-*+«-1m--*+* - 3 m- Fig. 19. A loaded beam. The induced reactions are found by taking moments about any suitable turning point. Now which point to take moments about ? The simple answer is, either of the two support points. That way, the moment of one of the unknown forces becomes zero; it is thus conveniently set aside, leaving us to calculate the other.

This law, above all others, is based on experiment, mostly undertaken by Galileo. If the first law helps us to understand dynamics, it is the second law that helps us to use it. The third law is perhaps the most subtle and the most difficult to understand. It states that whenever a force exists, there must be an equal and opposite force in the same system. This is not the same as stating that equilibrium must exist, as I hope to show. Equilibrium exists when the resultant of forces acting on a single body is zero.

This law, above all others, is based on experiment, mostly undertaken by Galileo. If the first law helps us to understand dynamics, it is the second law that helps us to use it. The third law is perhaps the most subtle and the most difficult to understand. It states that whenever a force exists, there must be an equal and opposite force in the same system. This is not the same as stating that equilibrium must exist, as I hope to show. Equilibrium exists when the resultant of forces acting on a single body is zero.

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