 By George E. Drabble

ISBN-10: 0491002084

ISBN-13: 9780491002080 By George E. Drabble

ISBN-10: 0491002084

ISBN-13: 9780491002080

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Extra resources for Applied Mechanics. Made Simple

Sample text

In the system we are used to, length and time are considered to be fundamental, and velocity and acceleration are then derived from them. But 'fundamental' is a bad word here. There is nothing fundamental about length. For instance, the origin of the metre was a decimal fraction of the length of a quadrant of the Earth's surface, and the origin of the second was a fraction of the solar day. Both these The Link Between Force and Motion 47 quantities are quite arbitrary in choice and, at the time of their original selection, could not be measured with any great accuracy (or what we today regard as great accuracy).

Both alternatives have been drawn in Fig. 12 (c). Notice that we do not need to know the length of the two lines if we know their directions; in fact, we measure these lengths after the triangle is completed, and thus determine the values of the rope tensions. In this case, both lines The Nature of Force 29 are found to be approximately 29 mm in length, which represents a force of 290 newtons to the scale we have chosen. Before leaving this little example, it is interesting to speculate on the effect of reducing the angle of depression of the supporting wire.

If we include Rn in the force system, as shown dotted in Fig. 14 (a), we can mentally delete (1) and (2) because the resultant replaces them. So we are down to only four forces. But we can repeat the process, this time with the two forces Ri2 and (3), giving us a second resultant, Rl23. This can be coupled with (4) and so on. What emerges is, of course, a polygon comprising vectors representing the five component forces. If these forces are in equilibrium, the polygon must close. What is more, there is no need to draw the various resultants at all.