By George E. Drabble
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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. Without introducing further calculation, it can be seen that the effect will be to elongate the triangle, so that the oblique sides become flatter, and proportionally longer. If, for instance, we make the wire absolutely horizontal, we finish up with a triangle whose long sides never meet, indicating that the resulting tension would be infinite.
You have to define your force in terms of 'the weight of a given mass' or 'the force to accelerate a certain mass a certain amount' or 'the force to compress a certain spring a certain distance'. So it is usually mass that is taken as a fundamental unit, while force is a derived unit defined in terms of a standard mass and Newton's second law. If mass, length and time are chosen as arbitrary fundamental quantities, all other quantities in dynamics can be expressed in terms of these three. Mass, length and time are called the dimensions in which all other quantities are expressed.
Examples of quantities which are related but not proportional include: the volume of a cube and the length of its side, the distance covered by a freely falling body and the time taken, the volume of a quantity of gas in a cylinder and its pressure, the weight and the pointer movement on the pendulum-type scale mentioned above. In Fig. 221 have shown what the graphs of all these related quantities would look like. The graphical evidence of proportionality is a straight line; indeed, the relationship between the quantities is said to be a linear relationship.
Applied Mechanics. Made Simple by George E. Drabble