{pdf} Physical problems for Robinsons V. N. Lange

Man constantly has to meet with the necessity of measuring some quantity in all domains of his activity, science or technology, industry or agriculture, space travel or medicine. The quantity may be the temperature of the air or the height ofa mOUDtain, the volume of a body or the age of an archaeological. discovery. In some cases the necessary measurements can be made with, instruments or tools suited for the particular purpose. For example, linear dimensions of a body are measured with rulers, tape-lines, micrometers, vernier callipers, temperatures are measured with thermometers, mass by using balances.
Such measurements are called direct. However, in most eases instead of performing a direct determination of the quantity in question one has to measure other quantities and then to calculate the sought one from appropriate formulas. Such measurements are called indirect. Thus, to determine the density of a substance we usually measure the mass and the volume of a body consisting of this substance and then divide the first value, obtained by the second. one.

Suppose it is necessary to determine the diameter of a thin capillary, in a common thermometer, say, for medical use. The inner diameter is so small that it is quite impossible to insert a ruler or any other tool. Besides, the ruler which you have at hand is too coarse an instrument for such a measurement. What is to be done? It proves expedient to use an indirect method of measuring the diameter of the capillary, rather than a direct one; it is possible to apply not one but many different methods. You will know one of them after studying the solution of problem No. 82 in this book. The standard method of measuring density is not always applicable either. Indeed, we shall encounter difficulties from the start if we decide to determine the mean density of the matter of a planet: you cannot put it on the scalel One has to devise devious ways two of which are described in the solutions of problems Nos. 108 and 112.

There are also problems in this book that do not require a quantitative determination of any observables, only a method of performing a certain operation should be proposed. They have in common with problems of the type mentioned above a certain peculiarity, either of the initial situation or of the set of objects which are permitted to be used. (It should be said, to be exact, that some of these problems only seem peculiar. For example, the mean density of the matter constituting the Earth was determined just in the way described in the solution of problem No. 112.