When dealing with an area or a volume of a complex object, introduce a simple model of the object such as a sphere or a box. These same strategies of breaking big things into smaller things or aggregating smaller things into a bigger thing can sometimes be used to estimate other physical quantities, such as masses and times. For example, to estimate the thickness of a sheet of paper, estimate the thickness of a stack of paper and then divide by the number of pages in the stack. Sometimes it also helps to do this in reverse-that is, to estimate the length of a small thing, imagine a bunch of them making up a bigger thing. For example, knowing some of the length scales in Figure 1.4 might come in handy. ![]() It helps to have memorized a few length scales relevant to the sorts of problems you find yourself solving. The product of these three estimates is your estimate of the height of the building. Then, estimate how big a single floor is by imagining how many people would have to stand on each other’s shoulders to reach the ceiling. For example, to estimate the height of a building, first count how many floors it has. Thus, imagine breaking a big thing into smaller things, estimate the length of one of the smaller things, and multiply to get the length of the big thing. When estimating lengths, remember that anything can be a ruler. The following strategies may help you in practicing the art of estimation: To make some progress in estimating, you need to have some definite ideas about how variables may be related. ![]() Familiarity with dimensions (see Table 1.3) and units (see Table 1.1 and Table 1.2), and the scales of base quantities (see Figure 1.4) also helps. You develop these skills by thinking quantitatively and being willing to take risks. As you develop physics problem-solving skills (which are applicable to a wide variety of fields), you also will develop skills at estimating. Many estimates are based on formulas in which the input quantities are known only to a limited precision. They allow us to challenge others (as well as ourselves) in our efforts to learn truths about the world. Estimates also allow us to perform “sanity checks” on calculations or policy proposals by helping us rule out certain scenarios or unrealistic numbers. Because the process of determining a reliable approximation usually involves the identification of correct physical principles and a good guess about the relevant variables, estimating is very useful in developing physical intuition. Rather, estimation means using prior experience and sound physical reasoning to arrive at a rough idea of a quantity’s value. (The physicist Enrico Fermi mentioned earlier was famous for his ability to estimate various kinds of data with surprising precision.) Will that piece of equipment fit in the back of the car or do we need to rent a truck? How long will this download take? About how large a current will there be in this circuit when it is turned on? How many houses could a proposed power plant actually power if it is built? Note that estimating does not mean guessing a number or a formula at random. ![]() Other terms sometimes used are guesstimates, order-of-magnitude approximations, back-of-the-envelope calculations, or Fermi calculations. On many occasions, physicists, other scientists, and engineers need to make estimates for a particular quantity. ![]() Estimate the values of physical quantities.By the end of this section, you will be able to:
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