Predicting Values

When scientists discover relations like the ones shown in the graphs in this section, they use them to make predictions. For example, the equation for the linear graph in Figure 1-16 is as follows:

$y = (0.08\ \text{cm/g})x + 13.7\ \text{cm}$

Relations, either learned as formulas or developed from graphs, can be used to predict values you haven’t measured directly. How far would the spring in Table 1-3 stretch with 49 g of mass?

$y = (0.08\ \text{cm/g})(49\ \text{g}) + 13.7\ \text{cm}$
$= 18\ \text{cm}$

It is important to decide how far you can extrapolate from the data you have. For example, 49 kg is a value far outside the ones measured, and the spring might break rather than stretch that far.

Physicists use models to accurately predict how systems will behave: what circumstances might lead to a solar flare, how changes to a circuit will change the performance of a device, or how electromagnetic fields will affect a medical instrument. People in all walks of life use models in many ways. One example is shown in Figure 1-19. With the tools you have learned in this chapter, you can answer questions and produce models for the physics questions you will encounter in the rest of this textbook.