1: Measurement
- Page ID
- 165693
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A student’s dormitory room measures \(3.1\,\mathrm{m}\) by \(3.8\,\mathrm{m}\) and has a ceiling \(2.6\,\mathrm{m}\) high. After completing their physics course, the student decides to celebrate by wallpapering every wall with the pages from their physics textbook: \(960\) pages of text printed on \(480\) sheets, each \(21\,\mathrm{cm} \times 28\,\mathrm{cm}\). The pages cover even the door and window. Is this possible?
This problem looks like arithmetic, but it captures something essential about physics: we cannot answer it without first deciding what to measure, what units to use, and how precisely we can compute the answer. Measurement is the foundation on which every later chapter of this book rests. Before we can describe motion, force, or energy, we have to agree on how to quantify length, mass, and time, and on how to manipulate numbers that span dozens of orders of magnitude, from the lower limit on the lifetime of a proton (more than \(10^{41}\,\mathrm{s}\)) to the duration of the shortest laser pulse yet produced (\(\sim 10^{-17}\,\mathrm{s}\)).
Learning Objectives
- Describe what physics is and how a physics problem differs from a pure math problem.
- Identify the SI base units of length, mass, and time, and express derived units in terms of them.
- Write numbers in scientific notation and use SI prefixes to compress large and small values.
- Convert quantities between units, including compound units and units raised to powers.
- Use dimensional analysis and significant figures to check and report calculations.
- Make order-of-magnitude estimates and judge when an estimate is good enough.
(You will return to the dorm-room problem in Problem 1.19 at the end of this chapter, once you have the tools to answer it.)