Measurement Corner #5: Measurement Uncertainty 3. For practice, use a stopwatch to measure how much time it takes you to read this The experiments you have done so far have mentioned uncertainty. This Measurement paragraph. Include uncertainty in your measurement. Corner, and the new few, will look at more details of what measurement uncertainty means and how you might find the uncertainty in a measurement. 4. Suppose that I gave you two measurements of how long it took me to read the paragraph: 15.91+0.02 s and 15.91+3.00 s. Are these measurements equivalent? If not, 1. As an example of why it is important to think about measurement uncertainty, measure the length of the arrow in the figure. what are the differences in these measurements? Which is a better measurement? Are either of the uncertainties in these measurements too small? Too large? A few more comments on reporting uncertainties are also in order. In these physics labs, your lab reports will be expected to include uncertainties in the form discussed above 1 2 4 S 7 8 10 (6. 1+0.1 cm for the length of the arrow). Other classes might use significant figures to report uncertainties. Using significant figures, the length of the arrow would be reported Figure 1: Measuring an arrow as 6.1 cm. This still does not mean the length is exactly 6.1 cm, but it is implied that the It looks to me like the arrow extends from 1.5 cm to 7.6 cm, so the length is 6.1 cm. uncertainty is 0.1 cm. Physicists prefer the reporting format of 6.140.1 cm because it is explicit about the uncertainty instead of relying on an assumed understanding. 2. Is the arrow's length exactly 6.1 cm? When you write lab reports, you also will be expected to comment on how you estimated It is likely that your measurement is close to mine, but you may well have said 6.0 cm or your uncertainty and what part of your measurement process produced the uncertainty. 6.2 cm. This measurement is a comparison of the size of the arrow to the size of the scale, Do not simply say that the uncertainty is the result of "human error". My uncertainty in a comparison in which the sizes don't match up exactly, or at least we can't see well enough to be sure that they match exactly. The uncertainty of a measurement is how sure measuring the length of the arrow is not because I made any mistake. If you make a we are of our measurement, or more specifically how far our measurement may be off. mistake, you should fix it before reporting! The uncertainty is inherent in the measurement process and the size of the uncertainty is limited by the tool used for the When we report a measurement in a lab report or journal article, our audience is likely to measurement, the ruler. The phrase "human error", which you may have been taught to want to know not only the magnitude of our measurement (6.1 cm in the above example), use in previous classes, is a platitude, not specific and thoughtful enough to be of any use but also how certain we are about our measurement. I think we can be fairly sure that the length of the arrow is in the range between 6.0 and 6.2 cm, even though it is not exactly 6.1 cm. Every measurement has a range of possible reasonable values. If I were to report the length of the arrow in a paper, I would say that the length is 6.140.1 cm. The first number here represents the center of the range of possible measurements. The second number represents the size of the range, also called the uncertainty in the measurement. Do you think my reporting of 0.1 cm as the uncertainty of the measurement is reasonable? If I report an uncertainty that is too small, people will think that my measurement is more exact than it really is. If I report an uncertainty that is too large, people will think that my measurement is not very precise. Either way, the report would be misleading to a reader who wants to know how certain I am about the measurement. A good estimate of the uncertainty is important. A rule of thumb: the uncertainty should be at least as large as the smallest marking on the measurement device; since the smallest markings on the ruler are 0.1 cm, my uncertainty has to be 0.1 cm or larger