Question

Only do exerice 1-9

220AL-E1 he uncertainty in an experimental quantity must be reported. Since there are a number of ways to do this we must state the meaning of the uncertainty. A Estimated uncertaint Sometimes we make several measurements that are identical. Eq 1-2 would yield ơx-0, which could lead to the mistaken impression that the uncertainty is zero when in fact the precision of the instrument is less than the random errors. We must estimate the uncertainty, and, in most cases, the precision of the instrument is used as the uncertainty common method is to report Ox together with the number of measurements n. The reader can quickly calculate ơ . In the remainder of this manual, we shall either quote the standard deviation or the estimated uncertainty as the uncertainty Sometimes only one measurement is made and often the precision of the instrument is used as an estimate of the uncertainty. Depending upon the instrument and the situation, the uncertainty could be less than the precision of the instrument or it could be more. For example, in measuring the length of a sheet of paper with a meter stick, we may estimate the distance between the smallest subdivision (mm) if we turn the meter stick onto its side to eliminate parallax. Therefore, the uncertainty in the measurement might be 0.5 mm or even 0.3 mm rather than the precision of the meter stick which is 1 mm. On the other hand, if we measure an object that is not right next to the meter stick, the uncertainty might be 2 or 3 mm. Often judgment is required in order to estimate the uncertainty in a single measurement. Table 1-2. Weight of a flea Weight. N W1 -1.96 x 10-4 W2 -1.94 x 10-4 W3 -2.01 x 10-4 W4 -2.00 x 10-4 W5 1.97 x 10-4 WG = 1.99 x 10-4 w7 -2.03 x 10-4 W8 1.98 x 10-4 Wy = 1.96 x 10-4 W10-1.95 x 10-4 W11- 2.00 x 10-4 W12- 1.97x 10-4 Measurement 4 10 Example 1-5: To illustrate these ideas, we might measure the weight of a flea twelve times with a balance of precision 0.01 x 10-4 N. The results are tabulated in Table 1-2 We shall employ the same symbol, , to denote estimated uncertainty in The mean weight, according to eq this manual. 1-1 is: W1 +W2 +...+ Wn Reporting uncertainties

Answer 1