Unformatted text preview: Using the maximum uncertainty method. .
The procedure for ﬁnding the uncertainty range for a calculated quantity using the maxunum uncertainty method is as follows. Suppose the desired quantity Q is calculated as a function of
the measured values A1, A2, A3,“: Step 1. Calculate the most probable value of the quantity Q, which we can call Qmp, 115ng
the measured values of each of the constituent numbers A1, A2, A3,.... Step 2. Change each of the quantities A1, A2, A3,... by the amount of its uncertainty.
Increase or decrease each of them in the direction that will result in an increase in Q. Step 3. Recalculate the value of Q using these new A], A2, A3,... valueS, which gives you a
new value that We label Qmax. The uncertainty of Q is the difference between Qmax and Qmp- Step 4. Round the uncertainty to one signiﬁcant ﬁgure, round the most probable value to the
same decimal place, and report the ﬁnal result with its uncertainty and units. Shortcut Note. When only addition and subtraction are involved in the calculation, the
overall uncertainty is just equal to the sum of the uncertainties of the constituent numbers. Examples. Example 1. The area-of—rectangle calculation at the beginning of this section is an example of the
primitive error propagation approach. which gave the result Area = 34.4 i 0.4 cm2. We can illustrate this approach with two further examples. Example 2.
Look at the density of a droplet of liquid, Density = p (rho) = Mass of drop/ Volume of drop = MDf VD. Suppose we have measured MD and VD and estimated their uncertainties,
MD = 0.0653 i 0.0001 g VD = 0.0592 i 0.0002 1111.
Find the most probable value of the density and the uncertainty. I9 ...
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- Fall '08