MeasurementsandErrorAnalysis - MEASUREMENTS AND ERROR...

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1 OBJECTIVE 1. To learn how to use the following measuring devices and understand the uncertainties associated with them. a) meter stick b) metric ruler c) triple-beam balance d) digital balance e) vernier calipers f) micrometer 2. Use the following general error propagation equation to analyze the errors involved in making calculations involving measurements with their own uncertainty. THEORY Refer to lab handout on Error Propagation . Using the Metric Ruler Consider the following standard metric ruler. The ruler is incremented in units of centimeters (cm). The smallest scale division is a tenth of a centimeter or 1 mm. Therefore, the uncertainty x = smallest increment/2 = 1mm/2 = 0.5mm = 0.05cm. Note that a measurement made with this ruler must be stated to a tenth MEASUREMENTS AND ERROR ANALYSIS LAB 2 22 222 General Error Propagation Equation fx y z fff xyz σ σσσ  ∂∂∂ =+ +  
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2 of a centimeter since the uncertainty is stated to a tenth of a centimeter. In the example above, the length of the object would be stated as x = 2.77 cm ± 0.05 cm. Using the Vernier Calipers The Vernier caliper is an instrument that allows you measure lengths much more accurate than the metric ruler. The smallest increment in the vernier caliper you will be using is (1/50)mm = 0.02mm = 0.002cm. Thus, the uncertainty is x = (1/2)0.002 cm = 0.001 cm. The vernier scale consists of a fixed metric scale and a sliding vernier scale. The fixed scale is divided into centimeters and millimeters, while the vernier scale is divided so that 50 divisions on it cover the same interval as 49 divisions on the main scale. Thus, the length of each scale vernier division is 49/50 the length of a main scale division. Close the jaws completely and note that the first line at the far left on the vernier scale (called the “zero” or “index” line) coincides with the zero line on the main scale. Carefully compare and see that the first vernier division is 0.02 mm short of the first main scale division, the second
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MeasurementsandErrorAnalysis - MEASUREMENTS AND ERROR...

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