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Unformatted text preview: Measurements & Error Analysis (Includes Pre Lab Assignment) Objective To learn the skill of performing careful measurements, understanding the nature of errors that occur during measurements, keep track of significant figures, use some basic data analysis techniques, plot graphs and estimate best fit lines through data points. This will be a collaborative experiment to measure the density of the given bjects and identify the material. o Apparatus Two metal cylinders each, Vernier calipers, mass balance, computer with Data Studio software. The Skills D eveloping some simple laboratory habits This laboratory experiment is designed to provide you with an appreciation for scientific methodology that includes setting up experiments, taking and analyzing data, and deriving proper conclusions compatible with a given theoretical background and hypothesis. In performing these measurements, I) You should fill every data column and calculate the answer before moving on to the next column. II) Let everyone in the group participate in the data taking - distributing the procedure among many people will reduce random error. III) Make sure that the result is compatible with your expectation. IV) Do not put away the experiment before you are sure that the overall conclusion makes sense. I ntroduction Taking data involves measuring something and entering the results in the lab notebook, and possibly in a computer as well. This something is a physical parameter that can be the length or mass of an object, or simply the time it takes for a certain event to occur. The measured values are collectively called data . Note that the word data is lural. p Data taking is fraught with errors . For example, assume that the width, x, of this paper that you are reading is 12.5 cm (centimeter). To state that x = 12.5 cm leaves the unanswered question, “How precise is the result?” Could the width be 12.4 cm or 12.6 cm? No experimental result is ever perfectly precise. For example, it is difficult to read a meter stick to an accuracy of better than 1 mm (millimeter = 0.1 cm). This is referred to as the resolution error or sensitivity . Typically, the value of the resolution error is the smallest value that can be read using the instrument. If we repeat the measurement several times, even with the same meter stick, most likely we will obtain different esults. For example, after five measurements we might record the following results for the width of the paper: r x 1 = 12.5 cm, x 2 = 12.4 cm, x 3 = 12.4 cm, x 4 = 12.5 cm, x 5 = 12.3 cm (1) This is to be expected, since it is impossible to repeat everything exactly the same way and each time we make a measurement we make a random error . One such source of error is the non-alignment of our eye with the marking of the meter stick which we are reading, i.e., the eye is not directly over the marking. The best way to reduce random errors is to average all the measurements. In general, the average value is a more accurate approximation of random errors is to average all the measurements....
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This note was uploaded on 09/30/2009 for the course PHYSIC2LA phy taught by Professor Robertclare during the Spring '09 term at UC Riverside.
- Spring '09