Uncertainties: Data Analysis Uncertainties: Data Analysis Laboratory Report Name - -MW/TTH Laboratory Report Name -- --MW/TTH A.1 Significant Figures. A.3 Significant Figures. Re-express the following numbers in normal notation to three significant figures. Express the following Results in normal notation to the correct number of decimal places. 0.524 1.524 0.524 + 0.22 16.04 16.07 28.309 -4.9 1.333 1,335 123 + 25.045 0.02544 0.02546 88.678 -22.0456 73,449 73,854 4390 + 15.5 0.06038 0.06034 2.34-5.369 2,909,112 2,904,999 A.4 Significant Figures. Re-express the same numbers in scientific notation to three significant figures. Note: these numbers in scientific notation should be consistent with their normal notation. The dimensions of a block of aluminum are as follows: a = 12.3 cm, b = 4.3 cm, and c = 5.61cm. 0.524 1.524 16.04 16.07 1,333 1,335 0.02544 0.02546 73.44 73,854 0.06038 0.06034 2,909,112 2,904,999 A.2 Significant Figures, Express the following products in scientific notation to correct number of significant figures. What is the volume of the block, V-abc, where your answer is given with the correct number 0.52 of significant figures? 0.022 16.04 2.54E-3 1.333ES Volume = 6.78E-5 in normal notation. 0.02544 25.44 units 73.445 Volume 1.000E-2 in scientific notation. 0.06038 units 3.0778E6 2,909,112 3.1480 Express the following quotients in scientific notation to correct number of significant figures. 0.524 0.022 16.04 2.54E-3 1.333ES 6.78E-5 0.02544 25.4 73,449 1.000E-2 0.06038 3.0778E6 2.909,112 / 3.14ED 10 11Uncertainties: Data Analysis Uncertainties: Data Analysis B. Expressing experimental error. Laboratory Report Name - ---MW/TTH In an experiment to measure the acceleration of gravity at the surface of the earth in the DFW Questions: Metroplex, 9.85 m's" (Ei) and 9.73 m/s' (Ex) are obtained. The accepted local value of g = 9.80 m/s (A) for DFW. 1. Were the measurements on the block in A.4 made with the same instrument? Explain your answer. Hint: Was the precision of the measurement the same in all cases? What is the % difference for the measurements? What is the % error of the first measurement E1? What is the % error of the second measurement Ez? 2. Does % error indicate accuracy or precision? Explain. C. Data Analysis: Statistical and graphical interpretation of tabular data. 1 (5) y1 (m) yz (m) Ya (m) y4 (m) ys (m) 0.00 0.00 0.00 0.00 0.00 0.00 0.25 0.26 0.36 0.28 D.36 0.38 0.50 1.03 1.42 1.10 1.45 1.51 0.75 2.59 3.19 2.82 2.48 3.07 1.00 4.80 4.36 5.12 4.63 4.85 1.25 8.24 7.91 7.44 8,09 7,38 3. Does % difference indicate accuracy or precision? Explain. 1. From the slope of the graph of t (s') versus y(m), what is the experimental value of the acceleration of gravity? m/s Hint: y = . yayroxb-0 => y=mx+b m = slope = = => 8=2(slope) 4. Suppose you are the first to measure the value of a physical quantity, like the acceleration 2. If the accepted value of the acceleration of gravity for Dallas is 9.80 m/s', what is the of gravity at the surface of the Earth (Galileo). How would you estimate the experimental percent error of the experimental value of the acceleration of gravity obtained above? uncertainty? %error = 12 13