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ME 3057 - EXPERIMENTAL METHODOLOGY & TECHNICAL WRITING Report/Worksheet/Writing Task: Lab number 2 Full Report: Partial Report: X Lab section: J NAMES: Shameek Agarwal, Date Turned In: 2/4/2012 , , Date Returned by TA: ____________________ Grader: _____________

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0001” of resolution and other with 0.001” and a caliper with a resolution of 0.001”. Analysis of part showed that maximum uncertainty aroused from instrument with highest resolution and that the best fit for uncertainty is with a standard error using K=3. The percentage error for the 0.001” micrometer, 0.0001” micrometer and the 0.001 caliper were 0.65%, 1.37% and 0.17% respectively. In part 2, a caliper was used to measure the dimensions of a 10mm gage block and error propagation was computed. The blocks density was calculated to be 7780.26 kg/m3. Analysis showed that uncertainties in measurement of individual dimensions cause an error propagation which couples to give a higher uncertainty in the calculated density. The error in the density value computed from the standard deviation was 391.78 kg/m3 while the same computed from the resolution uncertainty was 24.402 kg/m3 In part 3, the time period of a pendulum was measured first using a stopwatch measured over various cycles and then an oscilloscope with help of a sensor. The mean time period calculated for 1, 6, 13, 25 cycles is 0.85s, 0.88s, 0.88s and 0.89s respectively. It was also observed that the relative error decreases with increase in number of cycles, i.e. relative error is minimized when averaging large number of single measurements than few readings over multiple cycles. The relative error in measuring over 1 cycle was 5.12% whereas for 25 cycles was 0.62%.

1

MEASUREMENT OF UNCERTAINTY AND ERROR ANALYSIS

Part 1: Experimental Results Attached in Appendix A is multiple measurement s of the diameter of the piping section. The average value of the diameter calculated with the 0.001” Micrometer, 0.0001” Micrometer and the 0.001” Caliper are 6.263 mm, 6.391 mm, 6.339 mm respectively. The values measured are close to the manufactured specified value for the diameter which is 6.35mm with unspecified uncertainty. The measured values by the instruments lie within a range of ± 1.37% from the specified value. Some of the sources of error include variation in the diameter of the plastic tubing along different sections of the tube, human error in measuring could also affect the average result. Part 1: Analysis The mean and the standard deviation are presented in Table 1 and are calculated using Equation 1 & 2 ( ̅) ( ) ∑ √∑

( ̅)

(1) (2)

Table 1: Calculation of mean and standard deviation 0.001" Micrometer (mm.) 6.263 0.1718 0.0001" Micrometer (mm.) 6.391 0.2661 0.001" Caliper (mm.) 6.339 0.06707

Mean Std. Dev.

Resolution uncertainty is half of the resolution and the statistical error is calculated using Equation 3. ( ̅)

√

(3)

Table 2: Calculation of resolution and statistical uncertainty Sample value 0.001" Micrometer (mm) 0.0001" Micrometer (mm) 6.263 6.391

2

Resolution uncertainty (+/-) 0.0127 0.00127

Standard Error (+/-) k=1 0.0337 0.05220 k=2 0.0674 0.10440 k=3 0.1011 0.15660

0.001" Caliper (mm)

Sample value 6.339

Resolution uncertainty (+/-) 0.0127...

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