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Measurements Measurements Measurements are an important part of engineering. There would be no use in experimenting if there were no way to differentiate the results. Measurements are also important for design and manufacturing. Without accurate measuring instrumentation there is no way to build and reproduce products. In this lab we will discuss several different methods of measuring some specimens of aluminum tubing stock. To measure the stock, rulers, Vernier calipers, dial calipers and micrometers are going to be used. The specimens that we are going to measure are shown in the figures below. Figure 1. Specimen 1 Side View Figure 2. Specimen 1 Top View 1 Figure 3. Specimen 2 Side View Figure 4. Specimen 2 Top View First you should measure and record all dimensions shown on the figures above. These dimensions include length, external diameter, internal diameter, and thickness. Measure these dimensions using a ruler. Once they have been measured using the ruler then the dimensions large dimensions should be measured using Vernier calipers and the smaller dimensions such as thickness using the micrometer these values should be recorded on the following page. Then these values should be checked using the dial calipers. Once the values are found using each instrument calculate the volume of material in each specimen. Then compare your findings using the true percent relative error using the volume calculated by the ruler values as the approximate value and the volume calculated by the micrometer and Vernier calipers as the actual or true value. Also measure the mass/weight of each specimen and find from it the density ρ of each specimen. Each student should individually record all of the measurements. Also the mean and the standard deviation should be calculated. Once these are calculated check 2 and see if 95% of the measured values fall within mean value ± 2Sy (Sy being the standard deviation). Then write up a sample lab report stating the results. All the equations mentioned above can be found in the statistics handout. Using Vernier Calipers Figure 5. Vernier Calipers • The Vernier caliper is an extremely precise measuring instrument; the reading error is 1/50 mm = 0.02 mm. Depending on the exact Vernier caliper used, the reading error can be different than 0.02 mm. • It can be used to measure external diameter, internal diameters, lengths, and depths. • Close the jaws lightly on the object to be measured. • If you are measuring something with a round cross section, make sure that the axis of the object is perpendicular to the caliper jaws. This is necessary to ensure that you are measuring the full diameter and not merely a chord. • The top scale is calibrated in inches (U.S. Customary units). • The bottom scale is in metric units. • Notice that there is a fixed scale and a sliding scale. • The numbers on the fixed scale are centimeters or inches. • The unnumbered tick marks on the fixed scale between the centimeters are millimeters, and the numbered tick marks between the inches are one tenth of an inch (the unnumbered tick marks between the inches 0.025 of an inch). • There are ten numbered tick marks on the sliding scale for the metric side and 6 numbered tick marks on the U.S. Customary units side. The left-most tick mark on the sliding scale will let you read from the fixed scale the number of whole millimeters that the jaws are opened. Figure 6. Vernier Scale Example 3 • In the example above, the leftmost tick mark on the sliding scale is between 21 mm and 22 mm, so the number of whole millimeters is 21. • Next we find the tenths of millimeters. Notice that the ten tick marks on the sliding scale are the same width as nine ticks marks on the fixed scale. This means that at most one of the tick marks on the sliding scale will align with a tick mark on the fixed scale; the others will miss. • The number of the aligned tick mark on the sliding scale tells you the number of tenths of millimeters. In the example above, the 3rd tick mark on the sliding scale is in coincidence with the one above it, so the caliper reading is (21.00 + 0.30 + 0.00) mm. • If two adjacent tick marks on the sliding scale look equally aligned with their counterparts on the fixed scale, then the reading is half way between the two marks. In the example above, if the 3rd and 4th tick marks on the sliding scale looked to be equally aligned, then the reading would be (21.00 + 0.30 + 0.05) mm. • On those rare occasions when the reading just happens to be a "nice" number like 2 cm, don't forget to include the zero decimal places showing the precision of the measurement and the reading error. So not 2 cm, but rather 20.00 mm. • The same method is used for English units • When using a Vernier scale to write out each of the scales in an addition problem for an example I am going to use the numbers in the example problem above. 21.00 mm + 0.30 mm + 0.00 mm 21.30 mm Note that the last digit after the dot is typically not known for sure and is therefore estimated. It is a good estimate nonetheless and its inclusion in the reading is meaningful or has significance. Using Micrometers Figure 7. Micrometer 4 • The micrometer is an extremely precise measuring instrument; the reading error is 1/10000 in = 0.0001 in. Depending on the exact micrometer used, the reading error can be different than 0.0001 in. • It can be used to measure external diameters and thicknesses. • Use the ratchet knob (at the far right in the picture above) to close the jaws lightly on the object to be measured. It is not a C-clamp! When the ratchet clicks, the jaws are closed sufficiently. • The numbered horizontal tick marks along the fixed barrel of the micrometer represent a tenth of an inch and the unnumbered tick marks represent .025 of an inch • Every revolution of the knob will expose another tick mark on the barrel, and the jaws will open another .025 of an inch. • Notice that there are 5 numbered tick marks wrapped around the moving barrel of the micrometer. Each of these tick marks represents .005 of an inch. There are also nine unnumbered tick marks for each of the numbered tick marks. These unnumbered tick marks represent .0005 of an inch. There are 5 numbered vertical tick marks on the fixed barrel. Each of these represents 0.0001 of an inch. Figure 8. Micrometer Vernier Scale Example • In the example above the units are in mm. However, the procedures are exactly the same for US Customary Units. In the example, the jaws are opened (2.5+.120) mm, that is, 5 half-millimeters and 12 hundredths of a millimeter. • The micrometer may not be calibrated to read exactly zero when the jaws are completely closed. Compensate for this by closing the jaws with the ratchet knob until it clicks. Then read the micrometer and subtract this offset from all measurements taken (The offset can be positive or negative). • On those rare occasions when the reading just happens to be a "nice" number like 2 mm, don't forget to include the zero decimal places showing the precision of the measurement and the reading error. So not 2 mm, but rather (2.000) mm. • If the micrometer is in English units then exactly the same procedures are used, but the scales are different. • The same addition method that is mentioned above can be used here. 5 2.500 mm + .120 mm + .000 mm 2.620 mm Using Dial Calipers Figure 9. Dial Calipers The usage of Dial Calipers is the same as for Vernier except instead of the Vernier scale they have a dial scale that measures the fractions of inches/centimeters. Significant Digits While using these measurement tools we have to take significant digits into account. There are only so many digits that that can be accurately measured. When working with measuring tools and doing calculations we have to keep this in mind so that digits with no significance are not used in calculations. When taking measurements the last significant digit is the first estimated position. When estimating the last significant digit estimate the value in terms of tenths of the space between the tick marks. Take the figure below for example the arrow falls between 2.8 and 2.9 cm we don’t know for certain the last digit. However, it can be estimated to reasonable degree so we can estimate the value to about 2.82 all these are significant digits. However we cannot estimate a value more accurate than 2.82 to a reasonable degree of certainty say 2.823 as the last significant digit 2 has error in it. The error in the next digit 3 is much greater so we have even more uncertainty. Therefore as it was said above the last significant digit is first estimated position. Figure 10. Measurement Significant Digits 6 References All the Italicized information came from: http://www.physics.smu.edu/~scalise/apparatus The significant Digits information came from: http://dbhs.wvusd.k12.ca.us/webdocs/SigFigs/Measuring.html Student Name: Date: Ruler (units) Calipers (units) Micrometer (units) L1 N/A D1 d1 N/A t1 N/A L2 N/A D2 N/A d2 N/A t2 Mass (m1) of specimen 1, units Mass (m2) of specimen 2,units 7.
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