Appendix. Physical Constants. Micrometer

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1 Appendix Physical Constants g Gravitational acceleration m s 2 e Charge on the electron C k Coulomb constant N m 2 C 2 ɛ o Permittivity F m 1 µ o Permeability 4π 10 7 T m A 1 c Speed of light 299,792 m s 1 Micrometer The micrometer is a device used to measure small linear dimensions, and is shown below. It is similar in some respects to the vernier caliper, but there are some important differences. There is a fixed main scale on the barrel which has a horizontal line down its length; a sleeve rotates around the barrel. The barrel and sleeve measurements are added to obtain the final measurement. Start on the barrel. See how many full mm are visible, and whether or not the half mm is visible. Here, there are 8 full mm visible, along with the half mm, so start with 8.5mm. Next, see where the horizontal line on the barrel hits the sleeve. Each of the graduations on the sleeve is 0.01mm, so starting at 0, they are 0.01mm, 0.02mm, 0.03mm 0.04mm, 0.05mm, 0.06mm, 0.07mm, 0.08mm, 0.09mm, 0.10mm, 0.11mm, 0.12mm,..., 0.44mm, 0.45mm, 0.46mm, 0.47mm, 0.48mm, and 0.49mm - for a total of 50. [This is why you need the half mm on the barrel - every rotation of the sleeve only advances it along the barrel (50)(0.01mm) = 0.5mm] Here, the line hits between 0.07mm and 0.08mm, so add 0.07mm to the 8.5mm for 8.57mm. Finally, as mentioned above, the horizontal line hit the sleeve between 0.07mm and 0.08mm, so you will need to estimate a final digit, which is to 0.001mm. Here, you are almost to 0.08mm, so 0.009mm is good. The final measurement is then 8.579mm (0.8579cm). 1

2 You can access a virtual micrometer simulator at: Sample Measurements (3)(1mm) + (36)(0.01mm) + (2)(0.001mm) = 3mm mm mm = 3.362mm (0.3362cm) (10)(1mm) + 0.5mm + (20)(0.01mm) + (0)(0.001mm) = 10mm + 0.5mm mm mm = mm (1.0700cm) Even though (0)(0.001mm) = 0, this final digit is significant and needs to be recorded. Look at it this way - the measurement is not mm or mm - it is mm. 2

3 (12)(1mm) + (48)(0.01mm) + (7)(0.001mm) = 12mm mm mm = mm (1.2487cm) Be careful! Although you are beginning to see the half mm between 12 and 13, it is because you are almost there; i.e., it is not added in the measurement. Look at it this way - if you advance the sleeve to 0 (one and a half graduations) - are you at 13mm? No - you are at 12.5mm. Vernier Caliper (20 Division) The vernier caliper is a device used to measure linear dimensions and is shown below. It is actually quite simple to use. There is a fixed main scale; a movable vernier scale rides along the main scale, subdividing each graduation of the main scale. Since this is a 20-division caliper, the subdivision is 1mm/20 = 0.05mm. All measurements are made relative to the index - the first line on the vernier scale labeled 0. First, see where the index hits the main scale. Here, it is between 20mm and 21mm. Therefore, this measurement is 20.something mm. Next, look for which graduation of the vernier scale aligns with a graduation on the main scale (there will be only one). Moving to the right along the vernier scale from the index, the 13 th graduation aligns with the main scale, and (13)(0.05mm) = 0.65mm. The final measurement is then 20.65mm, or 2.065cm. A quick glance at the numbers on the vernier scale will get you this measurement directly. If you start counting from the index, you will see that the 25 represents 0.25mm, the 50 is 0.50mm, etc. Since you are three graduations past 0.50mm, you know that this is 0.65mm. You can access a virtual 20-division vernier simulator at: 3

4 Sample Measurements 89mm mm (2 nd graduation aligns) = 89.10mm (8.910cm) 40mm mm (index and final 0 align) = 40.00mm (4.000cm) 44mm mm (14 th graduation aligns) = 44.70mm (4.470cm) Note the different numbers on this caliper. On the main scale, the calibration is still cm, but labeled in mm (10mm = 1.0cm). On the vernier scale, the calibration is 0.10mm, 0.20mm, etc. However, this vernier is still used the same way. 4

5 Vernier Caliper (50 Division) This device is used exactly the same way as the 20-division vernier caliper; the only difference is that now each graduation on the vernier scale is 1mm/50 = 0.02mm. You can access a virtual 50-division vernier simulator at: 5