PHY121Spring 2021VL01Calipers PDF

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PRECISION INSTRUMENTS: VERNIER CALIPER AND MICROMETER Objective:  To use a metric Vernier caliper to obtain the dimensions of various objects.  To calculate the volume of a cylinder, sphere and a block using the dimensions obtained with the Vernier caliper.  To use a metric micrometer (screw gauge) to obtain the dimensions of various objects.  To calculate the volume of a sphere and a wire using the dimensions obtained with the micrometer. Part I: The Vernier Caliper When you use English and metric rulers for making measurement is sometimes difficult to get precise results. When it is necessary to make more precise linear measurements, you must have a more precise instrument. One such instrument is the Vernier caliper. The Vernier caliper was introduced in 1631 by Pierre Vernier. It utilizes two graduated scales: a main scale similar to that of a ruler and a specially graduated auxiliary scale, the Vernier, which slides parallel to the main scale and enables reading to be made to a fraction of a division on the main scale. With this device you can take inside, outside and depth measurements. Some calipers have both metric and English while others might have either metric or English only.

ENGLISH SCALE

Fig. 1 - Parts of a Vernier caliper

Fig. 2 - Dimensions that can be obtained with a Vernier caliper

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Notice that if the jaws are closed, the first line at the left end of the Vernier, called the zero line or the index, coincides with the zero line on the main scale (Fig. 3).

Fig. 3 - Vernier caliper with closed jaws

The least count can be determined for any type of Vernier instrument by dividing the smallest division on the main scale by the number of divisions on the Vernier scale. For our virtual experiment we will be utilizing a Vernier caliper with a 0.01 cm least count. Through Fig. 4 it can be observed that in this particular caliper, the Vernier scale is divided into 10 divisions which cover the same distance as nine divisions on the main scale. If the Vernier is moved so that the 1 mark on the Vernier coincides with the 0.1 mark on the main scale then the distance separating the index on the Vernier from the zero on the main scale will be 1/10 of a main scale division. Similarly, if the 2 mark on the Vernier is made to coincide with the 0.2 cm mark on the main scale, the distance between the index of the Fig. 4 - Vernier caliper with 0.01 least Vernier and the zero mark on the main scale will be 2/10 of count a main scale division and so on. The Vernier thus enables the reading to be taken to 1/10 of a main scale division by simply noting which line on the Vernier coincides with a line on the main scale. Since a main scale division in this case corresponds to 0.1cm, we are therefore able to read directly to 0.01cm. This quantity (0.01) is the "least count" of the instrument. Having first determined the least count of the instrument, a measurement may be made by closing the jaws on the object to be measured and then reading the position where the zero line of the Vernier falls on the main scale (no attempt being made to estimate to a fraction of a main scale division). We next note which line on the Vernier coincides with a line on the main scale and multiply the number represented by this line (e.g., 0, 1, 2, etc.) by the least count on the instrument. The product is then added to the number already obtained from the main scale. Occasionally it will be found that no line on the Vernier will coincide with a line on the main scale. Then the average of the two closest lines is used yielding a reading error of approximately 0.005cm. In this case we take the line that most nearly coincides.

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Fig. 5 displays a sample reading; notice the left end of the Vernier scale, the index of the Vernier scale, lands between the 0.4 and 0.5 marks of the main scale. To obtain the next digit look for the line from the Vernier scale that lines up with one of the markings of the main scale. In this case we have 7 lining up (the 8th Vernier tick mark). Therefore, the final reading is: Fig. 5- Vernier caliper sample reading 0.4+7*(0.01) = 0.4+0.07 = 0.47 +/- 0.005 cm. Or you can simply read it directly as 0.47 cm +/- 0.005 cm. If the reading must be presented in mm then you will have 4.7 mm +/- 0.05 mm. Fig. 6 shows us that the object that was measured is: 9.54 cm +/- 0.005 cm.

Fig. 6 – Second sample reading.

When working with calipers it is always essential to check that it is properly zeroed. If after calibrating the instrument there is still an offset then we must make note of the zero error which may be positive or negative. A zero error is present when the caliper jaws are fully closed and the index does not perfectly line up with the 0 mark of the main scale. A zero error may be positive or negative and must be factored into your readings before presenting your final measurements. Therefore, the corrected reading would be: Reading – Zero Error.

Fig. 7 - Checking for zero error for a Vernier caliper with jaws fully closed.

Fig. 7a: The index and the 0 mark of the main scale line up perfectly; therefore there is no zero error. Fig. 7b: The index is just to the right of the 0 mark of the main scale; therefore the zero error is positive. Notice that it is the 3rd tick mark of the Vernier scale that lines up with a marking of the main scale. Therefore the zero error is +0.02 cm. Fig. 7c: The index is to the left of the 0 mark of the main scale; therefore the zero error is negative. When obtaining the negative zero you must start the count from the last marking of the Vernier scale and move towards the left till you find the tick mark the lines up with a marking on the main scale. In this case we have the 7th tick mark (counting from right to left of the Vernier scale) that lines up. Therefore the negative zero error is -0.06 cm. PHY 121

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See Fig. 8 depicting sample zero errors and corresponding corrections, naturally when presenting the final results the +/-0.005 cm reading error must be included.

Fig. 8 - Zero errors and corrected readings.

Use the simulation and self-assessment exercises below to practice the use of a Vernier caliper. Note: The readings are displayed in mm and a comma is used instead of a decimal point. http://www.stefanelli.eng.br/en/virtual-vernier-caliper-reading-tenths-millimetersimulator/#swiffycontainer_1 https://www.stefanelli.eng.br/en/vernier-caliper-millimeter-self-assessment-1/#swiffycontainer_2

Part II. The Micrometer (Screw Gauge): The micrometer or screw gauge was invented by William Gascoigne in the 17th century, is typically used to measure very small thicknesses (e.g. foil, paper) and diameters (e.g. wires, strand of hair, spheres). It consists of a screw of pitch 0.5mm, a main scale and another scale engraved around a thimble which rotates with the screw and moves along the scale on the barrel. The barrel scale is divided into millimeters, on some instruments, such as ours, a supplementary scale Fig. 9 - Metric micrometer shows half millimeters. The thimble scale can have 50 or 100 divisions or graduations. The micrometer on Fig. 9 the thimble has 50 graduations. The pitch of the screw is determined by the distance traveled along the main scale for one full rotation (revolution) of the thimble. Since one revolution of the thimble advances the spindle 0.5 mm outward or inward then the pitch of the screw is 0.5 mm. To obtain the least count or accuracy of the micrometer: 𝑝𝑖𝑡𝑐ℎ Eq. 1 𝐿𝑒𝑎𝑠𝑡 𝐶𝑜𝑢𝑛𝑡 = # 𝑜𝑓 𝑑𝑖𝑣𝑖𝑠𝑖𝑜𝑛𝑠 LAB WORK VL1 | 4

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For the micrometer on Fig. 9 we would have: Least count = 0.5 mm /50 divisions = 0.01 mm. The object to be measured is inserted between the end of the screw (the spindle) and the anvil on the other leg of the frame. The thimble is then rotated until the object is gripped gently. A ratchet at the end of the thimble serves to close the screw on the object with a light and constant force. The beginner should always use the ratchet when making a measurement in order to avoid too great a force and possible damage to the instrument. The measurement is made by noting the position of the edge of the thimble on the barrel scale and the position of the axial line of the barrel on the thimble scale and adding the two readings. The micrometer should always be checked for a zero error. This is done by rotating the screw until it comes in contact with the anvil (use the ratchet) and then noting whether the reading on the thimble scale is exactly zero. If it is not, then this "zero error" must be allowed for in all readings. Fig. 10a shows no zero error since both zero marks are perfectly aligned. Fig. 10b clearly shows an offset with the 0 mark of the main scale lines up with the 2nd mark (0.02 mm) of the thimble; therefore, there is a positive zero error +0.02 mm. While Fig. 10c there is a negative zero error, notice the zero of the main scale lines up with the 0.46mm mark of the thimble, Fig. 10 – Determining the zero error on the micrometer. therefore, the zero error is -0.04 mm. Whenever you have a zero error on your instrument you must include it in your final reading as shown on Fig. 11.1 𝐶𝑜𝑟𝑟𝑒𝑐𝑡𝑒𝑑 𝑅𝑒𝑎𝑑𝑖𝑛𝑔 = 𝑂𝑏𝑠𝑒𝑟𝑣𝑒𝑑 𝑅𝑒𝑎𝑑𝑖𝑛𝑔 − 𝑍𝑒𝑟𝑜 𝐸𝑟𝑟𝑜𝑟

Fig. 11 - Checking for zero error, recording observed reading and corrected reading. 1

Image provided by Discover Physics for GCE “O” Level Science https://slideplayer.com/slide/9349877/

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Fig. 12 - Sample micrometer reading

To read the micrometer, simply add the number of halfmillimeters to the number of hundredths of millimeters. In the example in Fig. 12, we have 18.560 ± 0.005mm, that is 37 half millimeters and 6 hundredths of a millimeter.

A much simpler way to read the micrometer directly is: Record the value as read from the main scale: 18.50 Add the value as read from the spindle: 0.06 Thus, we have: 18.56 mm Therefore, when including the reading error we have 18.560 +/- 0.005 mm. If there had been a zero error we would need to factor it in too. In this particular case there was no zero error If two adjacent tick marks on the moving barrel look equally aligned with the reading line on the fixed barrel, then the reading is half way between the two marks. In the example above, if the 6th and 7th tick marks on the moving barrel looked to be equally aligned, then the reading would be 18.565±0.005mm. To practice how to use a metric micrometer, refer to the following interactive simulation, note that this is just to become acquainted on how to read the micrometer. https://www.stefanelli.eng.br/en/simulator-virtual-micrometer-hundredths-millimeter/ https://www.stefanelli.eng.br/en/micrometer-hundredth-millimeter-self-assessment/

Experiment Procedure: We will be using two simulations from the Amrita Online Labs website, please note that Amrita has updated their website and may require signing-in in order to access certain simulations. If after clicking an Amrita link you see the following:

Fig. 13. Sign in dialog window from Amrita webpage.

Please click the Login button and use the following information to gain access: Username/email: [email protected] Password: phystudent Otherwise, if you wish, you can create your own free account using your own Google, Yahoo, Facebook or myspace account. LAB WORK VL1 | 6

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Part I – Vernier Caliper: 1. Click on the link below to access the simulation: https://amrita.olabs.edu.in/?sub=1&brch=5&sim=16&cnt=4

Fig. 14 - Vernier caliper simulation

2. Click on the sphere so that it is placed between the caliper jaws. Use the mouse to drag the jaws closed. Use the magnified view of the Vernier and main scale to obtain and record the diameter of the sphere. 3. Click on the iron block and select what to measure first: Length, Breadth (Width) or Thickness. Obtain and record all 3 dimensions. Fig. 15 - Caliper with sphere 4. Click on the cylinder and obtain and record its diameter and length 5. Click on the beaker and measure and record its inner diameter and internal depth. 6. Click the Reset button and repeat steps 2-5, three more times. 7. Calculate the average of each reading. 8. Use the average dimension values for each object to calculate their respective volumes. Use the following formulas: Volume of the sphere: 𝑉𝑠𝑝ℎ𝑒𝑟𝑒

𝑑 3 4 = 𝜋( ) 3 2

Eq. 2

Volume of the block, where we are defining the breadth as w (width): 𝑉𝑏𝑙𝑜𝑐𝑘 = 𝑙 × 𝑤 × 𝑡

Eq. 3

Volume of the cylinder, note that sometimes the length of a cylinder can also be defined as height: 𝑑2 𝑙 Eq. 4 𝑉𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟 = 𝜋 4 PHY 121

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Volume of the beaker, same as Eq. 4, except that the diameter is the internal diameter di and the length l is the internal depth which we will call Depthi: 𝑉𝑏𝑒𝑎𝑘𝑒𝑟 = 𝜋

𝑑𝑖 2 𝐷𝑒𝑝𝑡ℎ𝑖 4

Eq. 5

Note: You can check each measurement reading by entering your value in the cell on the left panel of the simulation and click Check. It may not work on Chrome but if using IE, Firefox or Edge it will show a green check mark when the answer is correct. Fig. 16 – Check your result

Questions: 1. What does the smallest division on the main scale of the Vernier caliper correspond to? 2. What is the error of your measurements? 3. Inspect the Vernier scale and note that 10 Vernier divisions correspond to 9 main scale divisions. Prove that the Vernier caliper can be used to make readings to 1/10 of a main scale division. 4. Why is it required to make various measurements of the same object?

Part II – Micrometer (Screw Gauge): 1. Click on the link below to access the simulation: https://amrita.olabs.edu.in/?sub=1&brch=5&sim=156&cnt=4

Fig. 17 - Micrometer simulation

2. Change the least count from LC=0.01 mm to LC = 0.005 mm. Record the number of divisions in the thimble as 100. 3. Check for zero error: Click on the up/down arrows on the ratchet till the spindle is flush against the anvil. If there is a zero error, be sure to record it and indicate whether it is a positive or negative error. 4. Determine and record the pitch of the screw. Prove that the least count is 0.005 mm. 5. Click on the lead shot. Turn the spindle till it is flush against the lead shot. Record the observed and the corrected readings. The corrected reading is such where you factor in the zero error. Click on the lead shot on the left panel again to remove it. LAB WORK VL1 | 8

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6. Click on the drop down menu to select the wire from the list of objects. Obtain and record the diameter of the wire, both the observed and corrected readings. Remove the wire. 7. Select the plate as your next object and obtain and record its thickness. Must record both observed and corrected readings. 8. Click the Reset button and repeat steps 3-6, three more times. 9. Calculate the average of each corrected reading. 10. Using the average diameter of the lead shot calculate its volume. 11. Using the average diameter of the wire and knowing its length is 5cm calculate its volume. Note: You can check each measurement reading by entering your value in the cell on the left panel of the simulation and click Check.

Extra credit: Obtain the area of the irregular lamine, measure its thickness and calculate its volume. Use the formula Volume = Area  thickness. Grid scale: 1 square = 1mm. Questions: 1. What does one division on the barrel of the micrometer correspond to? 2. What does one division on the rotating thimble correspond to? 3. What type (name) of error is the "zero error" of the micrometer assuming it enters a calculation? 4. When performing this experiment in the laboratory premises we use a micrometer to measure the diameter of a human hair. Would you use a Vernier caliper to make the same measurement? Explain.

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