Experiment 1 Measurement

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1 Object To study the vernier scale principle and to learn the use of vernier calipers for the accurate measurement of length. To become familiar with the use of micrometer calipers for the accurate measurement of small lengths Theory Careful quantitative measurements are very important for development of physics, the most exact of the experimental sciences. The measurement of length is basic to many of the experiments performed by physicists. with rulers a) The use of an ordinary ruler, such as a meter ruler, is a simple way of measuring length. b) Readings on this scale should be made to fractions of a millimeter c) Start at 1 cm, not 0 cm. 1. The Vernier Principle: Fig.1.Ruler a) For small divisions on a scale, a vernier scale, invented by Pierre Vernier in 1631, can be used to measure the fractional parts more accurately. b) A caliper provided with a vernier scale is known as a vernier caliper. c) A vernier scale is an auxiliary scale that slides along the main scale. d) The graduations on the vernier scale are different in length from those on the main scale. In the vernier caliper, n - I divisions on the vernier scale correspond to n divisions on the main scale. Fig.2.Main and Vernier scales

2 For example, the vernier scale used in the experiment has 10 divisions that correspond in length to 39 divisions on the main scale. The zero mark of the vernier scale coincides with the zero mark of the main scale. The tenth vernier division is 1 division short of a mark on the main scale. It therefore coincides with a mark on the main scale. If the vernier scale is moved to the right until one mark coincides with a mark of the main scale, the number Of tenths of a main-scale division that the vernier scale has moved is the vernier division that coincides with any main-scale division. In Fig. 3, the second mark (signed l) on the vernier scale coincides with a main-scale mark, therefore the vernier scale has moved 1/10 of a main-scale division to the right of its zero position. Fig. 3. Main scale with vernier scale reading 0.1 i-) The vernier scale shows what fraction of a main-scale division is to be added; In Fig.4, the zero is to the right of the third mark on the main scale and the fourth mark (signed 2) of the vernier scale coincides with a main-scale mark. The reading is 0.3 cm (obtained from the main scale up to the vernier zero) and 0.2 mm (obtained from the vernier coincidence). The reading is 3.2 mm. Fig. 4. Main scale with vernier scale reading 3.2 mm 'Ihe Vernier Caliper: A widely used type of vernier caliper is shown schematically in Fig.5. The jaws c and d are arranged to measure an outside diameter, jaws e and f to measure an inside diameter, and the blade g to measure an internal depth. The knurled wheel W is used for adjustment of the movable jaw and the latch L to lock the jaw in position.

3 Fig.5. Vernier Caliper 2) of Small Lengths By Micrometer Calipers The most widely used device for the accurate measurement of small dimensions is the micrometer caliper, as shown below. Fig.1. Micrometer Caliper On one end of the heavy frame F is the anvil A. and on the other end is the cylindrical sleeve S. On the inside wall of S an accurate screw thread has been cut on the outside wall or the rod R and this rod is strongly attached to the thimble T. As R and T rotate, they advance a distance equal to one complete turn of T for each revolution. The total number of revolutions is shown by the S scale and any fractions of a revolution by the T scale.

4 One complete turn of T is 1/2 mm and the numbers on the S scale show the number of millimeters. Since there are 50 divisions on the T scale each of these divisions represents 1/50 of a revolution or an advance of R equal to 0.01 nun. Lengths can be measured to hundredth's of a millimeter. Various methods are used in marking the S scale-there may be twenty identical divisions per centimeter as in Fig. 2a, in which case each division represents lh mm or one revolution. For easy identification. the half-millimeter marks may be staggered. Fig. 2b. or the half-milimeter marks may be left out. From the diagrams of figure 2: the S scale reading is 6.5 mm : the T scale reading is 48.4 hundredths of a milimeter, The complete reading is therefore, 6.5mm + 0.4S4mm 6.984mm. If the micrometer calipers do not read zero when the gap between R and A is closed, they have a zero error and the reading is called the zero reading. The zero reading should be subtracted from all readings taken with the micrometer. Apparatus and Materials Required A rectangular metal block, a millimeter ruler, vernier calipers, a micrometer caliper with 25-mm section, 3 spherical specimens, and wire specimens. Procedure l) Measure the length, height and width of a solid metal block with the millimeter scale of a ruler. Length of the metal block = Height of the metal block =.

5 Width of the luetal block =.. a) From these data compute the volume of the metal block. (V= length x width x height). V=.. Volume of the metal block= 2) Repeat the above observations with the vernier calipers: a) Zero reading is the reading that the vernier caliper reads when closed. If the zero reading of the calipers is not zero, the zero reading should be subtracted algebraically from the reading of each dimension. Length of the metal block =. Height of the metal block =. Width of the metal block =.. b) Calculate the volume of the block and compare the volume to the one obtained with the ruler. V=.. Volume of the metal block= c) Express the difference in volume in cubic centimeters. Which result is more accurate? Explain briefly. NOTE: For each of the measuring devices studied make a rough sketch, similar to Fig. 8, to show the data connected with the instrument for;

6 a) The value of the main-scale division just before the zero of the vernier scale b) The value of the main-scale division just after the zero of the vernier scale c) The total number of vernier-scale divisions. d) The number of the vernier-scale division that coincides with some main-scale mark e) The observed reading (for example in Fig. 8 the reading is 6.27 mm). 3) To measure a dimension with micrometer, insert the object to be measured between A and R, and close the micrometer using H, until the micrometer makes a clicking sound. To read the scales; note the reading on S and note the reading on T. This can be found by observing which dimension on T matches exactly with the center line of S. Add S and T. This will give the reading of the micrometer. 4) Select the micrometer caliper with the milimeter scale. Note what the numbers on the S and T scales represent. Insert the 25 mm section and take about five observations of the zero reading of the instrument. Close the jaws each time with the friction head, H. 5) Measure the diameter of 3 spherical specimens and calculate their volume. Estimate the percentage error of your result. Diameter of the 1st sphere =.. Diameter of the 2nd sphere =. Diameter Of the 3rd sphere =. 6) Use the set of cube specimens. Take one reading of one side Of each cube using the micrometer calipers. Determine the density of each cube, expressing the results with the correct number of significant figures.

7 One side of cube =. One side of cube =.. One side of cube =.. Mass of cube = Mass of cube = Mass of cube = Density of cube = Density of cube = Density of cube = Results and Discussion Discuss the Results