Yanbu University College Name: Marks Obtained: Student s ID: Section: Date: General Physics I (PHYS 101) Lab. Exercise No. Accuracy of Physical Measurements PERFORMANCE OBJECTIVES After completion of this laboratory exercise the students will be able to: 1. Acquaint themselves with measuring procedures, accuracy of measurement and reading accuracy. Compare experimentally measured values of volumes with theoretically calculated values of volumes obtained by using mass-density formula. MATERIALS AND EQUIPMENT Vernier caliper, micrometer screw gauge, wooden cylinder, metallic cylinder, metallic cube, a piece of wire, and balance. BASIC MEASURING INSTRUMENTS THE VERNIER CALIPER 1. Construction The Vernier caliper is named after its inventor, Pierre Vernier. It is an instrument used for accurate readings to the ten-thousandth of an inch. The Vernier caliper consists of two scales: 1. A regularly graduated scale which is the part of fixed jaw is called the fixed main scale. The divisions on the fixed main scale indicate centimeters (), and each centimeter of the fixed scale is divided into 10 equal divisions. This means the minimum reading of the main scale is 1mm.. A Vernier scale which is the part of the moving jaw and it is arranged to slide along the fixed main scale. The Vernier scale is one division shorter than the fixed scale and it is also divided into 10 equal divisions. This means 9 mm length on the fixed scale is equal to 10 divisions on the Vernier scale. Vernier caliper can be used to measure the length of an object, inner diameter/width of a hollow cylinder, the depth of a hole, or outer diameter/width of a round object as illustrated in Fig. 1. Lab Exercise- PHYS-101 Page 1 of 9
Figure 1: A Vernier Caliper. Specifications of Vernier Caliper The two main specifications of Vernier caliper include: Measuring Range: It is the ability of the caliper for determining the dimensions of the object to be measured. Resolution: It is the measure of accuracy of the Vernier caliper when determining the dimensions of the object. 3. Types of Vernier Caliper The Vernier calipers are of three types which are given below: This Vernier is divided into 50 (n) divisions with a minimum reading of 1 1 0.0mm. n 50 This Vernier is divided into 0 (n) divisions with a minimum reading of 1 1 0.05mm. n 0 1 This Vernier is divided into 10 (n) divisions with a minimum reading of n 1 0.1mm. 10 4. Zero Errors of Vernier Caliper When the jaws are closed, the Vernier zero mark coincides with the zero mark on its fixed main scale. Before taking any reading it is good practice to close the jaws or faces of the instrument to make sure it is reading zero. If not then note the reading. This reading is called zero error. The zero error is of two types (i) positive zero error and (ii) negative zero error Lab Exercise- PHYS-101 Page of 9
First figure: no zero error, Second figure: negative zero error, Third figure: positive zero error Figure : Zero Errors on a Vernier caliper Positive Zero Error If the zero on the Vernier scale is to the right of the main scale, then the error is said to be positive zero error and so the zero correction should be subtracted from the reading which is measured. Negative Zero Error If the zero on the Vernier scale is to the left of the main scale, then the error is said to be negative zero error and so the zero correction should be added from the reading which is measured. Figure shows the different cases of the zero errors of the caliper. Lab Exercise- PHYS-101 Page 3 of 9
5. How to measure the Least count of the vernier caliper [0.5 mark] The Vernier scale consists of a main scale graduated in centimeters and millimeters. On the Vernier scale 0.9 is divided into ten equal parts. The least count or the smallest reading which you can get with the instrument can be calculated as under. Value of the smallest division on main scale (MS) -----------mm Total number of division on Vernier scale (VS) -----------div Value of thesmallest division on MS The least count of the Vernier Totalnumber of division on VS ------------mm ------------ 6. Calculate the zero error in your apparatus [0.5 mark] ZE ------------- 7. Reading Procedure of the Vernier Caliper To use a Vernier caliper follow the instructions given below: 1. Close the jaws of the Vernier caliper and note the zero error.. The object to be measured is closed by the jaws gently. If the object to be measured is of round shape, the object s axis should be perpendicular to the caliper because the full diameter of the object should be measured and not the chord of the object. 3. To read a Vernier caliper you first take the reading on the main scale where the zero of the Vernier meets it. (Do not make the mistake of reading the main scale at the metal edge of the Vernier a common mistake). In Figure 3 this reading is 18.0 mm (1.8) plus a small amount which will be given by the Vernier scale. 4. Look along the Vernier scale for a mark which is coincident with a mark on the main scale and read the Vernier at this point. In the photograph this is 0.3 mm (3x.01.03). You may decide that it looks more like the mark before or after this point as human eyesight is often unable to determine the exact point of coincidence. This results in a small margin of error in the instrument. 5. Add the readings taken in steps 3 and 4. This will give uncorrected reading, which in present case is 18.3 mm (1.83) as shown in Figure 3. 6. Obtain a correct reading by either adding or subtracting the zero error from the uncorrected reading obtained in step 5. Lab Exercise- PHYS-101 Page 4 of 9
Figure 3: Reading a Vernier Caliper 8. Finding the Area and Volume Using a Vernier Caliper Procedure: 1. Determine the zero error of the given Vernier caliper.. Follow the steps 1-6 to measure the side length of the given cube. Record your result in Table 1 and calculate its volume and surface area. 3. Follow the steps 1-6 to measure the diameter and height of a wooden cylinder. Record your result in Table 1 and calculate its radius, base area, surface area and volume. 4. You must use the appropriate units for both measured and calculated readings. 9. Observations Observations for a wooden cylinder [01 mark] Wooden cylinder Diameter of the cylinder (D 1 ) Length of the cylinder (L 1 ) Main scale (MS) Vernier scale (VS) div Fractional part (FP 0.01VS) Total reading (TR FP+MS) Correct reading (CR TR ZE) Lab Exercise- PHYS-101 Page 5 of 9
Observations for a metallic cylinder [01 mark] Metallic cylinder Diameter of the cylinder (D 1 ) Length of the cylinder (L 1 ) Main scale (MS) Vernier scale (VS) div Fractional part (FP 0.01VS) Total reading (TR FP+MS) Correct reading (CR TR ZE) Observations for a piece of wire [01 mark] Piece of wire. Diameter of the wire (D 3 ) Main scale (MS) Vernier scale (VS) div Fractional part (FP 0.01VS) Total reading (TR FP+MS) Correct reading (CR TR ZE) Observations for a metallic cube [01 mark] Metallic cube Length Main scale (MS) Vernier scale (VS) div Fractional part (FP0.01VS) Total reading (TRFP+MS) Correct reading (CRTR ZE) Breadth Height Lab Exercise- PHYS-101 Page 6 of 9
10. Calculations: Radius Radius of the given wooden cylinder R 1 D 1 [01mark] --------------- Radius of the given metallic cylinder R D --------------- Radius of the given Piece of wire R 3 D 3 --------------- Volume / Area of cross-section Volume the given wooden cylinder V 1 π R 1 L 1 [01mark] ---------------- 3 Volume the given metallic cylinder V π R L ---------------- 3 Area of cross-section of the given piece of wire A π R 3 ---------------- Lab Exercise- PHYS-101 Page 7 of 9
Volume the given metallic cube V 3 Length Breadth Height Mass -------------- 3 [01mark] The mass of the given wooden cylinder (m 1 ) --------------g The mass of the given metallic cylinder (m ) --------------g The mass of the given metallic cube (m 3 ) --------------g Density [01mark] Density of the given wooden cylinder m1 1 1 ------------g/ 3 Density of the given metallic cylinder m ------------g/ 3 Density of the given metallic cube m3 3 3 ------------g/ 3 Lab Exercise- PHYS-101 Page 8 of 9
11. Questions and Comments: [01 mark] 1. Compare the densities of the given solids.. Discuss the mass density relation in each given solid. 3. Convert the unit of density in kg/m 3 in each answer 4. If you need to improve the precision of density measurements, for each object, what will be your first step? End of the Lab Eexercise- Lab Exercise- PHYS-101 Page 9 of 9