Papua New Guinea University of Technology Department of Mechanical Engineering ME 311 – Experimental Engineering ME 261 – Statics Experiment 1: Introduction to mass principle. Title: Introduction to Mass principle Abstract Every physical object whether a living thing or non-living thing, from a crawling ant to a massive stone has what we called mass. Mass can be defined as the amount of matter intrinsic to a body and the numerical measure of inertia. Mass is both the property of a physical body and a measure of its resistance to acceleration (a change in its state of motion) when a net force is applied. The objects mass also determines the strength of its gravitational attraction to other bodies. The basic SI unit of mass is the kilogram (kg) which is in metric system and in British Imperial system of unit is the pound (lb.). The mass of an object can be determine using scale, spring balance, etc. Also it can be determined by using the density formula. Mass is used to determine the density of an objects. An important property of any material is its density, defined as its mass per unit volume. A homogenous material such as ice or iron has the same density throughout. We use the Greek letter ο² (rho) for density. If the mass m of homogeneous material has volume V, the density ο² is π = π/π£ . The density of some materials varies from point to point within the material such as earth atmosphere (which is less dense at high altitude) and oceans (which are denser at greater depth). In general, the density of a material depends on environmental factors such as temperature and pressure. The SI unit for density is the kilogram per cubic meter (1kg/mα΅). 1|Page Table of content Contents Introduction .................................................................................................................................................. 3 Theory ........................................................................................................................................................... 3 Experimental apparatus ................................................................................................................................ 3 Test procedure .............................................................................................................................................. 4 Results ........................................................................................................................................................... 4 Sample Calculation:................................................................................................................................... 5 Discussion of Results ..................................................................................................................................... 6 Summary ....................................................................................................................................................... 7 Bibliography .................................................................................................................................................. 8 Appendices.................................................................................................................................................... 8 2|Page Introduction It is known from experience that a heavier body has a great deal of inertia and a light body has very little. The concept of mass is used as a measurement of inertia Mass = amount of matter in a body The measurement of mass is by comparison with the standard kilogram (kg) of mass, a carefully prepare platinum cylinder that was about 2.2 lbs. The gram mass commonly used is 10-3 kg. In the S.I System of unit mass is measured in kilograms. Mass is proportional, but not equal to the local gravitational acceleration. Theory In most laboratories, mass is usually measured using a spring balance. A spring balance measures the weight of an object by opposing the force of gravity acting with the force of an extended spring. It works by Hooke's Law, which states that the force needed to extend a spring is proportional to the distance that spring is extended from its rest position. Therefore, the scale markings on the spring balance are equally spaced. Another method of measuring mass, especially for the irregular shaped objects, is by measuring the volume of the water displaced by the object and calculating using the formula: π → π = ππ π Where ρ is the density of water, m is the mass to be calculated and V is the volume of water displaced by the object. π= The third method is for the regular shaped objects where length, breadth, height, etc. are measured using ruler, micrometer, etc., the volume is calculated and then mass is calculated using the above formula where density is the density of the object to be measured. Experimental apparatus ο· ο· ο· - Spring Balance Steel Rule Four (4) Specimen Specimen 1: Small steel cylinder Specimen 2: Medium Steel cylinder Specimen 3: Large Specimen cylinder Specimen 4: Aluminium Cylinder 3|Page Test procedure 1. The spring balance was set to zero 2. Each specimen was weighed three times and the results were recorded on the tabulated sheet provided. 3. The steel rule was also used to measure the dimensions and the mass was theoretically calculated. Results Mass Balance System Specimen No. Spring Balance Trials M (grams) M1 M2 (g) (g) 93.4 95.5 M3 (g) 95.1 Mave= M1+ M2+ M3 (g) Absolute Error (ΔM) = Mmax - Mmin (g) 2.1 1. Small Steel 94.67 Cylinder 2. Medium steel 247.8 245.7 247.6 247.03 2.1 cylinder 3. Large Steel 596.8 600.5 598.3 598.33 3.7 cylinder 4. Aluminium 89.7 92.3 91.2 91.07 2.6 cylinder Table 1: The table shows the results obtained from weighing the specimens on the Spring balance. Relative Error (%) = ΔM (100)/ Mave 2.218 0.85 0.618 2.855 Instrument Specimen 1 Specimen 2 Specimen 3 Specimen 4 Height, h Diameter, d Height, h Diameter, d Height, h Diameter, d Height, h Diameter, d Vernier 25 mm 24.95mm 45.25 mm 29.9 mm 60.1 mm 40.25mm 46.8 mm 30.2mm Caliper Steel Rule 25 mm 25 mm 45 mm 30 mm 60 mm 40 mm 45 mm 30 mm Table 2: The table shows the results obtained from measuring the diameter and height of the specimens using the steel rule and the Vernier caliper. 4|Page Specimen No. Volume Calculation from Vernier Caliper, VVC (m3) =π*(d/2)2 Volume Calculation from Steel Rule, VSR (m3) = π*(d/2)2 Mass calculation from Vernier Caliper, MVC (kg) =ρ mild steel VVC = ρ Al VVC Mass calculation from steel rule, MSR (kg) = ρ mild steel VSR = ρ Al VSR Mave = MVC + MSR (kg) Absolute Error (ΔM) = Mmax - Mmin 0.09592 0.09631 0.09612 1.222 × 10−5 1.227 × 10−5 1. Small solid cylinder 3.177 x 10-5 3.181 x 10-5 0.24939 0.24971 0.24955 2. Medium solid cylinder 7.647 x 10-5 7.540 x 10-5 0.60029 0.59189 0.59609 3. Large solid cylinder 3.352 x 10-5 3.181 x 10-5 0.09084 0.08621 0.08853 4. Aluminium cylinder Table 3: Shows the calculated mass from obtaining the parameters of the specimens. 1.963 x 10-4 0.204 1.6 x 10-4 0.064 2.1 x 10-3 0.352 2.315 x 10-3 2.61 Sample Calculation: The calculations shown below are just for the first column only. Others are calculated in the same manner. Volume Calculation for Vernier Caliper, VVC (m3) π = ππ 2 β = π(0.012475)2 (0.025) = 1.222 × 10−5 π3 Volume Calculation for Steel Rule, VSR (m3) π = ππ 2 β = π(0.0125)2 (0.025) = 1.227 × 10−5 π3 Mass calculation for Vernier Caliper, MVC (kg) π = πππππ π π‘πππ π = 7850 × (1.222 × 10−5 ) = 0.095927 ππ Mass calculation for steel rule, MSR (kg) π = πππππ π π‘πππ π = 7850 × (1.227 × 10−5 ) = 0.0963195 ππ 5|Page Relative Error (%) = ΔM (100)/ Mave Average mass, mav (kg) πππ = 0.095927 + 0.0963195 = 0.09612325 ππ 2 Absolute Error (ΔM) βπ = ππππ₯ − ππππ 0.0963195 − 0.095927 = = 1.9625 × 10−4 ππ 2 2 Relative Error (%) πΈππππ% = βπ 1.9625 × 10−4 × 100 = × 100 = 0.204% πππ£ 0.09612325 Discussion of Results Absolute error is the difference in measurement between an actual value and the experimental value, or value that we get in any measurement. Absolute error is useful in every measurement if we want to get the accurate value, and is practically less than one. For example, if the true weight of a packet of rice is 1 kg and we reweigh it and get 0.98 kg, then our absolute error would be ((1.00kg – 0.98)/2) = ±0.01 kg). In our experiment, the absolute error calculated for mass of one of the specimen is ±π. ππππ × ππ−π ππ or ±0.00019625 kg, which mean the accurate value falls in this range. There are precautions to be taken to reduce absolute errors when doing experimental measurements. In our experiment, we measured the heights, diameters and the masses of the four specimens with different methods of measurements. For masses, we used a spring balance, a Vernier caliper and a 30 cm steel rule. For height and diameters, we only used the Vernier caliper and the 30 cm steel ruler. Using the spring balance, we took three (3) readings for mass of each specimen and the average was calculated, and using the Vernier caliper we took two (2) readings for height, diameter for each specimen, form which the masses were also calculated. Therefore, the precautions we took to reduce the absolute error were; ο· We made sure that the instruments were correctly calibrated ο· Three readings were recorded for mass and the average was taken (each specimen), and ο· Two readings were recorded for height and diameter of each specimen using two different measuring instruments (a steel ruler & a Vernier caliper) The accuracy limit between the weighing instrument ranged from between 2 and 4 grams. The large errors in the weighing accuracy was due to not calibrating the equipment precisely before measuring the specimens. During the experiment, only one mass balance system was employed. The Spring balance was used to measure the mass of the four specimens. In comparison, the Vernier caliper and a steel rule was used to measure parameters of the specimen and the mass was theoretically calculated. Therefore, a comparison was drawn between the spring balance and the Vernier caliper and steel rule. After calculation, by comparing the result from the two tables, the relative errors from the mass calculated 6|Page using the Vernier caliper were less than those of the mass balance system. So for measuring mass, using Vernier caliper and steel rule provide better accuracy than the mass balance system used. Measuring the parameters before calculating the volume then mass gives better accuracy because the limits of accuracy of the measuring instruments (Vernier caliper and steel rule) are very small which give better precision that result in less error. Despite the precisions, the results varied slightly due to the fact that the calculated mass of the specimen used densities of common material and not the densities of the specific material in which the specimens were made of. From the reviewing the result from only the spring balance, a relationship is evident in the result as the limit accuracy varies with the mass. The lightest specimen (Aluminum) seems to possess the largest relative error with 2.855%. It is then followed by the second lightest which is small steel cylinder with 2.218. The most accurate value in the comparison is the heaviest (largest steel cylinder = 0.618%) Summary Every physical thing has mass which in simple definition is the amount of matter present in a body. Three instruments were used to measure mass which is the spring balance, Vernier caliper and the steel ruler. The spring balanced was used to measure the experimental mass. The theoretical mass was calculated using the product of density and volume after measuring the parameters of the specimen. Using both method of measuring mass as stated above, the results showed closed approximation. We were able to determine the mass of the non-standard specimen. The close approximation was represented by using accuracy limits and errors. The spring balance had seemingly high errors compared to the theoretically calculated errors meaning a precise measurement could not be obtained. Therefore, in every calculation the approximated value of the measurement is paired with the errors to give at least a limits of precision in the final measurement. Overall the experiment was successfully, we were able to obtain all our results, however there were some errors made during the experiments which were mentioned in our discussion. Every experiment carried out, there were always errors made, therefore we took extra precautions when carrying out experiment in order to obtain best results and to avoid errors. Apart from the errors and the results discussed, the procedure were explained in simple English which is self-explained and can be understood. All the results were tabulated on the table above, and also the formula was provided. All the other necessary calculation was also done and tabulated on the table above. All in all, the lab was a success but the quality of the results was hindered by the state of the measuring instrument specifically the spring balance. 7|Page Bibliography ο· ο· https://en.wikipedia.org/wiki/Spring_scale https://www.google.com/search?client=opera&q=density+of+mild+steel&sourceid=opera&ie=U TF-8&oe=UTF-8 Appendices Densities used: ο· ο· Mild Steel = 7850 kg/m3 Aluminium Alloy 1100-H14 (99% Al) = 2710 kg/m3 8|Page