The Determination of Material Density

Goal: To determine the density of a solid body of known geometrical form and to estimate the errors of measurments. Aparatus: a solid body made for indentification of a material, balance, vernier calliper, micrometer. The main formulae: The density of a homogenous body ρ is numerically equal to the mass of unit volume: In this work the density of cylinder form body (1 Lt value coin) is determined. The volume is expressed by formulae: The dimensions of body are measured by micrometer. The mass is determined by balance. Procedure: 1. The dimensions of given solid body are measured. Each dimension is measured 5 times and the data written in the table. The measurements are taken by micrometer so the hundreth fractions of millimeter should be taken. 2. The mass of the body is determined by the use of balance m, m = 6.1 g 3. We calculate the arithmetical means of direct measurments of the body dimensions and, according to the formula calculate the average volume value . 4. The average value if searching body density is calculated by substituting the obtained numerical magnitudes into formula (1). 5. Errors of direct and indirect measuremens are estimated. N D, mm , mm ,mm , mm2 ,mm D,mm 1 22.27 22.272 0.002 4 x 10-6 5.83x10-3 16.21x10-3 0.016 α = 0.95 2 22.26 -0.012 144 x 10-6 3 22.26 -0.012 144 x 10-6 4 22.28 0.008 64 x 10-6 5 22.29 0,018 324 x 10-6 N h, mm , mm ,mm ,mm2 , mm Dh,mm 1 2.10 2.108 -0.008 64 x 10-6 3.74x 10-3 10.397x10-3 0.010 α = 0.95 2 2.11 0.002 4 x 10-6 3 2.12 0.012 144x 10-6 4 2.10 -0.008 64 x 10-6 5 2.11 0.002 4x 10-6 m, g Dm , g α m ± Dm 6.1 0.1 0.99 (6.1 ± 0.1)g 0.67 0.95 (6.1 ± 0.67)g The mass of the body is measured only once becouse the error of the balance is much bigger than the random one. The errors are calculated according to the formula assuming =0,95. Taking partial derivatives , and using formula (12) we arrive at Claculations: , kg , = 99.29 Result: , , Given body‘s density cannot be determined (in the table there is no suck value that would fit in the errors interval) so I can make assumtion that this body is made from alloy. (from wikipedia.org I know that 1 litas coin is made of 25% nickel and 75% copper alloy) Conclusion: 1. After doing all the calculations and measurments we determined the density of the body. 2. Because we cannot measure density in the direct way we have to calculate the error of indirect measurment( ). 3. The errors occured because: a)The edge of the coin is slightly higher then the coins main body. b)The coin may have had some form deformations because of the deprecation. c)Diffrent air temperatures in the room and air currents. Used literature: “Laboratory works in Physics“. - Vilnius.: „Technika“. 1999 m. 19-23 p.

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