OL-02 Density Measurement - Take data from video of experiment (1)

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OL-02 Density Measurement - Take data from video of experiment Bryant Hurtado Phys-2125 Physics Lab-1 September 7, 2022 1

TABLE OF CONTENTS Objective 3 Theory and Equations 4 Equipment 5 Procedure 3 Data and Observations 5 Results 8-10 Conclusions 13 2

OBJECTIVES In this laboratory experiment, the following objectives will be achieved: (i) Determination of densities of three metal cylinders, a rectangular solid, an irregular shaped solid, and a copper wire, by finding their volumes and masses. (ii) Identifying the materials by comparison of densities with the accepted values. EQUIPMENT 1. Triple- beam balance 2. Vernier Caliper 3. Micrometer 4. Electronic Balance 5. A ruler (inches and centimeters) 6. Graduated Cylinder 7. A roll of copper wire. 8. Wire Cutter 9. Irregular object (lead, zinc, etc.) 10. Three cylindrical metals (brass, iron, aluminum, steel, tin, zinc, etc.) and copper wire. INTRODUCTION: Physics is a science of measurement that involves measurements of various parameters. Therefore, we need to learn how to take accurate measurements and how to use these numbers for calculations. In any measurement the uncertainty associated with it and the number of significant figures should be of particular interest to the experimenter. It should be underlined that the number of significant figures to be kept in a reading depends on the measuring device used. In this experiment the dimensions of various objects will be determined by means of a meter ruler, a Vernier caliper, and a micrometer caliper and the probable error in these measurements will be determined. The mass of each object will be measured with a triple beam balance (or electronic balance if available) and the density of each object as well as the material from which it is made will be determined. Density is the measurement of the compactness of matter in a substance. This might be done experimentally by measuring the mass and obtaining the volume of the substance. The volume may be obtained depending on the shape of the substance. For example, if the substance is cylindrical in shape then its volume can be computed from the equation V = πr 2 h , where h is the height or length of the substance. If the material is shaped like a sphere, the density is 3

calculated from the equation volume V = 4/3 π r 3 (where r is the radius of the sphere). For a rectangle, the volume is L x W x H (Length x Width x Height). In the case of an irregularly shaped object, its density may be determined by submerging object in water contained in a graduated cylinder. Usually, an object displaces its own volume of water hence the difference in the cylinder reading before and after the immersion gives the volume of the object. Density denoted by a Greek alphabet, ρ, is usually expressed in g/cm 3 or kg/m 3 , and sometimes in lb/ft 3 . Density is one of the useful quantities scientists use to identify different materials with. THEORY: Density (ρ): ρ = Mass ( m ) Volume ( V ) ( g / cm 3 ) Volume of Cylinder: V = π r 2 h ( cm 3 ) = π d 2 h 4 ( cm 3 ) Note: r = radius of cylinder, and h = height of cylinder Percent Error: ¿ Accepted value − Computed value ∨ ¿ Accepted value × 100 ( % ) % error = ¿ Standard Deviation (σ x ): X ∑ k = 1 N ( ¿¿ K − ´ X ) 2 N − 1 σ X = √ ¿ Uncertainty (δ): for aequation : A = X p Y q Z r ,then : δ A A = p δ X X + qδ Y Y + r δ Z Z Final Answer: ρ ±δ ρ ¿ ) or ( ρ±σ ρ ¿ In order to make precise measurements one needs to use accurate devices that will minimize the errors in our measurements: a) Triple-Beam Balance We use it to find the mass of each object. It consists of three beams along each one slides a weight. One beam has a notch every 100 g, the next one every 10 g and the last one every 1 g. Since this beam consists of 100 divisions equaling a mass of 10 g then this balance can read to 0.1 g and estimate to 0.05 g. 4

b) Vernier Caliper A Vernier caliper is a common tool used to measure the length of an object, the outer diameter (OD) of a round or cylindrical object, the inner diameter (ID) of a pipe, and the depth of a hole. The Vernier caliper is more precise than a metric ruler because it gives an accurate measurement to within 0.01cm. and can be used to estimate to 0.001 cm. Figure 1 The Vernier consists of a main scale engraved on a fixed ruler and an auxiliary Vernier scale engraved on a movable jaw. The movable auxiliary scale is free to slide along the length of the fixed ruler. The Least count is the smallest measurement that can be taken by a measuring instrument. The least count is obtained by: Smallest division on main scale/No. of divisions on Vernier scale. In this picture, the Vernier’s main scale is calibrated in centimeters with the smallest division in millimeters. The auxiliary (Vernier) scale has 10 divisions that cover the same distance as 9 divisions on the main scale. Therefore, the length of the auxiliary scale is 9.0 mm. The Least Count of a measuring instrument is the smallest change in the measured quantity that can be resolved on the instrument's scale. Least Count = smallest division on the main Scale / Number of divisions in the Vernier Scale. For our Vernier Calipers, this comes to 0.1 cm / 10 = 0.01 cm = 0.1 mm. Once the Vernier is positioned to make a reading, the jaws are closed on the object and we make a note of where the first mark on the auxiliary scale falls on the main scale. In Figure 2, we see that the object's length is between 1.2 cm and 1.3 cm because the first auxiliary mark is between these two values on the main scale. The last digit (tenths of a millimeter) is found by noting which line on the auxiliary scale coincides with a mark on the main scale. In our example, the last digit is 3 because the third auxiliary mark lines up with a mark on the main scale. Therefore, the length of the object is 1.23 cm. 5

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