Assignment #1

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Physics 11000-1L11 Department of Physics and Astronomy Hunter College Laboratory Assignment #1 Density; Significant Figures I.D: 24242776 Aliyah Harrison Biological Science Date of Experiment: 02/06/2024 Time of Completion: 11:20am

Introduction : In laboratory assignment #1, “Density and Significant Figure”, we employed density equations to investigate how utilizing various instruments can lead to different measurements of identical objects. Initially, we assessed the density formula by estimating the mass (m) of air contained in the unoccupied lab room. We first estimated the volume by measuring the height, length and width of the room. Subsequently, we determined the volume first then the density of a metal block by utilizing a ruler, vernier calipers, micrometer calipers and an electronic balance to ascertain the height, length,width and mass. This lab experiment emphasized on accuracy, precision and significant figures. To evaluate accuracy, we computed the average value, while percent deviation was utilized to assess precision. Equipments and Methods: Meter stick, ruler, vernier calipers, micrometer calipers, electronic balance, metal block, lab room 1. A long meter stick along with the geometric tiles on the floor (“12 x 12”), were used to measure the height, length and width of the lab room. The volume of the room was determined to be 175.2m 3 and density was assumed to be 1.29 kg/m 3 , hence mass was calculated to be 226kg. 2. To determine the density of the metal block, it was first weighed on the electronic balance then the length, width and height of the block was measured with three different instruments: ruler, vernier calipers and micrometer calipers. Volume was determined using the readings from each instrument, then the density was calculated using these volumes and the weight of the metal block. 3. The gathered measurements and calculations from each instrument were analyzed then enabled us to assess the accuracy of each instrument and address the queries outlined in the data sheet. Additionally, we computed the percentage error for our findings. Safety Precautions: 1. Maintain a distance for peers while measuring the height of the room to prevent the meter stick falling and hitting anyone. 2. Be careful when using the metal block as it is heavy and can break stuffs or cause harm.

Data Collection: Part A: Volume, Density and Mass of Air Contained in the Lab Room. Table 1: Measurements of Lab Room. Lab Measurements Length 11.9m Width 6.4m Height 2.31m Table 2: Density and Mass or Air, Volume of Lab Room Density of Air Volume of the Lab Room Mass of Air 1.29kg/m 3 175.2m 3 226.kg Part B: Mass, Density and Volume of Metal Block. Table 3: Measurements of Metal Block. Mass (g) Length (cm) Width (cm) Volume (cm 3 ) Density (g/cm 3 ) Ruler 68.0 1.8 1.800 2.4 8.74 Vernier 68.0 1.800 1.800 2.365 8.88 Micrometer 68.0 1.8455 1.8455 2.4200 8.25

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Calculations: Figure 1: Calculation for Volume of Lab Room and Mass of Air.

Figure 2&3: Calculations for Volume and Density of the Metal Block.

Analysis: Equations: ( Delta L)^2 = (L_(meter ruler) - L_(avg))^2 + (L_(vernier) - L_(avg))^2 + (L_(micrometer) - L_(avg) ^2 Mass= D x V Density= M/V Volume= l x w x h

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Variables: (Delta L)^2 is average length l is height w is width h is height M is Mass D is Density V is volume m is meter cm is centimeter g is gram kg is kilogram Volume of room and Mass of air: We were tasked with determining the mass of the air in our laboratory room assuming it's empty. Initially, we measured the room's height, width, and length using a meter stick along with the tiles geometric to calculate its volume. Multiplying these dimensions yielded a volume of 175.2m^3. Next, we multiplied this volume by the given density of 1.29 kg/m^3 to obtain the estimated mass of air, which came out to be 226 kg, aligning with the precision of our data where the density had the fewest significant figures. Mass, Density and Volume of Metal Block: To determine the density of the metal block, it was first weighed on the electronic balance. Block had a mass of 68.0g. The length, width and height of the block was measured with three different instruments: ruler, vernier calipers and micrometer calipers. Length was 1.8cm, width was 1.8cm and height was 2.4cm using the ruler. Volume was computed to be 7.78cm^3 using formula l x w x h and density was 8.74 g/cm^3 using formula M/V. Length was 1.800cm, width was 1.800cm and height was 2.365cm using the vernier. Volume was computed to be 7.66cm^3 using formula l x w x h and density was 8.88 g/cm^3 using formula M/V. Length was 1.8455cm, width was 1.8455cm and height was 2.4200cm using the micrometer. Volume was computed to be 8.24cm^3 using formula l x w x h and density was 8.25 g/cm^3 using formula M/V.

Conclusion: Yes, the analysis of our data from the experiment verified the concepts. The measurements were more precise using the vernier and micrometer than the ruler. Micrometer provided the most accurate measurements. We can infer that employing increasingly precise measuring instruments yields more accurate measurements, evident from the data we collected from each instrument in the experiment. The micrometer demonstrates the highest precision, followed by the Vernier caliper, and the ruler offering the least accurate measurement. Despite the variations among the readings from the three instruments, their results closely align. The density calculations for the metal block, the derived densities are reasonably accurate, with a propagation error of 3.9%. This experiment validates the density theory, represented by D = m/V, showing that determining the mass and volume of any object facilitates density calculation. Acknowledgments : Lab experiments were carried out by me, no collaborator was involved in the completion of this lab. Appendix and References Dougla,Giancoli C.(2016). Physics: Principles with Applications.Pearson Prentice Hall. Department of Physics. (2024, Spring). Hunter College of the City University of New York. Retrieved from class website at https://www.hunter.cuny.edu/physics/courses/phys110-111-lab- online/repository/files/PHYS%20110%20lab%20man.pdf .

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