Lab Report 1 (PHYS 1570) (2)

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Jan 9, 2024

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1 Lab 1: Density 5 September 2023 Tyler Aligo Physics 1570-05

2 Contents Objective ........................................................................................................................................................ 3 Synopsis ......................................................................................................................................................... 3 Calculation ..................................................................................................................................................... 4 Conclusion ...................................................................................................................................................... 6 Appendix ........................................................................................................................................................ 7

3 Objective This lab focused on the use of a balance and ruler to measure a metal block's mass, size, and density. We may identify errors and distinguish between an actual value and an accomplished value by taking measurements. The final density estimate can then be used to establish the composition of our initial block. The focus of this lab will be on a few significant aspects. First, it will be learning the meaning of measurement uncertainty error. Next, we will learn how to determine the greatest possible error and propagational uncertainty. The main goal of this lab will be to find the density of the block and what metal the block represents. Synopsis I. Understanding and identifying the block's error is key to the experiment's theory. Having the ability to differentiate between a calculated value and a true value. We employ the volume with the equation: V= L*W*D L represents the length; W is the width and D represents the Depth. The mass density of the block can be found with the equation defined as mass per unit volume: 𝑃 = ? ? M represents the mass of the sample while V represents the volume calculated from the previous equation. We were able to verify the correctness of our calculated values and draw a conclusion thanks to the notion of error analysis. In order to complete the assignment, you need to use a ruler. A ruler often has small notches spaced 1 millimeter apart, bigger notches indicating the 5-millimeter point, and numerical notches indicating each centimeter point (1cm – 10mm).

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4 II. The discrepancy between a measured quantity and its time value is known as (measurement error). Systemic, random, and statistical errors are the root causes of the error. Depending on the measurement being utilized, a (great possible error) is specified as one-half of the measuring unit. The impact of a variable's uncertainty on the uncertainty of a function depending on it is known as (propagational uncertainty). To find the volume of the block we must find the average of the four measurements we took including the length, width, depth, and mass. To find the average we add all four measurements and divide it by the number of measurements we took. III. The percentage difference in this laboratory assessment involves comparing the established or accurate density value with the density value derived from collected data. By making this comparison, we can ascertain the percentage of error, which is a gauge of our experiment's precision. The term "known" signifies our established or true value, while "experiment" represents the value we've measured. It's worth noting that the disparity between the known and experimental values is always positive due to the use of absolute values. Consequently, a higher percentage difference corresponds to a larger margin of error, while a lower percentage reflects fewer errors. This process aids in evaluating the overall accuracy of an experiment or its results. Calculation I. Once the averages have been determined, we insert them into the previously mentioned volume equation. To determine the density of our brass and copper cylinders, our initial step involves calculating the volume of each using Equation (2), followed by the density

5 calculation using the relevant equation. The following section outlines the step-by-step calculations used to obtain the average values. Length : 5.4 cm + 5.3 cm + 5.2 cm + 5.4 cm = (21.3cm) 21.3/4= 5.3 cm Average Width : 4.2 cm + 4.2 cm + 4.2 cm + 4.2mcm = (16.8 cm) 16.8/4= 4.2 cm Average Depth : 2.3 cm + 2.3 cm + 2.3 cm + 2.3 cm = (9.2 cm) 9.2/4= 2.3 cm Average Mass : 141g + 141.2g + 141g + 141g = (564.2 cm) 564.2/4 = 141g Average Volume: V= (5.3 cm) (4.2 cm) (2.3 cm) = 51.198cm^3 II. After finding the volume we can then find P. To find measurement P we use the average mass discovered (141g) and divide it by volume (51.198cm^3) as shown below: P = 141.05 g/ 51.198cm^3 = 2.75 g/cm^3 Then we plug answer P into the equation: 𝜌 = 𝜌 ⋅ √ ( ∆? ?(𝑎𝑣𝑔) ) 2 + ( ∆? ?(𝑎𝑣𝑔) ) 2 + ( ∆𝐷 𝐷(𝑎𝑣𝑔) ) 2 + ( ∆? ?(𝑎𝑣𝑔) ) 2 𝜌 = 𝜌 ⋅ √ ( . 05 5.3𝑐𝑚 ) 2 + ( . 05 4.2𝑐𝑚 ) 2 + ( . 05 2.3𝑐𝑚 ) 2 + ( . 05 141𝑔 ) 2

6 𝜌 = 𝜌 ⋅ √(0.0094) 2 + (0.012) 2 + (0.022) 2 + (0.00035) 2 𝜌 = 𝜌 ⋅ √(0.000088) + (0.00014) + (0.00048) + (0.00000012) 𝜌 = 2.75 ⋅ √0.000708 𝜌 = (2.75)(0.026) = 0.071𝑔/𝑐𝑚 3 Density: = 2.75 ± 0.071𝑔/𝑐𝑚 3 Metal : Aluminum (2.70 𝑔/𝑐𝑚 3 ) % Difference: ( 2.75−2.70 2.70 ) ⋅ 100 = 1.8% Conclusion All in all, we arranged our measurements into a chart that we could insert into various calculations. Using a ruler and balance, we measured the block to get our measurements. After compiling our calculations, we used the volume, P, and density formulae to arrive at our final density of 2.75 g/cm3, with a 0.071. Additionally, we observed that one of the elements indicated in the charts that our density did match was aluminum, which had a density of 2.70 g/cm3. We concluded that even if the difference would not have been significant and our value was within the region of the correct measurement, it could have been the result of human error. To put it another way, our percentage inaccuracy reflected any potential errors in our readings of the ruler or scale, as well as the precision of the scale being employed. We reasoned that by utilizing this method, we could also discern between different materials, compare measurement errors that don't match up, and demonstrate the possibility that the fractional error equation may be utilized to infer the metal using the equations' results for density.

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7 Appendix Length (cm) Width (cm) Depth (cm) Mass (g) 1 5.4cm 4.2cm 2.3cm 141g 2 5.3cm 4.2cm 2.3cm 141.2g 3 5.2cm 4.2cm 2.3cm 141g 4 5.4cm 4.2cm 2.3cm 141g Average 5.3cm 4.2cm 2.3cm 141g Bibliography

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