Unit 1 Lab Report

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Yagmurov 1 Roman Yagmurov Prof. Tuero Phy2048L 1/28/2024 Unit 1: Measurement Lab Report Abstract: I measured the dimensions of a book that I had and of my room, after which I then calculated the mean, standard deviation, and relative error of my measurements of the book. I also used the mean data to calculate the volume of my book. I then calculated the volume of the room as well. Furthermore, interested in finding the weight of the air occupying my room, I decided to calculate it. After looking through various sources online, as well as my Physics textbook, I found that the density of air is 1.29 kg/m^3. This would be important as it would allow me to find the mass of the air in my room without actually having to weigh the air (I don’t think that’s possible yet with our technology). With this information in hand, I then calculated the weight of the air, which is just the measure of the force of gravity acting on it.

Yagmurov 2 Introduction: In this lab, I will be measuring the dimensions of certain objects, calculating statistical values regarding those dimensions, as well as finding the weight of air that is in my room. For this, it is important to know that volume is the measure of the amount of stuff that can fit into an object, that density is a constant ratio for an object, and that there will always be inaccuracies in measurement due to human error or uncalibrated equipment. I will be measuring everything with either a 32-cm ruler or a meter stick. General Principles: In this lab, I am measuring the dimensions of a book and the room that I am in, as well as finding the volumes of those two objects. Along with finding the dimensions, another goal of this lab is to find the mean, standard deviation, and relative error of the data. The mean is just the average of the data, and it helps see what the true value of the measurement may be. The standard deviation shows how off the measurements are from the mean, which can be used to see if the measuring methods or equipment is sub-par. The relative error is the ratio of the standard deviation to the mean, which is useful to see inefficiencies in experimentation. Since we are calculating volume of different objects in this lab, it is important to conceptualize what volume is. Volume is the physical measure of how much stuff can fit into an object based on its dimensions. Usually, to find out volume, you can either use water and a measuring cup or measure the object and do mathematical calculations, which is what I am using in this lab. Since I am measuring the volume of mostly rectangular shapes (a book and a flat-ceiling room), I will simply multiply the dimensions that I measure out. Furthermore, since the next part of the lab requires me to find out the weight of the air in the room that I will measure, I will need to use the concepts of density and weight. Density is a set ratio of a material/object that compares its mass to its volume; it is always constant for a material/object but almost all things have different densities. Weight is the measure of an object’s mass under the effect of gravity. In other words,

Yagmurov 3 weight is just mass multiplied by the acceleration due to gravity. In this lab, density will be useful as I can’t directly measure the mass of air, but I can calculate it by multiplying its density by the volume of the room it occupies. With the found mass, I can then simply calculate the weight of the air by multiplying the mass by the acceleration due to gravity on Earth. Methods: I measured the book with a ruler and recorded the findings, after which I utilized the formulas to find the numbers I needed. To measure the room, I used a meter stick and my height as an approximation to the height of the room, after which I used the necessary formulas and numbers to calculate the weight of the air. Results: In this lab, I had to measure the thickness, length, and width of a book. Here are the results: Measurement (cm) Width Length Thickness Trial 1 16 23.15 2.85 Trial 2 16.05 23.15 2.83 Trial 3 16.05 23.1 2.84 Trial 4 16.03 23.13 2.83 Trial 5 16.05 23.15 2.86 Trial 6 16 23.14 2.83 Trial 7 16.1 23.09 2.84 The mean values for each were calculated with the formula M = 1 N ∑ i N M i where N is the number of trials. The deviations of each value were calculated with d i = M i − M . The standard deviation was found using σ i = √ 1 N √ ∑ i N | d i | 2 . The relative error of the data set was found using ε L = σ i L . Here are the results:

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Yagmurov 4 Mean(cm) Width 16.04 Length 23.13 Thickness 2.84 Standard Deviatio Width 0 Length 0 Thickness 0 Relative Error Width 0 Length 0 Thickness 0 Volume of book was calculated simply with V = L ∗ W ∗ T = 16.04 ∗ 23.13 ∗ 2.84 = 1053.65 c m 3 The second part of the lab was to calculate the weight of the air in my room. To start, I measured the dimensions of the room and estimated the height, which I recorded: Measurement (m) Width 3, 1 Length 3, 0.5 Height 2.5, 2 The reason I have two sets of measurements is because my room has a little addition to it. I found the volume for the two sections the same way I did for the book, and then I added the two values together to get the total volume of 23.5 m^3. After searching the web, I found out that the density of dry, pure air is 1.29 kg/m^3. Using this density, we can multiply the density by the volume to get the mass of the air which is 30.4 kg. Now, I can multiply the mass by the acceleration due to gravity, g, which is 9.81 m/s^2 to get the total weight of the air in my room, which is equal to 297.8 Newtons. Conclusion: After doing all of the measurements and calculations, it can be said that even something as simple as measuring can be a difficult task depending on how accurate either the equipment or the person doing the measurements are. In this lab, I found out that my room is 23.5 meters cubed and that the density of air is 1.29 kg/m^3. I also found out that doing statistical calculations regarding data can be a repetitive and mind-numbing task. Overall, I

Yagmurov 5 learned that to have the most precision, it is best to take the mean of multiple measurements rather than just a singular measurement.

Yagmurov 6 References American Meteorological Society. Density of Air . 26 June 2017. Web-site. 29 January 2024. Moebs, William, Samuel J. Ling and Jeff Sanny. University Physics Volume 1 . 2016.

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