UMass Amherst PHYSICS 132 - Physics 132 Lab 1 (4 pages)

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Physics 132 Lab 1



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Physics 132 Lab 1

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4
School:
University of Massachusetts Amherst
Course:
Physics 132 - Intro Physics II
Intro Physics II Documents
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Phys 132 99 Volume of the Library Part 1 Experimental design 1 Methods Length and Width To measure the length and width we each measured the size of our feet and walked heel to toe along one section of the repeating cement square pattern We then multiplied this measurement by how many repetitions of this pattern we saw along two intersecting sides of the library Height To find the height we measured the height of each stair and counted how many stairs were between the first and second floors We then multiplied the number of stairs by the height of each stair We also assumed there was about 1 meter of extra space between the floors and ceilings of each floor Since there are 30 floors we multiplied the distance between the first and second floor by 30 This measurement is made under the assumption that each stair is the same height and each floor is the same height 2 Calculations Team member Length m Width m Height m Volume m 3 error Victoria 36 6 32 94 97 5 117 546 5 25 05 Zoe 33 46 33 46 93 75 104 960 11 66 Julia 37 13 33 41 93 75 116 298 1 23 72 Eliza 31 14 28 02 93 81 146 5 13 67 Part II Statistical Analysis 1 The mean and standard deviation for each of the three measurements Value Length m Width m Height m Mean 34 58 31 96 94 5 Standard deviation 2 43 2 28 1 76 2 The volume calculated from the means was 104 439 m 3 We think the uncertainty in this volume is 2 000 m 3 because each of our measurements varies by a few meters from one another and sometimes more Physical simulation of the Monte Carlo Method Draw Length m Width m Height m Volume m 3 1 37 13 33 41 93 115 368 2 33 46 33 41 93 75 104 803 3 36 6 33 46 93 75 114 810 4 37 14 33 46 97 5 121 164 5 36 6 32 94 93 75 113 025 6 37 13 33 41 93 75 116 298 7 33 46 33 46 93 104 120 8 33 46 33 46 93 75 104 960 9 37 13 28 02 97 5 101 437 10 37 13 28 02 97 5 101 437 Mean 35 92 32 31 94 73 109 742 1 What is the average and standard deviation for the volumes you have calculated using this method Average 109 742 m 3 Standard Deviation 7 137 2 Calculate the percent error on each of the three dimensions Percent error Length m Width m Height 3 89 1 08 024 3 Based on our calculated values for percent error the length will have the greatest impact on the uncertainty of the volume because it has the highest percent error of the three dimensions When random values of length are chosen the average is 3 89 greater than the expected which was our average This value varies the most of our values according to the random test Computer Simulation of the Monte Carlo Method 4 The rand or void function returns a random number in the range of 0 to RAND MAX RAND MAX is a constant in which the value is usually 32767 5 The NORMINV function calculates the inverse of the Cumulative Normal Distribution Function for a supplied value of x and a supplied distribution mean standard deviation Using a Computer to do the Monte Carlo Method 6 The mean of the volume is 104 249 m 3 and the standard deviation of the volume is 10 418 7 Our estimate was too low The uncertainty or standard deviation is over 10 418 8 The percent error of the volume calculated from the monte carlo test and the volume calculated from our average is 0 1 This value is closer to the product of all of the percent errors rather than the sum 9 Looking at percent errors is important because percent error gives us an idea of how accurate the random test calculates mean compared to the mean we calculated from our measurements 10 We think the volume we calculated will be higher than the actual volume because most of us measured the length to be greater than the width and I think they may actually be equal Also our measurements of height were based off of assumptions 11 Our measurements were not tight to the exact dimensions of the building but instead the boundaries just beyond the fence around the building We would ve gotten a closer measurement if our steps lined the exact edge of the walls of the building While most of our measurements were off by a few meters some of them were very close to the exact dimensions of the library length and width 12 The standard deviation from our Monte Carlo simulation was 10 564 Our average measured volume was 109 742 m 3 The actual volume of the library is 94 000 m 3 Our average volume measurement was off by 1 5 standard deviations 13 We individually measured the length width and height after agreeing upon a method It would have been more beneficial to us to communicate while we were measuring as well to ensure our values were in the same range We definitely could have measured the dimensions differently and more effectively For example we could have used satellite images of the library and referenced them with our own measurements and tally of cement squares and bricks surrounding the library Our height measurement also involved many assumptions which may have not been true If we wanted to walk from floor to floor and measure each floor that would have been far more accurate than applying the measurements of 1 floor to all of the floors


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