UMass Amherst PHYSICS 132 - Physics Lab 1 (2) (5 pages)

1 Describe your methods of measuring the dimensions of the library For both the length and width we measured the smaller squares outside of the library approx 60cm per square and counted how many squares it took to go from one side of the building to the other which ended up being a total of 55 squares for both width and length For the height we took the height of the 3rd floor library using the meter stick inside the library which was 248 cm and multiplied it by 26 floors Those were our methods of measuring the dimensions of the library 2 Calculate the volume of the library using the dimensions you measured and record them for the second part of this lab Trial Length m Width m Height m Volume m 3 Kyle 33 50 33 50 65 00 72946 25 Orrin 33 55 33 55 69 20 77891 69 Vicky 33 00 33 00 64 48 70218 72 Sam 33 20 33 20 66 00 72747 84 33 50m x 33 50m x 65m 72946 25m 3 33 55m x 33 55m x 69 20m 77891 69m 3 33m x 33m x 64 48m 70218 72m 3 33 2m x 33 2m x 66m 72747 84m 3 Representing your data 3 Calculate the mean and standard deviation of each of the three dimensions length width height using the four measurements taken by your table using the same method Mean length 33 3125m Standard deviation of length 0 2247m Mean width 33 3125 m Standard deviation of width 0 2247m Mean height 66 17 m Standard deviation of height 1 8327m 4 Calculate the volume of the library using the means for each dimension Just making a educated guess what do you think is the uncertainty in this volume What was the reasoning behind your guess 33 3125 m 33 3125 m 66 17 m 73430 348m3 There is uncertainty in this volume due to the height Our uncertainty estimate is about 10 000 m3 We estimate this uncertainty because it is hard to determine the height of the building since we don t know if all the floors are of the same height We also did not account for the fact that the basement and the 1st floor of the library are slightly bigger than floors 2 26 5 What is the average and standard deviation for the volumes you have calculated using this method Average 72818 4499m3 Standard Deviation 1854 054m3 6 Calculate the percent error on each of the three dimensions 72818 4499m3 98353m3 98353m3 x 100 25 96 error 72818 4499m3 73430 348m3 73430 348m3 100 0 83 7 the percent error which of the three dimensions will have the greatest impact on the uncertainty of the volume Justify your answer Out of the three dimensions the height would have the greatest impact on the uncertainty of the volume because the height is must greater than the length and width so it would be more likely to have a greater impact if the number was incorrect When we were measuring the height it was more likely that the height was off by a greater number compared to both width and length since we didnt account for the attic of the library basement and other unknown floors 8 What does rand do Feel free to use the internet to look up this function rand returns a random number that is greater than or equal to 0 and less than 1 9 What does NORMINV do To help you understand how this function works it may be helpful to adjust the values of the average and standard deviation Feel free to use the internet to look this up as well NORMINV calculates the inverse of the Cumulative Normal Distribution Function for a supplied value of x and a supplied distribution mean standard deviation 10 What is the mean and standard deviation of the volume of the library calculated using the spreadsheet Attach a copy of your spreadsheet to your lab report Mean 73378 232m3 Standard deviation 2087 563m3 11 Compare your uncertainty measured with this technique to the educated guess you made in question 4 Was your estimate of the uncertainty too high Too low Just right Our estimate of uncertainty was too low We expected to be off by about 10 000 m3 while in reality the difference was about 25 000 m3 12 Calculate the percent error on the volume and compare this value to the percent error of the dimensions Is the percent error equal to the sum of the percent error or the percent errors of each dimension multiplied together Percent error of volume 0 769 Percent error of length 0 0135 Percent error of width 0 0075 Percent error of length 0 064 sum of the errors 13 Why do you need to look at percent errors when comparing the volume with its other dimensions You need to look at other percent errors when comparing the volume with its other dimensions because it tells you how far the calculation is from the actual answer and lets you compare to the other dimensions and you would be able to tell which dimension is causing the percent error to increase or decrease 14 Make an educated guess on how your measured volume compares to the actual volume of the library Do you think it will be higher or lower Explain your reasoning We expect our educated guess to be much lower than the actual volume of the library We expected this because it was very difficult to come up with a method to measure the height We decided to measure one floor from inside the building but that number did not account for the much larger first floor and basement making our estimate lower than the actual volume 15 Evaluate your method of measuring the volume of the library What are the strengths and weaknesses of your method A strength of our method was being able to measure the outside of the library with the small square tiles as a reference The tiles outside were easy to measure and 55 tiles fit the outline of the library perfectly for both the width and the length So we don t believe that our calculations for the width and the length were too far off from the actual A strength for measuring the library was measuring a floor of the library because we know that the library has 26 floors so that was probably the best option in our case A weakness of our method when counting the width and length of the library would probably be not accounting for the bricks that make up the library or not considering that the library is not a perfect square rectangle Another weakness in our method for measuring the height of the library would be not taking the basement of the library into account and we only measured one floor of the library which could also be a weakness We also do not know if all the floors in the library are of the same height or if there are extra floors an attic 16 Ask your …