PLEASE ANSWER ALL OF THE QUESTIONS and write the number to the question like Part 1 question 1., 2., etc

1 Uncertainty in Measurements 1.1 Manual In this laboratory activity you'll consider the precision and limitations of your measuring tools. You'll also work with your classmates to share measurements and calculate statistical confidence in a larger data set Materials Required . cell phone with stopwatch app (or equivalent stop watch device) . paper, bristol board, or similar cardboard of moderate weight (slightly thicker paper preferred) . 3 nickels . pencil or pen (ideally fine tipped) . can of soup (284mL) Part 1 - Limitations of a Stopwatch 1. Locate the stopwatch application on your cell phone (or an equivalent timing device). 2. Determine your stopwatch's maximum precision. (I.e. what's the smallest unit your stopwatch can show?) 3. Start your stopwatch and attempt to stop at exactly 10s. Record your results for 10 attempts in a table. (Be honest. This is about statistics more-so than landing on 10s exactly.) 4. Calculate the mean value of your data. Also calculate the standard deviation of your data. Recall that the mean value of /V measurements of x is given by: Nc Vka/ \\b/ 5. Calculate the percentage difference between your calculated volume your soup can and the "standard" volume provided by your TA. 6. Optional - Calculate the density of your soup can- (Assume the labeled mass of your can is accurate to :33.) Part 3 - Statistics on a Shared Data Set For this activity you'll upload your soup can dimensions and calculated volume to a shared spreadsheet. Your TA will provide a link to an editable google spreadsheet document (it will only be editable during your lab session). Comment on the consistency of the data set. {Are there any obvious outliers? Could there be different types of soup cans included? Single population or multiple populations?) 1. Calculate the mean and standard deviation of the volume data set, showing your calculation. 2. Use an automated tool {Matlab, Pythoanupyter. Excel or Google Sheet, other) to do a computed calculation of the mean and standard deviation. 3. Compare your manual and automatically calculated results. Report For this experiment a report is required. Try to keep your writing clear but concise. (Your report should be written in your own words. Copying the work of others is plagiarism. Plagiarism violates Policy 60, and can result in serious academic penalties.) 3. Using your ruler, record the diameter and height of your soup can. Include uncertainty in your measurement. In this instance, a reasonable estimate of uncertainty would likely be half of the smallest increment on your tool. (E.g. h = 6.4 + 0.3cm if your smallest increment was ~0.5 cm. If you added finer increment markings, your uncertainty might be smaller.) 4. Calculate the volume of your soup can. Include a calculation of the uncertainty in the volume. Recall that for simple measurements, in the case of addition or subtraction: (at Aa) + (b+ Ab) = c+ Ac and (at Aa) - (b+ Ab) = c+ Ac where Ac = VAa- + Ab2. In the case of multiplication or division: (at Aa)(b + Ab) = c Ac and (at a) = C+ Ac (b + Ab) where Ac Aa 2 Ab 2 + C a bRecall that the mean value of /V measurements of x is given by: H= N and the standard deviation of the measurements is given by: Z(X - H) 0 = N 5. Briefly describe your measurements, considering the accuracy and the precision of your data set. Describe what mean and standard deviation tell about data in general, and specifically about your time measurement data. Part 2 - Fabrication and Use of a Measuring Tool In this activity you'll construct your own ruler using a piece of paper and 3 nickels. Stacked together, 3 nickels provide a reference "standard" and will have a total thickness of 5.28 mm. (Even if you have a ruler, don't use it for this activity, though feel free to check your improvised ruler's accuracy after the activity is complete.) 1. Using your 3 stacked nickels, construct a ruler by making marks as closely as possible to every 5 mm. The ruler markings should cover at least 12 cm. If you think you can add even finer markings you're welcome to do so. 2. Photograph your ruler and include your photo with your report