PHY 113 LAB MEASUREMENT OF A TABLE WORKSHEET Name: Kimani Partners: Mattew ? Sebastian E Jordan TA: Parva Barbhaya Lab Title: Measurements of a Table Objective: What physics concepts/theory/laws were being investigated in this lab? What physical quantities were measured? Was the theory verified by your experimental results? Answer in two to three sentences. To practice the concepts of significant figures, mean value, standard deviation of the mean, and normal distribution by making multiple measurements of the length and width of a table; to find the area of the laboratory table using wooden rod and then metric ruler To practice the propagation of errors by determining the uncertainty in the measurement if Experimental Data: Record the estimated mean values and standard deviations you found in your experiment using the wooden sticks Mean Value Standard Deviation # of Measurements (N) Length (cm) 185 30 Width (cm) 4 30 Record the measured mean values and standard deviations you found in your experiment using the meter stick. Measured Value Standard Deviation # of Measurements (N) Length (cm) 182. 7 0. ) 30 Width (cm) 75 . 8 0. ) 30Record the number of measurements within 1 and 2 standard deviations from the mean for both length and width. % within to % within +20 Length (cm) 10 % 100 % Width (cm) 83% 100 % Data Analysis: Using the formula for the standard deviation of the mean, find the uncertainty in the length and width of the table from your wooden stick method data set. Wooden Stick Data Set Uncertainty/Error AL (cm) 1. 278 30 AW (cm) O. 730 Now record the uncertainty in the length and width for the meter stick measurements. Remember this uncertainty is determined based on the smallest readable increment on your measurement device. Watch out for units. Meter Stick Data Uncertainty/Error AL (cm) 0 . 1 AW (cm) O.1 Multiply the average values of the length and width from the wooden stick data to find your estimated area for the table: 14060 CM Multiply the measured values of the length and width from the meter stick data to find your calculated area for the table: Atheor = 13848.66 Cm2Now, using the rules of error propagation, find the uncertainty in both the estimated area and calculated area. Show your work: Estimated: 185 + 1.278 185 + 0. 691% 76 + 0. 730 76 + 0. 761% 1. 5 52 1 of 14060 Measured : = 232. 27 182.7 + 0.1 75.8 + 0.1 182.7 + 0.055). 75.8 + 0.13% . 185% .8 13848-6 AAest = 232 cm 2 = 25 - 62 AAcalc = 25.62 cm Results: Report your values for both the estimated area and calculated area with their uncertainties. Aest + AAest = 14060 + 232 cm2 Acalc + AAcalc = 13848.66 + 25.62 cm' Do these two values "agree" with each other? Look at the overlap of their uncertainties if there is any. What does it mean for there to be overlap? Is this sufficient to say they agree? Or is there some amount of confidence with which you can then say they agree based on how much overlap there is? Address these questions in your discussion to the best of your ability.Discussion and Conclusion: Discussion must include: A paragraph stating the experimental results A paragraph discussing how well the two different measuring methods agree with each other. Making sure to answer all the questions at the bottom of the previous page. Discuss if and why the wooden stick method can work so well. You may not know the probability theory behind it ('central limit theorem' for the curious), but should be able to make an intuitive argument. Paragraphs should be short, 2-4 sentences