Physics Laboratory Report PHY 151 M0 Error Analysis This section is completed by the student Student Name Bugs Bunny Partner s Name s Daffy Duck Date Today TA name Tweety Bird This section is completed by the TA VI 1 20 Data table 5 Calculation of T and T 10 Final result 5 VI 2 50 Table 10 Plot 15 Slope intercept and slope intercept uncertainty 20 Final result 5 Report Grade TA Signature This is an example report Do not use it as your report and do not use the data from this report Comments in red are editorial in nature and intended to point out key aspects of the report They do not need to be included in your reports Please note that the actual assigned tasks in M0 are different from this report as it is intended only as a guide to show what your reports should look like Under no circumstances should you copy the data or the text contained here LAB REPORT FOR M0 EXPERIMENT ERROR ANALYSIS VI 1 In this experiment we measured 5 periods of a simple pendulum 10 times Measurement 1 2 3 4 5 6 7 8 9 10 1 Period Avg 1 Period Std Dev 1 period SDOM 5 Periods sec 8 88 8 84 8 90 8 66 8 69 8 65 8 75 8 66 8 71 8 66 1 748 0 0196 0 0062 1 Period sec 1 776 1 768 1 780 1 732 1 738 1 730 1 750 1 732 1 742 1 732 sec sec sec The 1 period column is 1 5 of the 5 period column so 5T 8 88 s T and therefore for measurement 1 T 1 776 s 5 5 I calculated the average value of T and its standard deviation T using EXCEL T is 0 0196 s given by T T 0 0062 s N 10 T 1 748 0 006 sec Note that the uncertainty is specified to one significant figure and that the smallest power of ten e g 8 x 10 3 or 008 is equal to the power of 10 of the uncertainty The intermediate step of calculating the duration of 1 period has an extra significant digit because it is an intermediate step to calculating the average period Placing a box around my answer removes any ambiguity about which digits are the answer and which are intermediate Reported answers are in the format x x Also note that the columns in the table and the calculated answer all have appropriate units You should include units on all tables graphs recorded data and calculated reported answers Calculations for average standard deviation need not be shown as these are output directly from Excel Other calculated values in the table have at least 1 example shown explicitly This is an example report Do not use it as your report and do not use the data from this report VI 2 In this experiment we measured the elongation x of a spring as function of the mass hanging from its end as shown in the table Although the meter stick can be read to a fraction of a mm the fact that the mass spring assembly moves so easily makes it difficult to read to that level of precision so we have chosen to read to the nearest mm x1 58 6 cm x x1 xm For 40 grams x 58 6 cm 54 6 cm 4 0 cm Note I ve listed the equation and one example for the calculated column x Mass g 40 60 80 100 120 140 160 200 220 240 260 280 300 xm cm 54 6 52 5 50 2 47 8 45 4 42 7 40 4 35 7 33 4 30 9 28 5 26 0 23 5 x cm 4 0 6 1 8 4 10 8 13 2 15 9 18 2 22 9 25 2 27 7 30 1 32 6 35 1 From my data I plotted the mass vs the elongation as shown using EXCEL It is expected that you will have the trend line and equation for all plots of data that are linear Non linear plots e g Malus Law in PHY152 and 257 do not require a trendline All plots should have properly labeled axes including units and an appropriate title This is an example report Do not use it as your report and do not use the data from this report M0 Mass vs Spring Elongation 350 y 8 3264x 8 9804 Suspended Mass g 300 250 200 150 100 Data 50 Linear Data 0 0 5 10 15 20 25 30 35 40 Elongation cm From the slope of the line s k g I can determine the spring constant k By using the least squares method in EXCEL LINEST I calculated the error in the slope as well Excel returned the following values Slope s g cm s g cm 8 3264 0 0318 8 9804 0 6901 Intercept b g b g Once again note that this is an intermediate step and I am not formally reporting this answer so I can carry a few extra significant figures They must be properly rounded when I report my answer The calculation to get the least squares fit LINEST need not be shown as this is an output directly from Excel s 8 33 0 03 g cm b 9 0 0 7 g k and therefore k gs g k 980 cm s2 8 3264 g cm 8159 9 g s2 s We chose the error analysis equation based on the form of the quantity we are trying to determine the uncertainty in You should practice doing this There are some worked examples in the prologue of your lab manual This is an example report Do not use it as your report and do not use the data from this report 2 k k g s Since g 0 g s 2 2 k gs 0 s gs s g s s s therefore k g s 2 k 980 cm s2 0 0318 g cm 31 2 g s2 k k 8160 30 g s2 Note the shown work Failure to show enough work for the TA to follow your calculations will result in lost points Any calculation that you show insufficient work for will get 0 points You should explicitly show the equation you are using to calculate a quantity whether it s a result or an uncertainty and you should show the numbers being used substituted into that equation The equations and calculations and only the equations calculations may be hand written All text tables reported answers etc must be typed Not typing these things will result in lost points Please note a few things about this sample report First each section required by the manual is headed by a Roman numeral to clearly identify where the work you did for credit is for grading purposes Second please note that all work is shown except results obtained directly from an Excel calculation We recommend using a word processor for your calculations but it …