This is an example report. Do not use it as your report and do not use the data from this report. 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 and TT (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 5 Periods (sec) 1 Period (sec) 1 8.88 1.776 2 8.84 1.768 3 8.90 1.780 4 8.66 1.732 5 8.69 1.738 6 8.65 1.730 7 8.75 1.750 8 8.66 1.732 9 8.71 1.742 10 8.66 1.732 1 Period Avg 1.748 sec 1 Period Std Dev. 0.0196 sec 1 period SDOM 0.0062 sec The 1 period column is 1/5 of the 5 period column, so 58.88 s and therefore for measurement 1 1.776 s55TTT I calculated the average value of T and its standard deviation T using EXCEL. Tis given by 0.0196 s0.0062 s10TTN  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 1 For 40 grams, 58.6 cm 54.6 cm 4.0 cm.mxxx x  Note-I’ve listed the equation and one example for the calculated column x. Mass (g) xm (cm) x (cm) 40 54.6 4.0 60 52.5 6.1 80 50.2 8.4 100 47.8 10.8 120 45.4 13.2 140 42.7 15.9 160 40.4 18.2 200 35.7 22.9 220 33.4 25.2 240 30.9 27.7 260 28.5 30.1 280 26.0 32.6 300 23.5 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. 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) 8.3264 8.9804 Intercept, b (g) s (g/cm) 0.0318 0.6901 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 and therefore kskgsg k = (980 cm/s2)(8.3264 g/cm) = 8159.9 g/s2 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. M0, Mass vs Spring Elongationy = 8.3264x + 8.98040501001502002503003500 5 10 15 20 25 30 35 40Elongation (cm)Suspended Mass (gDataLinear (Data)This is an example report. Do not use it as your report and do not use the data from this report. 22gskkgs Since g = 0, 220ssksgs gs gss    therefore k =gs 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