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Lab name is Introduction to Analysis in Physics. The main goal of this lab is how to use LINEST within Excel to obtain a slope of a linear line and the uncertainty of the slope. You will find all the instructions on the file Analysis instruction-2It has two parts.Part 1 (Activity using Excel’s LINEST function, Page 1-4): You will verify the Columbus law by using the given data in the module. Data is given in the excel file named Columbus data.xlsx. Follow all the instruction steps given in the write-up instruction file. A video has been attached named analysis video. The video also clearly explains all the instructions. Watch the video to get a clear idea. Part 2 (Student Measurement and Analysis, Page 4-5): You will draw a circumference VS diameter plot by using 6 cylindrical items from your household items and you will perform LINEST. Page 5-8 is the appendix for LINEST and other excel help. Graph instructions are also given in the appendix. Perform all the work and submit it on the upload link. The total grade point for this lab is 20. 10 for part 1. and 10 for part 2. Follow the rules I have mentioned before in my 1st announcement. Step 5: known Y: D column/force values. known X: C column/ 1/r^2 values.Best fit line: follow step 8 for values.Step 9: When adding the best fit line in the plot, remember your x is 1/r^2, not the time. coulomb_fitting.pdf introduction_to_analysis_in_physics_physics_2.pdf coulombs_data.xlsx error_and_measurement_calculus_based.pdf Unformatted Attachment Preview This is the guidance for the fit fitting of both linear and power fit of data that was collected by a real actual apparatus that detects the interact and interacting force between two charged objects. >> And the objects were charged and the distance was varied to measure that Coulomb interaction between them at each distance. This is the data that I collected, the position or that you see here. >> This r is actually in separation between the, the two objects are just, theyre just spheres. >> And they are, they have been charged each approximately with the same amount of charge, at least as far as I can tell. >> And so what we wanna do is we want to look at the linear analysis and then look at a powerful. >> So here is R, which is the a column, and d is the fourth column. >> So we wanted to look at are squared, so that would just be a2 and then just the square of that, right? >> And then I copy the formula down. >> And then I want to look at one over R squared. >> And the reason I want to do that is because I want to plot force versus one over R squared. >> And thatll give me a linear relationship, or at least we hope it does. >> So this would just be one ove, well equals sign one divided by b two. And then, and then, and then copy the formula down and take a quick look. >> Lets plot f versus one over r-squared. >> Not R-squared, but one over r squared. >> And if you look at the equation in the write up, the slope should be Coulombs constant times the product of the two charges. >> Now we assume that each charge is the same, so it would just be Q squared. >> So if I want to insert and if you want to look at a recommended chart, I always choose XY and make sure here that you are plotting indeed the force versus one over R squared. >> And thats what we have here. So Im gonna go ahead and choose that one. Of course, I can. Do some editing. >> I can give it a chart title by adding chart elements appear, Axis Titles, error bars, legends, axis, just all kinds of different edits. >> So all you have to do is just click on the, the chart and then go to Add Chart Elements and then do your editing. >> But right now what we would like to do is perform a lioness on this. So Ill go down to the first output, a equals two and then here and be 13.99 to the nine, and that is my value of k. And then to run a line list, I highlighted a two by five matrix here, f of x. >> And here Im already on Linus, but its an under statistics, statistical. >> And I hit OK. >> My y values, of course, is the force and the x is the one over r squared. >> I do not want to force it to Z, i want to actual intercept, and that would be my slope. Of course, using that slope, you can now determine what Q is because youve got K, You got the slope. >> So you set k q squared equals to the slope and software Q. >> And to get all the other information, you hit shift control and then Enter. >> But before you do that, you need to highlight your appear in your, in your toolbar and then control shift enter. >> And here you have your intercept in B 14, your uncertainty in your slope, and a 15. >> And so in some cases in general physics lab, you, the slope is very meaningful. >> And the interests that the uncertainty is included in that result along with the units, of course. >> Alright, so thats doing a lioness. >> Now for your part, you can calculate little q and place that in your summary. >> And dont forget the units of charge, those of you that havent had any physics at all, or the unit of charge is a coulomb. >> So it could be a micro coulomb and nano Coulomb, Millie Coulomb, whatever little q would be right over here is the power fit. >> And so what Id want to do is plot f >> Versus r squared. >> So Im going to highlight this hit Control and get that one as well. >> And then insert the chard. >> And there you go. >> Now you would say, well, you know the inverse square law, which you saw in the universal gravitational force, one over R squared, the gravitational attraction between two masses. Here youre seeing it between two charges. >> Its an empirical model, but it seems to work. >> However, my eyes are the ones that measured those separations between those two charged particles. >> So it may not be ideal, but to check that, you simply click on the data here and run a trend line and it defaults to linear. >> But you can choose power and you can include the equation there. >> I mean, just to, just to illustrate that result that you do have. And if I increase the size, I can actually see it. >> And not quite a one over r squared at it, maybe one over R to the 1.3 or something like that. >> So theres a lot of, theres a lot of reasons why you may not get a one over r squared. >> Thats not too important right now. >> A few things, of course, are clearly the errors, random error in me reading exactly what that separation is for each one of those trials. And other reasons is Coulombs law is for charged particles assuming spherical symmetry, and they were indeed spheres. >> But again, how those separations were measured are critical. >> And so perhaps youll have a better time reading those separation that I did. >> Well, these are the little things that again, with Excel you can do. >> Again, click on the chart design here, and then you can label your chart different things and so forth. >> Well, I hope that at least thatll get you started. >> Be sure to ask your TA if theres any issues that you have. >> Okay. >> Take care. Introduction to Analysis in Physics Introduction In physics, you will often encounter linear systems. When analyzing linear equations, the slope generally contains useful physical information. Importantly, in many cases it may also be useful to know the uncertainty associated with the slope. A powerful tool within Excel helps us to obtain both. For statistical analysis of a large data array, visuals are often used to educate the reader as to what the analysis looks like for a large (repeated) set of measurements of a system. Excel contains a mechanism to analyze these systems as well. Lab Objective The student in this lab will learn how to use LINEST within Excel to obtain a slope of a linear line and the uncertainty of the slope. The student will also learn how to curve fit for nonlinear relationships. Activity using Excel’s LINEST function LINEST is a function within Excel which will perform a least-square fitting routine. The function will provide uncertainties for the determined slopes and y-intercepts. In this exercise, you will use data collected from two charged particles interacting with each other. Because they are charged, there exists a Coulomb force between them that varies with distance: 𝐹(𝑟) = 𝑘 𝑞1 𝑞2 𝑟𝑟 For our purposes, let us assume that both charges, 𝑞1 𝑞2 , are the same, Thus, their product simply gives us q2. In this exercise, we will determine the value of q. Note that r above is the distance between these two charges, and k is Coulomb’s constant. The Forces were measured using a calibrated force meter (you will interact with this as well in another module). The distance was varied. 1. Open up Excel. Label the A1 cell as “r (meters)”. Label B1 as r2 (meters2). Label C1 as 1/r2. Label D1 as Force (N). Finally, in cell A13, type k = and in cell B13 type 8.99E9. 2. The video associated with these steps can be opened anytime to outline the steps. 3. LINEST ANALYSIS: After the data is entered, shade a 2-column by 5-row matrix under the imputed data from A14 through B18. With the 2 x 5 matrix remaining shaded, click on the equation bar at the top and then click the fx function. [Note: At the end of this write-up is an appendix which gives the structure of LINEST output. Please refer to it. You may utilize the instructions of that appendix as well. 4. When a box appears, select a category. Chose STATISITICAL and then LINEST. 5. The following is the input (see appendix for LINEST output format): (a) Known_y’s: B3:B11 (You have just selected column B as your dependent variable.) (b) Known_x’s: A3:A11 (You have just selected column A as your independent variable. Note: time is always the independent variable) (c) Const: TRUE (You have selected that the line is in the form of y = mX + b.) (d) STATS: TRUE (You have instructed Excel to provide error estimates of the slope and intercept.) 6. Click OK. Make sure all of the cells are still highlighted. You should see a number in cell A14. This is your slope, which here represents kq2. Follow this next step very closely (your 2 x 5 matrix should still be highlighted). Highlight the entire equation in the equation box including the “equal” sign. Simultaneously press the Ctrl/Shift/keys and the immediately press Enter. More output should now be visible. The uncertainty of the slope is displayed in cell A15, and should be 0.011128. Cell B14 should be -0.05644. This is your y-intercept. Cell B15 should be the uncertainty in the y-intercept. Cell A16 is you R2, which should be very close to 1.00 when a potentially good fit is achieved. 7. Cell B16 is termed the variance in y. Cell A17 is termed the Fisher F–statistic, which is sometimes used to check for the integrity of the model chosen to fit the data. Here, we chose the linear model. To understand why it may be important to examine the error analysis using further statistical methods, let’s look at the output for the uncertainty of the slope and intercept. Note: Though our R2 value looks very close to 1.00, the uncertainties are a better way to determine the quality of the fit. Therefore, when doing analysis, we will extract these uncertainties whenever possible. 8. Next you will determine the best fit line. Label E1 as “Fit 1”. Click on the cell E2. In that cell, in the equation box, type =$A$14*C2+$B$14. Hit enter. Take a moment to understand this equation. (The dollar signs ($) surrounding the column heading denotes that the value within that particular cell is a constant). Now select cell C3 and click the small square in the bottom right corner of the cell and drag it down to C11. This will copy the formula from E3 to the rest of the E11. You may copy down the formula any way you wish. This is the short way. 9. Creating a Graph: (Refer to the video help in the module for graphing Coulomb’s Law.) Highlight cells for 1/r2 and force values. With the cells highlighted, go to Insert Chart. Chose scatter plot. You should see one (not two) set of data points plotted with force along the y-axis and 1/r2 along the x-axis. It should (very) linear. On your Tool Bar, make sure you are back at the Home position. To add a Best Fit, click on the Chart you just created and go to the Tool Bar up top and hit the Select Data button. [Note: You may see an option to first hit Design. This will then allow you to see the Select Data button.]. Once you have the select data button, hit it and you will see “add” series. Add the best fit data with it being the y-values (make sure all other items in that box is empty, and then just highlight the best fit data to appear in the y-list), and the x-values being the time. You can label the series as “Best fit”. Now hit OK. To then change the chart type by going back into Design mode and hitting Change Chart Type. For the Best fit, change that to scatter with straight line. Then click OK and you should see your data plotted with the Best fit line. Now, go back to the Design mode and in the left top corner, hit Add Chart Element. There, you can add titles for the axes and other editing. 10. Right-click on the tab name and re-name the tab as Linear. 11. Add a new tab and call it Power. Follow the steps in the video. Copy and paste column’s B and D into this new tab spreadsheet. Plot Force vs. r2 by inserting a chart. It should show the force decreasing with a power relationship. Click on the chart and right-click to add a trendline. Chose power and place the equation on the chart to see by what power the force varied. 12. Add a third tab and call it “summary”. In the summary, show your calculation of the charge q using the value of k and the slope. Don’t forget the units (Coulomb). Lastly, write a summary of your work. [Note: You are merely trying to establish good habits. Do your best to receive full credit.]. Save the file as you will do another activity below in a fourth tab. Student Measurement and Analysis Create a fourth tab in your spreadsheet. Name it pictures. In this section, the student will be able to perform some basic measurements and use LINEST to get a meaningful slope and uncertainty. The student needs six items that are cylindrical, but uniformly so such that they do not look like a cone. For example, a AA battery, a cylindrical drinking glass, and a coin are all good examples of this shape. The equation for circumference is 𝐶 = 2𝜋𝑟 = 𝜋𝑑. In the above equation, C is circumference, and d is diameter. Instructions 13. Take a picture of each item and paste them in the fourth tab. 14. Use a ruler and a tape measure which can easily wrap around an object. Measure the circumference and the diameter for each of your cylinder. 15. Make a fifth tab and call it measurement. Tabulate the diameter in column A and circumference in Column B. Plot and label your graph. Perform a LINEST on your data and report your slope and uncertainty. Make sure you label what your slope is and the uncertainty. Insert a textbox that summarizes your findings and especially report if your values are reasonable. Make a case for any error (no human error!!!). In other words, what reasons caused a less than perfect result? 16. Save the file and upload to Canvas. APENDIX: EXCEL HELP LINEST Instructions: 1. Before creating using Excel to create a LINEST matrix, your will need to have 2 columns of data each with the same number of cells. You should have established which column represents the y values and which represents the x value. This decision is important because it will determine what the relevant value that is being found from your slope. 2. To create your matrix, highlight a 2x5 selection of empty cells. Then go up to the formula bar at the top of the workbook and click the function button. This button should look like this: 𝑓𝑥 3. Select the LINEST function from the list of options, it will be listed under statistical functions. After selecting LINEST click OK. 4. In known y’s select the column that you have determined holds your y values. Only include the numerical values; don’t include any column headers or titles. Repeat this step for the x values, in the known x’s prompt. 5. In the Const opening type “true” to tell Excel to calculate the y intercept. In the Stats opening type “true” to tell Excel to calculate all 10 desired values in the matrix. When finished click OK. 6. Alternatively, if you feel more comfortable typing in the formula bar, you can type the equation directly. For example if your y values were in cells A1 through A15 and your x values were in cells B1 through B15 your formula would look like this: =LINEST(A1:A15,B1:B15,TRUE,TRUE) 7. Once you have the formula inserted, your slope value should now appear in the top left cell of your matrix. To make the rest of the values appear, select your 2x5 matrix again. Then highlight the entire formula in the formula bar and simultaneously press Ctrl + Shift + Enter. Then all of the values should appear. The values will appear in the following order: slope y-intercept Uncertainty in slope Uncertainty in y-intercept R2 value Standard error in y estimate F statistic Degrees of freedom Regression sum of squares Residual sum of squares The top four cells will be the most important for the work done in general physics labs, but you should still be aware of what the other cells are and what they tell you about your data. For example, the R2 value is an indicator of how well your data fits to the line, you want this value to be as close to 1 as possible. Insert Scatter Plot Instructions: 1. Once you have your data make sure you have all of your x values in one column and all of the corresponding y values in another column. 2. To create your scatter plot, go to the insert tab on the tool bar and choose a scatter plot. To do this click the icon that looks like two axis with points plotted (“Insert Scatter (X,Y) or Bubble Graph”) and select the first option (“Scatter”). 3. Once the graph area appears. Click the “Select Data” data button in the Design tab under Chart Tools. 4. Under “Legend Entries (Series)” click Add. Type an appropriate series name or you can leave it blank and the series name will default to series 1, series 2, etc. Then click inside the Series X Values text box and then highlight the column of x values. Do the same for the Y values. Make sure to delete the default “={1}” from the y value box before highlighting your y value column. Once all of your values are entered click okay. 5. Repeat step 4 for as many series as you needed. Once all your series are entered click okay. Your data should now appear on your graph. Insert Column Bar Graph Instructions: 1. Before you can make a column graph you need to have two columns of data, with the labels of categories (this can be numerical or qualitative) in the left-hand column and the numerical values for each category in the right-hand column. 2. Highlight your columns and go to the insert tab on the tool bar. Click the “Insert Column or Bar Graph” icon and select the first option (“Cluster Column”). The graph should appear on the sheet. Edit Graphs Instructions: 1. To edit titles: a. Double click on the default “Chart Title”. b. This should allow you to type in the chart title text box. Additionally, it should open the Format Selection Pane. c. You can the title’s color, font, style, etc. in the format pane by selecting chart title and clicking text options. 2. To add chart elements: a. Go to the design tab under the “Chart Tools”. b. Click on the “Add Chart Element” button on the far left of the toolbar. c. From there you can choose trendlines, axes titles, error bars and more. d. All of these chart elements can be further edited in the Format Selection pane. 3. To open Format Selection Pane: a. If the Format Selection pane is not open, click anywhere on the graph. Then go to the Format tab under “Chart tools”. b. Click the Format Selection button on the tool bar. c. The Format Selection pane should open and be set on whatever chart element you clicked on. d. To edit a different element, click on the small downward facing arrow next to the text “[Selected Element] Options” in the selection pane and choose any element to edit it. 4. To add Error Bars: a. With your chart selected, go to the Design Tab under “Chart Tools” in the toolbar. Click the “Add Chart Element” button and go to error bars. Click on the type of error bars you want. b. To edit the error bars, go to the Selection Format pane. To change the type or value of the error bars click on the third icon that looks like a small bar graph (“Error Bar Options”). c. The style, color, and other details of the error bars can also be changed in the Selection Pane. r (m) r^2 (m^2) 1/r^2 (1/m^2) 0.42 0.37 0.28 0.21 0.15 0.13 0.11 0.1 0.087 0.08 0.07 F (N) 25 29 41 80 136 181 242 297 360 412 484 Test your knowledge: Pick whether the below scenario is random or systematic 1. Measuring the length of an object using a caliper to the nearest hundredth of a millimeter. 2. Mis-calibrated current source meter. 3. An effect that was not thought of during the collection of data, but it biased the results. Test your knowledge: Place an X if it does not apply, and a Y if it does. ACCURACY ______ _______ _______ _______ PRECISION ______ _______ _______ _______ You make a bunch of measurements of the gravitational acceleration constant (close to Earth’s su ... Purchase answer to see full attachment