Link for part B http://www-ed.fnal.gov/data/phy_sci/relativity/student/data/Will upvote for sure! Thanks

A. Predict decay length of a charmed meson (20 pts) 2. Now you will calculate the velocities for the rest of the ~900 momenta. In the Pivot table gth is the distance in the laboratory frame traveled by the charmed meson between editor, click on Add to the right of Rows and select Momentum; two new columns should now he time it is created and the time it decays. A meson half-life (the average time time it decays. The charmed meson half- appear - Momentum and Calculated Field - wiping out the previous entry in cell CI. Change the ring which it exists) is 4.0 x 10-13 seconds. heading name of the latter to Velocity and adjust the number of decimal places to 6 by clicking on the "" buttons above column C (the second Momentum column). Remem 1. Consider a charmed meson moving at a speed of 0.999c (99.9% the speed of light, well known value should be in units of c (for example, 0.998409c, meaning 99.8409% the speed of light). to be 5 x 10" mis). Ignoring Special Relativity and the effects of time dilation for now, what 3. Are all the values in the new calculated column close to the speed of light, but below it? (5 life? (10 pts) Remember from basic Kinematics how Distance, Velocity and Time are related. pts) If not, check your formula and modify as needed. If you find any values that are equ Show your work on the hand-in sheet and include units in your answer. the speed of light, it is because you did not choose enough decimal places (you chose 2 or lower) in your Velocity column. 2. Repeat the above calculation, this time using Special Relativity. (10 pts) Assume that the frame) and decays in a time equal to its charmed meson moves at a speed of 0.999c (in the lab frame) and decays 4. Generate a plot of Decay Length (Y-axis) vs. Velocity (X-axis) - first add the units (in half-life (in its rest frame). Note that the Decay Length will be a function of the dilated time in parentheses) to these headings (em and e) in the spreadsheet. Select both the Decay Length and the lab frame. Show your work on the hand-in sheet and include units in your answer. Velocity columns (Command-click on Mac, Control-click on Windows) then in the GS menu ba go to Insert-->Chart. Drag it to a convenient part of the spreadsheet. Double-click on the chart to B. Download data from Fermilab Experiment E687 and input to spreadsheet (20pts) You will acquire meson data from Fermilab of particles' Decay Length (how far they travel in the laboratory frame before they decay) vs. Momentum. You will then calculate the Velocity from the Momentum and generate a Decay Length vs. Velocity graph. 1. Launch a Web browser, and navigate to: bring up the Chart editor (CE); in the Setup tab select Scatter chart (Chart style) and choose the http:/www-ed.final.gov/data/phy_scifrelativity/student/data/ appropriate column for your Y (Series, in CE) and X (X-Axis, in CE) axes. You should see a f for some reason this Fermilab website is not responding, download the file fermilab_data.csv graph like this: from the course folder in the Files section (Lab 9) of the Canvas course page. This is a backup of the data. olativity 2. Briefly read the page. At the bottom of the page is a table describing the datasets you can in Chart editor You will be most interested in dataset 2 (momentum & decay length data). When you are ready, click on the "'s click on the "start the data server" link in the middle of the page. You should get a series of screen refreshes, starting with the one below: Fermi National Accelerator Laboratory Data Archive - Microsoft Internet Explorer -ox Decay Length (cm) vs. Velocity (c) Fle Edt New Favorites Tools Heb Back . . * 2 0 search Favorites Med. B. .DY Address http:/www-ed.final.gov/data/phy_soilrelativity/student/datalarch7 .htmil#banner Google . Fermilab Search Web Search Site News ( Page Info . up . Highlight Ofemmieb Welcome to the Fermi National Accelerator Laboratory Data Archive my examine the gray the flight of the Charmed Meson between the time it was produced and the time it decayed not obeyed Special Relativity, what characteristics of the should the trend of this graph have? Recall the non-relativistic n-relativistic calculation for Decay Length that generating datasets for Fermilab E687 did Section 1, Question 1, and qualitatively apply that the the dataset to arrive at your answer. (10 pts) 6. Note that the data from FNAL has some statistical variance, as with real experiments; there is a spread in the data as you have seen with previous Physics labs you may have completed - such After the refreshes are over, you will have a number of download options. Choose the browser as Intro to Experiment (reaction time number of decays from a option for Dataset 2 (file size 18K). This will display the data in HTML. form on your screen, in radioactive sample). Calculate the following values in your Google Sheets document and two columns, Momentum and Decay Length, in units of GeV/c and em respectively. take a screenshot of it for inclusion into your lab report: 3. Using your mouse, drag and select the numerical data (skip the headings) and Copy, either using Edit-->Copy or using your right mouse button. Go to Google Sheets (http://docs.google.com/spreadsheets) and press the large + to start a Blank spreadsheet. At the top, give your spreadsheet an appropriate name, select Edit-->Paste special-->Paste values only to transfer the Fermilab data. You should see the same two columns you saw on the FNAL website; click on the headings and enter the same units you saw on that website. 4. Look at the column containing the measured decay lengths (in cm) of the charmed mesons. Which of the two calculations you did in Part A above gives a result closer to the actual data? (5 pts) 5. Find an algebraic expression for the velocity v of a particle in terms of its relativistic momentum p and its rest mass me. (10 pts) To do this, you will need formula for the relativistic momentum in terms of velocity and rest mass, and then solve for Show your work and your final formula on the hand-in sheet. 6. Using the formula you found in Step 5, calculate the velocity of the charmed meson in the first row of your copied dataset. (5 pts) It should have momentum p = 21.53285 GeV/c. You will need to use the charmed meson's rest mass: 1.865 GeV/c. Instead of MKS units, you will now be working in units of GeVic (momentum) and GeV/c (mass) - you may notice that in your final expression for v the c's will cancel out if you write out the variables with significantly simplifying the calculations to find the Charmed meson's velocity from it momentum. The answer will therefore be given in units of c - the speed of light, c.g. In vacant cells either below or 0.996343c, and should have enough significant figures - otherwise your answer could be above the graph, insert formulas in cells (and name them in cells rounded to c. Write your answer in your lab report. adjacent to them, for: AVERAGE ( valued. [value2, -]) -Mean Decay Length, Min Decay Length, Max Decay AVERAGE ( 42:4100, B2:8100) Length Returns the -Mean Velocity, Min Velocity, Max Velocity O _ valuel The first value or range to co See example statistical formula valuez. - [optional] repeatable creation on the right. Additional values or ranges to consider when cal . Generate and Analyze a Decay Length vs. Velocity plot (60pts) Using the expression you derived in Part B, Step 5, you will have the spreadsheet do the Include a picture of your graph and the above values in your lab repetitive task of calculating the velocity of approximately 900 data points from their AVERAGE (82:890] 0.909 report. momentum. Minimum Decay Length Minimum 1. In Google Sheets, click on the CI cell, to create a new calculated column. Go to the menu and select Data-->Pivot Table. For the Data Range enter A1:B903, below that select Existing Sheet, Consider two different charmed mesons, one moving with the lowest velocity and the other moving with the highest velocity (according to your dataset). Assume each particle, in its rest and type "Sheetl!CI" in the line below that. You will not immediately see a Calculated Column, frame, decays in a time equal to the meson half-life. as you would've if you were using either LibreOffice, OpenOffice or MSWord; instead, you will see some cells in columns C & D labeled Columns/Rows/Values and a Pivot table editor on the 7. a. Which one - the slower or faster meson - would have a greater lifetime in the laboratory right. frame? Calculate the ratio of the faster meson's lifetime in the laboratory frame to the slower meson's lifetime in the laboratory frame. (5 pts) On the right, click on Values and select Calculated Field; starting with a "=", enter the formula (only the right side of the equation) from Part B.5 and make sure you enter the variable your b. Looking only at the Velocity, which one - the slower or faster meson - would have a greater otting exactly as it appears in the column heading. Also, in Summarize By, select Custom. You decay length? Calculate the ratio of the faster meson's decay length to the slower meson's decay should see you first calculated Velocity in cell CI; remember that the unit of this value is c length. (5 pts) hows an error or no result, make sure in your expression in your formula that p is replaced by Momentum and with me replaced by 1.865. Also, check that it 8. Based on question 1 above, you would expect a faster meson in the dataset to always have corresponds to the equation you wrote previously. If you are still having difficulty, see this table greater decay lengths than a slower meson. Is this supported in your plot? [Hint: consider the of a fix to a few common Co.. statistical analysis you did above] (10 pts) 9. Do a "Gedanken" experiment (a thought experiment; Einstein liked to do these): Imagine you Examples of entering a formula into Google Sheets (GS) are riding along on one of these charmed mesons during its lifetime. Will the dimensions of the Example Formula Correct GS Entry INCORRECT GS Entry laboratory change? Which dimension (in the direction of motion or perpendicular to the direction Momentum*2 "Momentum"*2 of motion), and how (stretched or contracted)? (10 pts) v - p' v = 2p + mo 2"Momentum + 1.865 10. If you are riding along one of the charmed mesons, will you see the lab people's clocks sqrt(Momentum*2 + 1.865~4) (Momentum*2 + 1.865-4)^1/2 running slower or faster? (10 pts) pz + my - OR - mentum"2 + 1.865-4) (1/2) *NOTE: To find out where Einstein and Lorentz erred about perceived length cont namelym that a camera or eye would not see the contraction, watch this 3min 15sec video: What is your value for Velocity in cell CI (which contains the first velocity point)? (5 pts) https:/www.youtube.com/watch?y=c8-12c404-0&1=400s