Pre-Lab Excel Problem Read and follow the instructions carefully! Below you are given a problem which you are to solve using Excel. If you have not used the Excel spreadsheet a limited tutorial is given in Appendix A. You are to hand in the enclosed worksheet with the attachments you are instructed to include. The Problem: An object is moving in a straight line with a constant acceleration. Its position, relative to a given coordinate system, at intervals of one second are measured. Data sets of the position as a function of time are given on the pages titled "Data Sets." The final digit of your PSU student ID number is the number of the data set which you will use. Using this information you are to determine the acceleration of the object via two methods. 1) Plot the position vs time, i.e. the position is plotted on the Y axis, and the time on the X axis. Insert a trendline in the graph curvefitting this data to a polynomial of degree two. You will obtain an equation of the form Y = N 1 X 2 + N 2 X + N 3, where N 1, N 2, and N 3 are numbers. Compare this to the theoretical relationship between the position and time, i.e.; 1 2 y at v0t y 0, and determine the acceleration "a". [note: y is the position at time t, v o is 2 velocity at t = 0, and y o is the position of the object at t = 0.] 2) Since this is a constant acceleration motion problem, and the initial velocity is zero, the velocity v at time t can be calculated from the equation v = 2y/t. For each value of t calculate the corresponding value of the velocity v. Plot velocity vs time and insert a linear trendline of this data in the graph. You will obtain an equation of the form Y = N 1 X + N 2. Compare this to the theoretical equation v = at + v 0 and determine the acceleration.
WORKSHEET (Fill in and attach this cover sheet to your work.) Name: Data set number: Attach an Excel printout with (see example spreadsheet #1) 1. Your Name 2. Your Data Set Number 3. Titled Columns of the Position and Time Data 4. Graph of Position vs Time Data with Trendline. 5. The acceleration of the object is Attach a second Excel printout with (see example spreadsheet #2) 1. Your Name 2. Your Data Set Number 3. Titled Columns of the Position and Time Data 4. Titled Column of the calculated velocity. 5. Graph of Velocity vs Time Data with Trendline. 6. The acceleration of the object is
DATA SETS Your data set number is the last digit of your PSU student ID number. DATA SET #1 DATA SET #2 DATA SET #3 TIME POSITION TIME POSITION TIME POSITION SECONDS METERS SECONDS METERS SECONDS METERS 0 0 0 0 0 0 1 0.51 1 0.8 1 1.55 2 2.2 2 4.1 2 5.8 3 4.3 3 9.2 3 13.7 4 7.8 4 15.7 4 24 5 12.5 5 24.8 5 37.4 6 18.1 6 35.8 6 53.8 7 24.3 7 49 7 73.7 8 32.2 8 63.7 8 96.1 9 40.6 9 80.8 9 122.1 10 49.3 10 100.4 10 149.7 DATA SET #4 DATA SET #5 DATA SET #6 TIME POSITION TIME POSITION TIME POSITION SECONDS METERS SECONDS METERS SECONDS METERS 0 0 0 0 0 0 1 2.1 1 2.4 1 3.1 2 7.9 2 9.9 2 11.2 3 17.7 3 22.7 3 27.1 4 31.8 4 39.9 4 47.7 5 48.9 5 62.5 5 74.8 6 72 6 90.3 6 108.3 7 98.2 7 122 7 146.9 8 127.8 8 160.2 8 192.2 9 162.3 9 202.4 9 243 10 199.7 10 250.3 10 300.3
DATA SETS (CONTINUED) DATA SET #7 DATA SET #8 DATA SET #9 TIME POSITION TIME POSITION TIME POSITION SECONDS METERS SECONDS METERS SECONDS METERS 0 0 0 0 0 0 1 3.3 1 4.2 1 4.4 2 14.2 2 15.8 2 18.1 3 31.6 3 36.3 3 40.1 4 55.8 4 64.4 4 71.8 5 87.7 5 99.3 5 112 6 125.7 6 144 6 162.3 7 171.7 7 196.4 7 220.7 8 223.9 8 255.9 8 288.1 9 283.5 9 423.8 9 364.1 10 349.7 10 400.2 10 449.8 DATA SET #0 TIME POSITION SECONDS METERS 0 0 1 4.8 2 20.2 3 45.3 4 79.9 5 124.8 6 179.7 7 245.4 8 320.3 9 404.9 10 499
APPENDIX A: EXCEL (For Office 2007 See Also Appendix B) In this appendix we will give you general information to get you started using Excel. The information is not exhaustive. Instructions are also given on how to work out the pre-lab problem using Excel and construct the spreadsheets and graphs shown in Example Spreadsheets #1 and #2. These instructions are given in italics. We assume your computer is already turned on. To Load Excel, Click on Start Click on Microsoft Office Click on Excel To get out of Excel Click on File Click on Exit Cells of an Excel Spreadsheet GENERAL INFORMATION The cells are labeled by their column and row (for example: B5). The columns are A, B, C, etc. Rows are 1, 2, 3, etc. A cell can hold data (a number), text, or a formula. The cell designation is used as a variable in a formula. For example, if A4 contains the number 10, and C5 contains the formula =A4 + 3, then the cell C5 will display the number 13. To enter data in a cell: Move the cursor to the cell and click. Type the number. Hit Enter. To enter a formula in a cell: Move the cursor to the cell and click, Type = (i.e. the equal sign) followed by the formula Hit Enter. To enter text in a cell: Move the cursor to the cell and click.
Type the desired text. Hit Enter. To clear a cell: Move the cursor to the cell and click. Hit Delete. To replicate (copy) a formula down a column: Click on the cell containing the formula. At the lower right of that cell is a small square called the fill handle. Move your cursor to the fill handle. Hold the mouse down and drag down the column. Click once more. (Note: In the formula, any cell name used as a variable will have its row number increased by one for each downward step. For example: =A7 + B4 =A8 + B5 =A9 + B6 The basic symbols in formulas are: + add - subtract * multiply (This is the only way to show multiplication) / divide ( ) parenthesis ^ power; For example, if D10 contains the number 3, then = 2 ^ D 10 gives 8 = D10 ^ 4 gives 81 To obtain information on math and trig functions, Click on Help Click on Index Scroll to Functions and click on it Click on Math and Trig Functions Note; all trig functions assume the angle is in radians. To display a specific number of decimal places Highlight the region of the spreadsheet you wish to modify. Go the formatting toolbar (second row of buttons) and click on the button with the arrow and.0 in the first line and.00 in the second line.0.00 to increase the number of decimal places, or the button next to it on the right.00.0 to decrease the number of decimal places.
To print a selected area of a spreadsheet Highlight the region of the spreadsheet to be printed Click on File Click on Print Under "Print What" choose "selection" Click ok To display formulas for each cell instead of data Hold down the CTRL (Control) key and type ` (key left of the 1 (one) key). To return to a display of data repeat the above. HOW TO SOLVE THE PRE-LAB PROBLEMS USING EXCEL Open the Excel program. In cell A1 type the text "Name:". In cell C1 type your name In cell A3 type the text "Data Set Number". In cell C3 type the number of your data set. In cell A5 type the text "Time (seconds)" In cell D5 type the text "Position (meters)" As a tutorial, use the position and time data listed on Example Spreadsheet #1. For your pre-lab problems use the data set from the pages titled "Data Sets" whose number is the last digit of your social security number. In column A, in cells A7 through A17 enter your time data. In column D, in cells D7 through D17 enter the corresponding position data. Procedure for graphing data and fitting a polynomial trendline to the data We will graph the position and time data which was entered into your spreadsheet. First to graph your data. Click on the Chart Wizard symbol, a small icon on the top row consisting of a histogram three blue, yellow, and red columns. Click on XY (scatter) Click on upper "sub-chart type", the one with only data points and no lines showing. Click on next of
If the series page is not to the front, click on "series". If no series is shown in the series box, click on add. If more than one series is shown in the series box, delete all but the first. Click on the little box with the red arrow on the line for x-values Highlight the time data, A7 through A17 and click on the upper right "X" in the Source Data x Values Box to close it. Click on the little box with the red arrow on the line for y-values Highlight the position data, D7 through D17 and click on the upper right "X" in the Source Data y Values Box to close it. Enter the text "Position vs Time" in the "Name" box. Click next In this Chart Options step, insert titles on the x and y axes, and put in major vertical and horizontal grid lines. If checked, uncheck the "show legend" box. Click next For Chart Location choose "as object in sheet 1" Click on finish You can move the graph to a different location on the spreadsheet by moving the curser to a area near the inside near the edge of the graph. Holding down the left click button of the mouse a cross of arrows will replace the single arrow of the curser. Continuing to hold down the left click button, you can now move the graph to a different location on the spreadsheet. Move the graph to a position below your data. Now we will add a trendline, curve fitting the data to a polynomial of degree two: Click anyplace on the graph. Click on Chart at the top of the screen Click on Add Trendline Click on Polynomial and set the "order" equal to 2. Click on Options Turn on ( ) Display Equation Turn on ( ) Display R 2 Click on OK Click on the equation, hold the left click button down, and move the equation to an area of the graph were it can be easily read. If the graph has a gray background, place the curser on the background and right click the mouse. Click on Format Plot Area Click on Area Patterns "None" Click on ok. Print the spreadsheet.
You have now finished the first problem. To get ready to do the second problem we first have to erase the graph which is on the spreadsheet. To do this, place the curser inside near the edge of the graph and click the right click button on the mouse. Then click on "clear." Erase the graph on the spreadsheet. To do the second problem we need to calculate the velocity v at each time t, using the equation v = 2r/t. In cell G5 type the text "Velocity (m/s) " In cell G7 type the number " 0 " In cell G8 type the equation " =2*D8/A8 " Replicate the formula in cell G8 down the G column to cells G9 through G17. Now we have the velocity and time data needed to solve the second problem. We draw a graph of velocity verses time and curvefit the data to a linear trendline. First let us draw the graph. Click on the Chart Wizard symbol, a small icon on the top row consisting of a histogram of three blue, yellow, and red columns. Click on XY (scatter) Click on upper "sub-chart type", the one with only data points and no lines showing. Click on next If the series page is not to the front, click on "series". If no series is shown in the series box, click on add. If more than one series is shown in the series box, delete all but the first. Click on the little box with the red arrow on the line for x-values Highlight the time data, A7 through A17 and click on the upper right "X" in the Source Data x Values Box to close it. Click on the little box with the red arrow on the line for y-values Highlight the velocity data, G7 through G17 and click on the upper right "X" in the Source Data y Values Box to close it. Enter the text "Velocity vs Time" in the "Name" box. Click next In this Chart Options step, insert titles on the x and y axes, and put in major vertical and horizontal grid lines. If checked, uncheck the "show legend" box. Click next For Chart Location choose "as object in sheet 1" Click on finish Move the graph to a position below your data. Now we will curve fit the data to a linear trendline: Click anyplace on the graph. Click on Chart at the top of the screen Click on Add Trendline
Click on "Linear". Click on Options Turn on ( ) Display Equation Turn on ( ) Display R 2 Click on OK Click on the equation, hold the left click button down, and move the equation to an area of the graph were it can be easily read. If the graph has a gray background, place the curser on the background and right click the mouse. Click on Format Plot Area Click on Area Patterns "None" Click on ok. Print the spreadsheet. As explained in the problem, from each of the equations of the trendlines of the graphs, one can determine the acceleration of the object.
Name: John Q. Student Data Set Number: 5 EXAMPLE SPREADSHEET #1 Time(Seconds) Position (meters) 0 0 1 3.1 2 11.8 3 27.9 4 48.2 5 75 6 108.3 7 146.9 8 191.4 9 243.2 10 299.9
Name: John Q. Student Data Set Number: 5 EXAMPLE SPREADSHEET #2 Time(Seconds) Position (meters) Velocity (meters/second) 0 0 0 1 3.1 6.2 2 11.8 11.8 3 27.9 18.6 4 48.2 24.1 5 75 30 6 108.3 36.1 7 146.9 41.97143 8 191.4 47.85 9 243.2 54.04444 10 299.9 59.98
APPENDIX B: OFFICE 2007 EXCEL We will graph the position and time data which was entered into your spreadsheet. First, to graph your data: In the Insert toolbar, within the Charts block, click on Scatter. Then click on the first sub-chart type (the one with data points only). In the Design toolbar: Under Chart Layout click on Layout #10. Click on Select Data. Click on Remove to remove any incorrect series.then click on Add series. Click on the little box with the red arrow on the line for x-values. Highlight the time data, A7 through A17, and click on the upper right X in the Edit Series box to close it. Click on the little box with the red arrow on the line for y-values. Highlight the position data, D7 through D17, and click on the upper right X in the Edit Series box to close it. Enter the words Position vs. Time in the Name box. Click OK (twice if necessary) to see the graph. In the graph, click on the words Axis Title on the vertical axis. Type in Position (meters). Then click on the graph. Click on the words Axis Title on the horizontal axis. Type in Time (seconds). Then click on the graph. You can move the graph to a different location on the spreadsheet by moving the cursor to an area inside the graph, near its edge. Holding down the left- click button of the mouse a cross of arrows will replace the single arrow of the cursor. Continuing to hold down the left-click button, you can drag the graph to a different location on the spreadsheet. Move the graph to a position below your data. Now we will add a trend-line, curve-fitting the data to a polynomial of degree 2. Click anyplace on the graph. In the Layout toolbar, click on Trend-line. Then click on More Trend-line Options. Choose Polynomial and choose the order 2. Click on Display Equation and Display R- Squared Value. Click on Close. Click on the equation, hold the left-click button down, and drag the equation to an area of the graph where it can be easily read. If the graph has a gray or colored background, click on the background. Under the Format toolbar, click on Shape Fill. Click on No Fill. To print the spreadsheet (Data and Graph),highlight the data and the graph. Click on the Office button (at the upper left of the screen). Click on Print. Click on OK. OFFICE 2010 EXCEL To print the spreadsheet (Data and Graph), highlight the data and the graph. Click on the File tab (at the upper left of the screen). Click on Print. Click on Print. You have now finished the first problem. To get ready to do the second problem we first have to erase the graph which is on the spreadsheet. To do this, place the cursor on the graph and click. Then hit Delete on the keyboard. To do the second problem we need to calculate the velocity at each time t, using the equation v = 2y/t.
In cell G5 type the words Velocity (m/s). In cell G7 type the number 0. In cell G8 type the equation =2*D8/A8. Replicate the formula in cell G8 down the G column to cells G9 through G 17. Now we have the velocity and time data needed to solve the second problem. We draw a graph of velocity vs. time and curve-fit the data to a linear trend-line. First we draw the graph: In the Insert toolbar, within the Charts block, click on Scatter. Then click on the first sub-chart type (the one with data points only). Place the cursor on the lower left corner of the graph window and drag the graph to the right until all the data is visible. If the graph has become distorted drag the right corner to the right to correct it. In the Design toolbar: Under Chart Layout click on Layout #10. Click on Select Data. Click on Remove to remove any incorrect series.then click on Add series. Click on the little box with the red arrow on the line for x-values. Highlight the time data, A7 through A17, and click on the upper right X in the Edit Series box to close it. Click on the little box with the red arrow on the line for y-values. Highlight the velocity data, G7 through G17, and click on the upper right X in the Edit Series box to close it. Enter the words Velocity vs. Time in the Name box. Click OK (twice if necessary) to see the graph. In the graph, click on the words Axis Title on the vertical axis. Type in Velocity (m/s). Then click on the graph. Click on the words Axis Title on the horizontal axis. Type in Time (seconds). Then click on the graph. You can move the graph to a different location on the spreadsheet by moving the cursor to an area inside the graph, near its edge. Holding down the left- click button of the mouse a cross of arrows will replace the single arrow of the cursor. Continuing to hold down the left-click button, you can drag the graph to a different location on the spreadsheet. Move the graph to a position below your data. Now we will add a trend-line, curve-fitting the data with a linear fit. Click anyplace on the graph. In the Layout toolbar, click on Trend-line. Then click on More Trend-line Options. Choose Linear. Click on Display Equation and Display R-Squared Value. Click on Close. Click on the equation, hold the left-click button down, and drag the equation to an area of the graph where it can be easily read. If the graph has a gray or colored background, click on the background. Under the Format toolbar, click on Shape Fill. Click on No Fill. To print the spreadsheet (Data and Graph), highlight the data and the graph. Click on the Office button (at the upper left of the screen). Click on Print. Click on OK. OFFICE 2010 EXCEL To print the spreadsheet (Data and Graph), highlight the data and the graph. Click on the File tab (at the upper left of the screen). Click on Print. Click on Print. As explained in the problem, from each of the trend-line equations, you should now determine the acceleration of the object.