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1 Physics 100 Lab 1: Use of a Spreadsheet to Analyze Data by Kenneth Hahn and Michael Goggin In this lab you will learn how to enter data into a spreadsheet and to manipulate the data in meaningful ways. There are several choices for spreadsheets on the Truman student computer image. I will try to make what follows as generic as possible so they apply to any of the spreadsheet programs. The basic functionality is similar for all of the choices; they just differ in some details. When the details differ, I have chosen the more popular spreadsheet: Excel. But even the details for that change from version to version. When in doubt, ask! Many of you have probably done some of the following but not all of it. Quickly work through what you know how to do so you can spend time on the parts you don't know. 1. Start the spreadsheet of your choice. This should open a new Workbook and will provide you with a new Sheet. On this sheet is a large number of (currently empty) Cells. Each cell is designated by a column and a row label. Columns are labeled A, B, C,... and are vertical in nature. Rows are labeled 1, 2,3,... and are horizontal. Thus each cell can be designated by column-row, like A1, C5, R145, etc. This is much like one does with labeling points on a graph (x 1, y 1 ). If you need to change the width of a column simply move the cursor up to the region where the A, B, C,... are. When the cursor lies on a column line it will change to something like this:. When this symbol appears you simply hold down the left mouse button and drag the column in either direction. You can do the same with the height of the rows. This is a helpful feature if the text to appear in the cell is longer than the width of the column or if you wish to have taller rows. It is also simple to change the size and type of font. (Highlight the cell or cells and make adjustments in the boxes above the A & B columns. 2. Basic math calculations: to perform math calculations you must click on a cell (that is, a cell where you want that calculation to be performed) and type the "=" sign. The "=" tells the spreadsheet you are about to enter a formula. If you do not type the = then the equation or whatever you type appears as text and no calculation will be performed. Notice the "=" text box. Use the following syntax: +,, * for multiplication, / for division, and ^ for powers. Example: to do the following operation in cell A1: you would type in an open cell: = 3 + (5*4) + (1/2)*(4/2)^2. When you finish typing, you press enter and the result appears. You ll notice the equation will overlap the cell, but that s okay. You can always see the whole equation (or whatever) in the text box. Try it. Your answer should be 25, appearing in the cell.

2 ** Notice: "25" appears in the cell, but if you click on that cell you will see the "25" in the cell, but the equation which yields the 25 in the text box try it. Try this one in cell B2: Answer: 3. You can also have the spreadsheet read values from another other cell and perform an operation on that value. That is one of the real values of the Spreadsheet. It lets you do calculations based on the results of other calculations or entries. Another tremendous function is that the spreadsheet can repeat the same calculation over and over on new values, without you having to re-enter the equation more than one time. First clear the previous work from cells A1 and B2. {Click on them and then press the Back Space ( ) key or Delete key to delete}. Now, suppose you wanted to look at the relationship y = x {a parabola} for a number of values of x: x = 0, 1, 1.5, 2, 2.5, 3, 4, & 5. in cell A1 type x (no = ) and then ENTER and in cell B1 type y and ENTER. Without the = these are just text cells, so no calculation will be done. Thus, x and y are the headings for two columns of numbers or results. In cell A2 through A9 type the values of x listed above. In cell A2 type 0 and then move to the next cell, either by clicking with the mouse or by using the down arrow ( ) on the keyboard. go to B2 and type the equation: A2^ Don t forget the = sign first. This instructs the spreadsheet to take the value in cell A2, square it and add 3. When you type this and press ENTER you get the result 3. ( = 3) Now you could type the equation over and over again, but that s what the spreadsheet is for. Notice in each cell below B2 you want the same equation, except you want to insert A3 in place of A2, and then A4 in place of A3, etc. Here s how to do it quickly: start in the cell with the equation you want (B2). {Click on cell B2, which will highlight it there will be a dark-lined box around the cell}. Move the cursor, which is normally a white cross, to the lower right corner of this cell. The Cursor will become a Black Cross. With a Black Cross on the corner of this cell, LEFT CLICK and HOLD. Drag the cursor down as far as you want to copy the equation (to cell B9 in this example) and then release the left mouse button. With this process properly performed, you should be able to click in the various cells (B3, B4,., B9) and see the copied equation. NOTE #1: In the process of this click & drag operation, you increment by one all cell designations: For example, if the formula in T6 is: = A1^2 + B37 D14

3 and you do this process, then in cell T7 you end up with: = A2^2 + B38 D15. NOTE #2: it does not matter what cell you are at and what cell or cells you are using in your calculation. Notice in the example above that we were at T6 and called in A1, B37 and D14 all at the same time. The next cell, T7 has each of these bumped (incremented) up by one value. (NOTE #3: you can also increment in horizontal rows if you want, by clicking and dragging to the right but that isn t something you need for our purposes today). NOTE #4: there are other ways to do this operation; if you are comfortable with one of these other methods, by all means use what you already know if it works well for you. 4. Sometimes, you want the spreadsheet to read a value from a cell, use it in an equation, BUT you don t want to increment it. For example, suppose you wanted to do this calculation 10,000 times: y = Kx 2 + 5, where K is some value (like 1 or 2 or 7.6) that is the same in each calculation. Now you could just type in the 1, 2 or 7.6 and be done. But you also may want to change the K sometimes (as in try it 10,000 times with K = 1 and then 10,000 times with K = 2). In this case you want to pick a cell to be the value of K and type - let s use cell C3. Then to prevent C3 from being incremented use $C$3 instead of C3 in your calculations. The $ signs mean DON T INCREMENT. Let s try it. In cell C3 type 1. This is our first try with a value of K. In cells D1 through D10 type these values of x: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. now type the equation in cell E1: = $C$3*D1^2 + 5 Do it for the rest of the cells (E2 through E10). Look at any of the cells - notice how D1 is changed to D2, D3, D4,... but $C$3 is the same. Now, go to cell C3 and type a 2 (to replace the 1). When you press ENTER notice all the values in cells E1 E10 change to reflect the new value of K. Try K = 0 all the E values should be 5 (since the equation is 0 + 5, regardless of the value of x). ** Save this work for the next part ** 5. Plotting: Finally, let s make a graph. We will do it for the equation y = Kx which you have already typed in. Type in the value of K = 2.55 (type 2.55 in Cell C3) and press ENTER. Now we want to graph y vs. x for this equation and its results. first, Click and drag over the cells (D1 - D10 and E1 - E10). A highlighted 3

4 rectangle will appear. (yes?) Now go to the top of the page, click on Insert, click on Scatter in the Charts section. Follow these steps 1. The first step will be a choice of graph style from the icons. You need to decide if you want to connect the data points or not. Most of the time you will NOT want the data points connected. Select the appropriate icon. 2. A plot of the data should appear. At this point it is very basic. You can now use the Chart Tools to modify the layout and add things like labels and a trendline to your chart. There are some pre-defined layouts under the Design tab. See what they do. 3. We usually want more control over a chart than what the pre-defined layouts allow. Go to the Layouts tab and add labels to your chart. 4. The Format tab allows you to dress up your chart by changing font properties, etc. You can play around with these if you want. 5. You will want to add trendlines to some of your plots. The simplest trendline is a linear fit to data that expresses a linear relationship. The data you have just plotted are not linear. These data represent a power law. See if you can add a trendline to your chart. You can modify background colors and the symbols on the graph by clicking on the graph or on the symbols. Since you will probably be printing in black ink, I strongly suggest not using colors. Go back to the first sheet (Click on the tab labeled Sheet 1) and change the value of K to Click on the chart tab, and see the new result. NOTE: to print two sets of data (i.e., to compare the graphs for two values of K), here s what you could do: Column D could be the value of x Column E could be the values of y for K = 2.55 Column F could be the values of y when K = (use a separate cell, not C3, for a second K value) Then, to plot, you have to highlight all three columns. The spreadsheet will automatically place different symbols for each column. Try IT. If you wish to change something on your chart try double clicking on it and see if it will allow you to edit. Gridlines will be of great use to you when you need to determine slopes by hand. We will explore graphing in more depth in a future lab.

5 PRACTICE EXERCISES: Remember to include units in each calculation of slope and intercept. A. Plot the following data and find the slope of the line: sec meters B. On a separate graph, plot these data and find the slope and y-intercept of the line. sec meters C. Plot these two sets of data that represent the motion of two balls rolling downed an inclined surface. Make a proper graph, with titles, labels, and lines through the data. Time Distance of Distance of (seconds) BALL 1 BALL

6 Lab #1 Assignment 1. Make a graph of the following data. It is data representing the motion of an object as a function of time. (Plot time along the horizontal axis). Draw a best-fit line through the data. Calculate the slope and intercept for this line. Calculations: time (seconds) position (meters) On the same graph, plot the following data. Again, draw a line, calculate slope and find the intercept. time (seconds) position (meters) Calculations: 3. On a separate graph, plot the following data of speed vs. time. Draw a line, and find the slope and intercept. Calculations: time (seconds) speed (m/s) At what time do you predict the speed to be zero (0.0 m/s)? State your answer to one decimal place (e.g., 2.4 sec) TURN IN: This page with calculations in the boxes, two graph pages.

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