In this exercise you will analyze a video clip. The clip shows a ball rising in a glass of water. You will determine the position of the ball as a function of time by stepping through the video clip frame-by-frame and by reading the time and the position coordinates of the ball off each frame. You will construct a spreadsheet with columns for time and position and use this spreadsheet to find the velocity as a function of time. The slope of the velocity versus time graph yields the acceleration of the ball. You will use this acceleration to determine the mass of the ball.
To play the video clip or to step through it frame-by-frame click the "Begin" button. The "Video Analysis" web page will open. You can toggle between the current page and the "Video Analysis" page by pressing Alt-Tab. Choose the archimedes_1.avi video clip.
 | Play the video clip. When finished, the video clip will rewind automatically and stop at frame 0. |
| In the setup window choose to track the y-coordinate of one object. |
| Go to the "Take Data" window. Click "Start taking data". A
spreadsheet will open up. Pick the point on the ball whose position you will track. Position the cursor over that point. When you click the left mouse button, the time and the y-coordinate of your chosen point will be entered into the spreadsheet. (The x- and y-coordinates of the cursor (in units of pixels) are measured with respect to the lower-left corner of the frame.) You will automatically step to the next frame of the video clip. Repeat for each frame in the video clip. Then click "Stop Taking Data". |
| Click "Calibrate y". The video clip contains a calibration marker. Position the cursor over the lower edge of the marker and click the left mouse button. Then position the cursor over the upper edge of the marker and click the left mouse button again. This will enter the y-coordinates of the edges of the marker into the boxes labeled "y1" and "y2". Enter the distance between those positions (in m) into the box marked Dy. For the example positions, you would enter 0.25 into the box marked Dy. Click "Done". | ||||||||||||||||||||||||||||
| Highlight your table, click "Edit, Copy" on your browser's menu bar, open Microsoft Excel, and paste the table into an Excel spreadsheet by clicking "Edit, Paste" on Excel's menu bar. | ||||||||||||||||||||||||||||
| Your spreadsheet will have three columns, time, y1, and y1(m).
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| Produce a graph of velocity versus time.
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| Position the cursor in an empty cell. On the menu bar click tools
(in Excel 2007 click data), data analysis, regression. For the input
y-range choose the entries in column D. For the
input x-range choose the entries in column A. (Put
your cursor in the appropriate textbox and highlight the chosen cells.)
Under output options check new worksheet, and under residuals choose
residual plots and line fit plots. Click OK.
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| The regression function finds the best fitting straight line for your data. Under SUMMARY OUTPUT, X Variable, you will find the slope of this line, and the standard error in this slope from the fit. The slope of the velocity versus time graph is the acceleration. | ||||||||||||||||||||||||||||
| Now find the mass of the ball using Archimedes' principle.
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| What is the measured acceleration of the sphere? |
| What is the mass of the sphere? |
| What would the mass of the sphere be if its average density were equal to the density of water? |
| What percentage of the volume of the sphere will be above water when equilibrium has been reached? |
To earn extra credit add your name and e-mail address to your spreadsheet. In full sentences answer the questions (in blue) posed above.
Save your Excel document (your name_exm1.xls) and attach it to an e-mail message to mbreinig@utk.edu.
