Coefficient of friction

Objective:

In this exercise you will analyze a video clip. The clip shows a block sliding on a table being pulled by a 2N weight. You will determine the position of the block 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 block 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 a velocity versus time graph yields the acceleration of the block.

The mass of the block is m_block=0.206kg. The 2N weight has a mass of m_hanging=0.204kg. The magnitude of the total force acting on the system is the weight of the hanging mass minus the magnitude of the frictional force f between the block and the table, F=w-f. We expect the magnitude of the acceleration to be equal to a=F/m_total=F/0.410kg. After having measured a, we can therefore find F. We then use f=w-F to find the frictional force and f=mN to find the coefficient of kinetic friction.

Procedure:

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 friction_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 x-coordinate of one object.
	Go to the "Take Data" window. Click "Start taking data". A spreadsheet will open up. Take data as described in a previous exercise.

Calibrate your data as described in that previous exercise, choose an origin and add a calibrated column.
[The stick in the frames between the two white cards is a meter stick. It is 1m long. The distance from the left edge of the left white card to the right edge of the right white card in the first frame is one meter.]

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, x1, and x1(m).

If your spreadsheet looks similar to the one shown above, type =(C3-C2)/(A3-A2) into cell D2. This yields the average speed of the block in the small time interval between the first and the second frame of the video clip.

Copy this formula into the other cells of column D. This will yield the average velocity during successive time intervals. If the last entry of column A is in row i, let the last entry of column D be in row i-1.

On the menu bar click tools, data analysis, regression. For the input y range choose column D. For the input x range choose the corresponding cells of column A. Under output options check new worksheet, and under residuals choose residual plots and line fit plots. Click OK.

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.

Questions:

	What value do you obtain for a?
	What value do you obtain for F?
	What value do you obtain for f?
	What is the coefficient of kinetic friction?

To earn extra credit add your name and e-mail address to your spreadsheet. In full sentences answer the four question posed.

Save your Excel document (your name_exm5.xls) and attach it to an e-mail message to your instructor.