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 2 N 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  mblock= 0.206 kg.  The 2 N weight has a mass of  mhanging= 0.204 kg.   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/mtotal = F/(0.410kg).  After having measured a, we can therefore find F.  We then use f = w - F to find the magnitude of the frictional force and f = μN to find the coefficient of kinetic friction.  Here N is the weight of the block, N = mblockg.

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.

bullet"Play" the video clip.  When finished, "Step up" to frame 0.  In some browsers you have to click "Pause" first..
bulletIn the setup window choose to track the x-coordinate of an object.
bulletCalibrate and take data as described in lab 1.
[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.]
bulletHighlight and copy your data table.  Open Microsoft Excel, and paste the table into an Excel spreadsheet.
bulletYour spreadsheet will have two columns, column A, time (s), and column B, x (m).  Produce a graph of position (vertical axis) versus time (horizontal axis).  Label the axes.
bulletType v (m/s) into cell C1.  Type =(B3-B2)/(A3-A2) into cell C2.  This yields the average speed of the block in the small time interval between the first and the second frame of the video clip.
bulletCopy this formula into the other cells of column C.  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 C be in row i-1.
bulletOn the menu bar click data, data analysis, regression.  For the input y range choose column C.  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.
bulletThe regression function finds the best fitting straight line for your velocity 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:

bulletWhat value do you obtain for the magnitude of a?
bulletWhat value do you obtain for the magnitude of F = mtotala?
bulletWhat value do you obtain for the magnitude of f = w - F?
bulletWhat is the coefficient of kinetic friction μ = f/( mblockg)?
bulletDoes your value lie in a reasonable range?  (reference table)

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.xlsx).  Go to Blackboard, Assignments, Extra Credit 5, and attach your document.