Force and Acceleration

Objective:

In this exercise you will analyze a video clip. The clip shows a cart on an air track being pulled by the gravitational force acting on a hanging mass. You will determine the position of the cart 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 cart 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 cart.

The board in the clip indicates is that the mass of the cart is m_cart= 0.196kg. The hanging mass has m_hanging= 0.007kg. The magnitude of the force acting on the system is the magnitude of the weight of the hanging mass, F = m_hangingg. We expect the magnitude of the acceleration to be equal to a = F/m, where m is the total mass that is accelerating, i.e. m = m_cart+ m_hanging.

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 pull_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.

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 cart 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.

In cell D1 type v1 (m/s).

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. We expect it to be equal to a = F/m.

Questions:

	Assuming the masses written onto the board are correct, what value do you expect for the magnitude of the acceleration a?
	What value do you obtain from the slope of your measured velocity versus time graph for the magnitude of the acceleration a ?
	What is the percentage difference?

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

Save your Excel document (your name_exm4.xls) and attach it to an e-mail message to your instructor.