Physics Laboratory 2

Freefall - The acceleration of gravity

Objective:

In this lab you will analyze a video clip.  The clip shows a person dropping a ball.  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 a velocity versus time graph yields the acceleration of the ball.  We expect the magnitude of this acceleration to be equal to g = 9.8m/s2 and the direction to be downward.

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 one of the ball_x.avi video clips. 

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.  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 (("Home, Paste" in Excel 2007).
Your spreadsheet will have three columns, time, y1, and y1 (m).

If your spreadsheet looks similar to the one shown above, click column B and chose insert column.
Label the new column time^2.

Note:  You may have chosen you y-axis to point upward or downward.  This choice determines if your calibrated y values increase or decrease as a function of time.

Into cell B2 type = A2^2.
Copy the formula into the other cells of column B.  The entries in column B now are the squares of the entries in column A.
To copy a formula, position your cursor in the cell that contains the formula, choose edit, copy from the menu bar, highlight the cells that will receive the formula, and choose edit, paste from the menu bar.

Produce a graph of position versus time.
On the Excel menu bar click Insert, Chart, XY (Scatter), and pick one of the subtypes.
Click Next, Series, Add.  (In Excel 2007, right-click the chart and choose Select Data, Add.)
Position your cursor in the X-Values text box,  and highlight all the entries in the time column.
Now position your cursor in the Y-Values text box, erase any entries in this box, and highlight all the entries in the y1 (m) column.
Type Position into the Name text box.
Click Next, (in Excel 2007 choose Layout,) give the chart a title, and label the axes.  The label for the x-axis should be "Time (s)", and the label for the y-axis should be "Position (m)".
On the menu bar click tools (in Excel 2007 click data), data analysis, regression.  For the input y range choose column D ($D$2:$D$20.  For the input x range choose the corresponding cells of columns A and B ($A$2:$B$20).  Under output options check new worksheet, and under residuals line fit plots.  Click OK.
The regression function finds the best fitting polynomial of the form y = a + bx + cx2 for your data.  Under SUMMARY OUTPUT, Intercept, you will  find the coefficient a.  Under SUMMARY OUTPUT, X Variable 1, you will  find the coefficient b, and the standard error in this coefficient from the fit.  Under SUMMARY OUTPUT, X Variable 2, you will  find the coefficient c, and the standard error in this coefficient from the fit.  
For motion with constant acceleration we expect that y changes as a function of time as y = x0 + v0t + (1/2)at2, where a is the acceleration.  So we expect that the X Variable 2 from the fit is equal to (1/2)a.  We expect the  magnitude of 2 times X Variable 2 to be equal to that of the gravitational acceleration g within experimental error.

Open Microsoft Word and prepare a report using the template shown below.

Name:
E-mail address:

Laboratory 2 Report

In a few sentences summarize the experiment.  Which video clip did you choose?

Insert your position versus time graphs into your Word document.

Highlight the graph in Excel, choose edit, copy from the menu bar, switch to Word, position your cursor at the insertion point and choose edit, paste from Word's menu bar.

Describe your graph.

What is the magnitude of the average acceleration and the uncertainty in the the magnitude of the average acceleration of the ball?  What is the direction of the acceleration?

How does your experimental value of the magnitude of the acceleration compare to the accepted value of the magnitude of the acceleration of a free-falling object (g = 9.8m/s2)?
Reminder: percent difference = Image1333.gif (1578 bytes)
What factors do you think may cause the experimental value to be different from the accepted value?  In other words, what are some possible sources of error?

Save your Word document (your name_lab2.doc) and attach it to an e-mail message to mbreinig@utk.edu.