Accelerated Motion

Objective:

In this exercise you will analyze a video clip.  The clip shows a cart moving on an air track.  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 a plot of position of the cart versus time.

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.
bulletClick "Calibrate".  Then click "Calibrate X".
The video clip contains calibration markers.  Each white card is 10 cm = 0.1 m wide and the space between card is 10 cm = 0.1 m wide.  Position the cursor over some marked position in the left part of the frame, for example the left edge of the leftmost card, and click the left mouse button.  Then position the cursor over some marked position in the right part of the frame, for example the left edge of the sixth card from the left, and click the left mouse button again.  This will record the x-coordinates of the chosen positions.  Enter the distance between those positions into the text box in units of meter.  For the example positions, you would enter 1 into the text box.  Click "Done".
bulletClick the button "Click when done calibrating".  A spreadsheet will open up.
bulletClick "Start taking data". 
Pick the point on the cart whose position you will track, for example the little post sticking out of the top of the cart.  Position the cursor over that point.  When you click the left mouse button, the time and the x-coordinate of your chosen point will be entered into the spreadsheet.  You will automatically step to the next frame of the video clip.
bulletRepeat for each frame in the video clip.  Then click "Stop Taking Data".
bulletHighlight and copy your table.  Open Microsoft Excel, and paste the table into an Excel spreadsheet.
bulletYour spreadsheet will have two columns, time (s), and x (m).  Produce a graph of position (vertical axis) versus time. (horizontal axis.
bulletOn the Excel menu bar click Insert, Chart, XY (Scatter), and pick one of the subtypes.
bulletRight-click the chart and choose Select Data, Add.
bulletPosition your cursor in the X-Values text box  and highlight all the entries in the time (s) column.
bulletNow position your cursor in the Y-Values text box, erase any entries in this box, and highlight all the entries in the x (m) column.
bulletType Position vs Time into the Name text box.
bulletSelect your chart, chose Layout or click the + button next to the chart, 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)".
bulletNote:  You may have chosen you x-axis to point towards the left or towards the right.  This choice determines if your x values increase or decrease as a function of time.
bulletStudy your graph.  Does the plot of position versus time resemble a straight line?   Does the cart move with constant velocity?
bulletRight-click the data in your position versus time graph and choose "Add Trendline".   Choose Polynomial, Order 2. and click "Display equation on chart".  An equation of the form y = b1x2 + b2 x + b3 will be displayed where b1, b2, and b3 are numbers.  What do the coefficients b1 and b2 tell you?   (For motion with constant acceleration we expect that x changes as a function of time as x = x0 + v0t + (1/2)at2, where a is the acceleration.)
bulletIs the trendline a good fit to the data?  Does the cart move with constant acceleration?  What is the direction of the velocity?  What is the direction of the acceleration?

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

Name:
E-mail address:

Extra Credit, Module 2

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In one or two sentences state the goal of this exercise.

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Insert your graph with trendline into your Word document.

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Describe your graphs. 
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Does the plot of position versus time resemble a straight line?  Do you expect it to resemble a straight line?

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Does the cart move with constant velocity?  How do you know?

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Does the cart move with constant acceleration?  How do you know?

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What is the direction of the velocity?  What is the direction of the acceleration?

Save your Word document (your name_exm2.docx), go to Blackboard, Assignments, Extra Credit 2, and attach your document.