CONSTANT ACCELERATION

PURPOSE: To study and analyze the motion of an object undergoing constant acceleration.

THEORY: An object undergoing constant acceleration should obey the following equations.

1. 2.

3. 4.

5. 6.

where D X is the change in position (distance traveled), t (or D t) is the elapsed time, V_o is the initial velocity, V_f is the final velocity, is the average velocity, and a is the acceleration.

EQUIPMENT: Computer, VideoPoint Software, graph paper and straight edge.

PROCEDURE: There are several video files from which to chose. From the "PASCO" subdirectory chose one of the following: pasco03, pasco04, pasco05, pasco06, pasco07, pasco35, pasco36, or pasco37. With the VideoPoint software mark the position of the object as it accelerates. There is a step-by step procedure at the end of the laboratory for using VideoPoint for this experiment. You should have reviewed the introduction provided with the VideoPoint CD and the Walkthrough on the CD or the Web sight. This data can be copied into the provided data table or the table may be printed out. Record the x-position and time on the provided table and calculate the velocity and acceleration for each interval possible. Use this data for the following graphs.

Graph the results. Make two graphs X verses t, and V verses t. Use the graphs and information in the data table to find the following. Make only one graph per page and make the graph take up at least half of the page both horizontally and vertically. Make sure you label the graph, the axis, and indicate the units the numbers on the graph represent.

1. The slope of the velocity verses time graph. Draw the best straight line through the data (do not play connect the dots). The slope of the line is the rise over the run for the line drawn through the data. Remember that the numbers on the axis have units and so will the slope.

2. Find the average acceleration for the car for the entire experiment. Add up all of the accelerations and divide by the number of accelerations added.

3. The slope of the velocity verses time line should be the average acceleration. Find the percent error in agreement of the acceleration calculated from the slope of this line and the average of the accelerations from the table. Treat the average acceleration as the expected average.

4. Find the area under the velocity verses time graph. The area being calculated is a trapezoid. The area of a trapezoid is the average height times the base. The line drawn to find the slope should cross the y-axis (velocity-axis at t=0) This distance from the origin to this crossing is one of the heights. The other height is the distance from the line to the x-axis (time-axis) at the last recorded time on the graph. The base will be the value of the last time plotted.

5. Find the total displacement by subtracting the first and last positions..

6. The area under the curve and the total distance traveled should be the same value. Find the percent error in agreement of these two numbers.

Watch some of the files in the "NASA" subdirectory and analyze the motion of the moving object and justify your answer as to whether or not its acceleration is approximately constant.

QUESTIONS:

1. The area under the velocity Vs time curve is the total distance traveled. What is the area under the acceleration Vs time curve?

2. What is a negative acceleration?

3. Consider the velocity Vs time graph. If the scale used for plotting the velocity were changed the angle at which the line through the data is drawn would change. Would this change the slope of the line?

STEP - BY - STEP Procedure for VideoPoint

Start VideoPoint.

Click left mouse button while the pointer is anywhere inside the "about VideoPoint" dialogue box.

In the "open" dialogue box do the following.

Select the drive letter of the CD drive in which VideoPoint is located.

Select movies folder and the appropriate folder under movies (here the "pasco" folder).

Under filename select the appropriate file to be loaded.

Press "OK".

The "Number of points" dialogue box will appear. Make sure "1" is selected and press "OK". The movie and software should now be loaded.

On the menu bar select "Movie" and "Full Screen" using the left mouse button.

Record data -When the cursor is inside the movie screen it appears as a target. Place this target cursor on a point on the top cart and press the left mouse button, the movie will advance one frame and the data is recorded. Repeat this process until all frames of the movie have been used. Be consistent and use the same point on the cart each time to record the data. Ignore any carts moving on lower tracks, they can be used for relative velocity experiments.

Calibrate the movie.

Move the cursor to the "meter stick" tool button at the left of the screen (6th button from top) and click the left mouse button.

The "Scale Movie" dialogue box appears. Select continue with the left mouse button.

Put the target cursor on the left end of the meter stick in the first movie frame and press left mouse button - repeat for the right end of the meter stick.

On the menu bar select "Movie" and "Normal Size".

Graph the data.

Select "Graph" tool button on tool bar at left side of the window with left mouse button. (8th button from top) - "Plot Series" dialogue box will appear.

The horizontal axes should be "time".

The vertical axis should be "Point S1" and "X".

The position, velocity, and acceleration options should be highlighted by clicking the left mouse button when the cursor is on the word.

Press "OK" and the graphs should appear.

Fit equations to the graphs.

With cursor on each graph click left mouse button then select the "F" flag and click left mouse button again.

By using the left mouse button select the following.

For position choose" type of fit"= "polynomial" and "order of fit" = "2" and "OK".

For the velocity select "type of fit" = "linear" and "OK".

For the acceleration select "type of fit" = "Average" and "OK".

For each graph the equation or average is displayed with the plots.

For position Ax² + Bx + C (A = ½ a ; B = V_o ; C = X_o ; and x represents to t).

For velocity Ax + B (A = a; B = V_o ; and x corresponds to t).

For acceleration the average is the average acceleration.

These values should be compared to the corresponding values from your plots Record the data.

With cursor inside table area click left mouse button to select table.
Put mouse in title area of table and click and hold left mouse button and drag the table to top of window.

Place the pointer on lower right corner of table (cursor should be double arrow) and drag the corner of the table to make the table larger so all the data can be seem.

Record the time and the X-position of data in data table.

DATA TABLE

Average acceleration = ________ Area under curve = ________

Acceleration from slope = ________ Total distance traveled = ________

% error in acceleration = ________ % Area in distance = ________

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