PROJECTILE MOTION

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

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. For projectile motion the same set of equations hold, however there are two sets of these equations one for the horizontal (X) direction and one for the vertical (Y) direction. It is assume that the acceleration in the X direction is zero and that the acceleration in the Y direction is -g or - 9.81

m/s². The X and Y problem share the same time. In the chart below D R is used instead of D X.

EQUIPMENT: Computer, and VideoPoint Software

PROCEDURE:. From the "PASCO" subdirectory chose one of the following: pasco104 (30° ), pasco106 (45° ), or pasco108 (60° ). With the VideoPoint software mark the position of the object as demonstrated in the "Instructions for using VideoPoint". There is a "step - by - step" procedure for using VideoPoint for this experiment at the end of the document.

For the Y direction calculate the distance traveled, and average velocity for each time interval possible. Make a graph of velocity verses time and find the slope of the line. This should be the acceleration (-g or -9.81 m/s²). Find the percent error in this acceleration. The Y-intercept should be the initial velocity in the Y direction. The initial velocity of the projectile can be calculated from V_oX = V_o Sin q . Use this data and the data given it the documentation that the angles are 30°, 45°, and 60° for the three videos and calculate the initial velocity of the projectile.

For the X direction, plot the position verses time curve and find the slope of the line. The expected value should be V_o Cos q , where V_o is the value obtained from the Y direction. Compare these values and find the percent error.

QUESTIONS:

1. Is the velocity in the X direction about constant? Justify your answer.

2. Is the acceleration if the Y direction also about constant?

3. Look at all three videos and judge which would have the greater range.

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

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 comes up - make sure "1’ is selected and press "OK"- The movie and software should now be loaded.

Record the data.

On the menu bar select "Movie" and "Full Screen".

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.

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

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

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

Graph the data (x-direction)

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 appears.

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 in on the word.

Press "OK" and the graphs should appear.

Graph the data (y-direction)

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 appears.

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 in 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 press the 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 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, the X-position and the Y-position of data in data table

DATA TABLE

From the intercept with the Y-axis of the Velocity Vs Time graph for the

Y direction

V_yo = __________ V₀ = V_Yo/Sin q = __________

From the slope of the Velocity Vs Time graph for the Y direction

a_Y = ___________ % error = __________

From the slope of the Position Vs Time graph for the X direction

V_xo =__________ V_xo = V_o Cos q = __________ % error = _______

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