EXPERIMENT 4: Video Motion Analysis of Projectile Motion

When a volleyball player strikes a ball during serve, the ball slows down until it reaches the top of its path. Then the ball speeds up on its way back down. The graphs of the x and y components of the velocity vs. time would show these changes. Is there a mathematical pattern to the changes in x and y components of the velocity? What is the shape of the distance vs. time graph? What does the acceleration vs. time graph looks like?

If the ball has a rotational motion (spin), then the interaction of the ball with the surrounding air becomes significant. The vertical acceleration is not the free fall acceleration anymore; the motion in the horizontal direction will have an acceleration as a result of this interaction.

In this experiment, you will use VideoPoint software to collect distance and time data for a ball struck at a certain angle. The software will provide the data for velocity and acceleration. Analysis of the graphs of motion will answer the questions asked above.OBJECTIVES

Collect position (x and y) and time data as the ball travels up and down
Analyze x vs. time, y vs. time, vx vs. time and vy vs. time graphs
Determine the accelerations on x and y directions from the slope of the velocities graphs
Estimate the horizontal and the vertical components of the forces acting on the ball

MATERIALS

Windows PC

VideoPoint software

PRELIMINARY QUESTIONS

Think about the motion of a ball thrown in the air at a certain angle as the combination (or resultant) of two independent motions: motion in the x- direction and motion in the y- direction. Describe in words the two motions.
Make a sketch of your prediction for the horizontal position (x) vs. time and horizontal velocity (vx) vs. time graphs.
Make a sketch of your prediction for the vertical position (y) vs. time and vertical velocity (vy) vs. time graphs.
Describe in words what these graphs mean.

PROCEDURE

1) From VideoPoint, open the file DSON003.mov (located in the VideoPoint Movies file)). Enter “1” in the opening window (The number of objects to be located) then select “OK”. There will be three windows displayed: a data table, graph and the image of a volleyball player).

2) Viewing the movie. Click on the top of the image window, to obtain a full screen view. Using the arrows on the bottom of the screen, view the movie. Observe the path of the ball.

3) Using the arrows at the bottom of the screen, return to the first frame. Click on the ball, centering the marker on the ball as good as you can.

4) When you click on the ball, the position ( x and y ) is recorded on a data table. Click on the ball on all the frames. Note, the positions are recorded in pixel position not meters. You will need to scale the pixel values to an appropriate length scale.

5) Scaling the movie. On the main toolbar, select “Movie” then “Scale Movie”. Enter the reference length value (from frame #1), verify units, then select “Continue”. Click on the right arrow button of the movie frame and advance the movie to the 17th frame. Click on the bottom of the server then again at the top of the server (you are assigning this distance on the movie to be equal to the reference length entered in the previous menu).

6) Creating (Horizontal Motion) Graphs in VideoPoint. From the left side vertical toolbar, select the GRAPH button. Select “time” on the Horizontal Axis and “x” on the Vertical Axis. Select “Position”, “Velocity”, and “Acceleration” then click on “OK”. You have just created 3 graphs (x-position vs. time, x-velocity vs. time, and x-acceleration vs. time). Maximize the newly created graph window for closer inspection.

Graph Questions (x-direction):

a) What is the shape of the x-position vs. time graph?

b) What is the shape of the x-velocity vs. time graph?

c ) What is the shape of the x-acceleration vs. time graph?

7) Fitting Graphical Data. Click on the x-position vs. time graph then click on the “F” button in the upper right corner. Select an appropriate function (Average, Liner or Polynomial) and order of fit (if applicable) to fit the graph then click on “Apply”. Repeat for the x-velocity vs. time and x-acceleration vs. time graphs? After you have performed fits on all of the graphs, print out a copy of your graphs.

Fit Questions (x-direction):

a) How do the parameters of the respective fits for the graphs compare?

b) Is there a relationship between the coefficients on the various graphs?

c) If your answer to (b) is “yes”, what are the relationships you observe?

8) Analysis of Vertical Motion. Repeat steps 6 & 7 for the vertical direction and create graphs for y-position vs. time, y-velocity vs. time, and y-acceleration vs. time. Analyze these graphs as described above in Step #7. Be sure to print a copy of your graphs.

Graph Questions (y-direction):

a) What is the shape of the y-position vs. time graph?

b) What is the shape of the y-velocity vs. time graph?

c ) What is the shape of the y-acceleration vs. time graph?

Fit Questions (y-direction):

a) How do the parameters of the respective fits for the graphs compare?

b) Is there a relationship between the coefficients on the various graphs?

c) If your answer to (b) is “yes”, what are the relationships you observe?

9) One More Thing. Obtain a graph of y-position vs. x-position.

Questions:

a) What is the shape of the graph?

b) What does this graph represent?

c) What is the difference between this graph and the position graph obtained in step (8)?

FINAL ANALYSIS

1) Using the x-position vs. time graph, describe the motion in x direction. Constant velocity or accelerated motion? Positive or negative direction? Calculate The net force acting on the x direction (Fx=max).

2) Using the y-position vs. time graph, describe the motion in y direction

3) Using vy vs. time graph, find the acceleration on y direction. Explain the significance of the portion with negative vy. Where did the ball slow down, and where did it speed up?

4) Calculate the net force acting on the vertical direction and compare it to the weight of the ball.

5) From the initial velocity values (x- and y- components), estimate the initial angle of the ball strike.

6) How does the spin (rotational motion) of the ball influence the path of the ball?