Volleyball Data

Here is our data. 
 
Force is a push or pull exerted on an object, according to our textbook.  In this case, the hand of Rachel Iaquinello exerted a force on the volleyball to spike it toward the force meter, which measured the force that the ball hit the meter at.  The force meter measured the force it was hit at, and the data was transsferred to Logger Pro and turned into a graph.  Impulse, also according to the textbook, is the product of the average net force exerted on the object (volleyball) and the time interval over which the force acts (the amount of time Rachel's hand hit the volleyball).  This can also be found by taking the force graph produced in Logger Pro and taking the integral of the area beneath the curve (the force).  An example of how we found the impulse is below, and an example of the graph from the force meter is below it .   Force can be found by multiplying mass times acceleration, giving units of g*m/s*s or Newtons (N).  Impulse, being force times the time interval, gives you units of N*s.   

Forces for 4 tests in N (found in the graph and data of the force meter): 27, 29.3, 147.4, -4.7
Average force: 51.92 N

Impulse in N*s (in the order of the forces above): 46.09, 48.88, 67.04, -48.29
 
Work is related to force.  Work is, according to the textbook, the transfer of energy by mechanical means (hitting the volleyball) where a constant force (the hand of Rachel) is exerted on an object (the volleyball) in the direction of motion, and that force is multiplied by the object's displacement (the distance the hand moved in hitting the ball, in this case 0.72 m).  Work is measured in N*m or Joules (J).
   
Work (in the order of the forces above) in J: 19.4, 20.88, 106.12, 3.384




This data has to do with types of motion, using the tracker program.  The three pictures are in order so that all of the data found in the tracker program is displayed, starting with time 0.228 sec, 0.3 sec, and 0.366 sec.  
(The image will not allow data to be typed above this line, so this is where the expalnation begins of all of this data.) 
The "t" in the charts is the time interval as measured with the high speed camera with 500 frames per second.
The "x" and "y" are the x and y positions of the projectile (volleyball) as it moves from an origin (where the ball starts to be measured in this one). 
The "vy" stands for the velocity, in the y direction, of the projectile as it is falling and is then hit.  This is found by the equation: distance of projectile moved/time interval.  Also, velocity can be found by finding the slope of the line in the position (distance) vs. time graph (or the derivative of the displacement graph) The units are m/s.
The "ay" stands for the acceleration, in the y direction, of the projectile as it is falling and hit.  This can be found by the equation: change in velocity/time interval.  Also, acceleration can be found by finding the slope of the line in the velocity vs. time graph (or the derivative of the velocity graph).   The units are m/s*s.
The "p" stands for momentum, the product of the projectile's mass and the projectile's velocity in kg*m/s, according to the textbook.
The "K" stands for the kinetic energy of the projectile as it is falling and is then hit by Rachel, found by the equation 0.5*mass of projectile (0.226 kg)* (velocity of object)squared, measured in J.
Luckily for our group, we used the tracker program to find the velocity, acceleration, momentum, and kinetic energy, only having to adjust a few numbers (the mass of the volleyball mainly).  When analyzing the video, we had to change the frames per sec to 0.002 to adjust for 500 frames per sec on the high speed camera.  We then analyzed the video using the meter stick as our guide for setting our distance.   The following graphs below are the position (t, y), velocity(t, vy), and acceleration (t, ay)graphs, based on their labels.    



Discussion:
Above, we can see Rachel in the middle of another great spike that will be just the right speed, and when aimed properly, will get past all of the other team's defenses, giving the win to Rachel.  The only way this is possible is to be positioned so that with the maximum force and minimum work needed, Rachel can spike with ease.  Based on the data shown, it is clear that it does not take much movement of the hand, or energy, to make a volleyball move.   If Rachel can simply continue moving her arm the same distance only differing the acceleration of the arm, she can achieve any number of forces, trying to use the least energy spent to be ready for a surprise hit back.         



















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