Physics 215 Project Spring 1998.
Basketballs Colliding in Midair
 
 
Scott P Civils
 
Abstract

    Two basketballs were thrown towards each other and collided in mid air. A video was made of the process and used as input for the "World in Motion" program. The paths of the basketballs were marked on the video and after inputting length and time scales and the mass of the basketball the program computed graphs showing the time variation of momentum and energy. The observed graphs were compared to ones simulating the motion produced in the "Interactive Physics" program. This allowed us to determine what forces were acting on the basketballs.

 
 
CONTENTS

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Fixed Image with Marked Data Points
 
 

    The above image shows the data points made with each step and some data relating to the objects in the image. The meter rule on the ground benchmarks distance for the "World in Motion" program. Time is benchmarked by setting the Frames Per Second (FPS) in "World in Motion" to the FPS rate at which the video was made.


 
Movie of the Motion of the Basketballs

 

 
Above is the actual video of the two balls colliding.


 

 

Graphs of the Change of Momenta of the Balls and the Center of Mass
 

 

    This graph shows the momentum in the X direction (red and green) of both balls ( 1 and 2) and the total momentum in the X direction (blue). The point where the lines cross (approximately zero momentum for each ball) is the point where the balls collide with each other. It can be seen from this graph that total momentum in the X direction varies slowly during the experiment. The individual momenta are decreasing in magnitude with time before the collision and stop increasing or decrease after the momentum changes produced during the collision.

 
 
    This graph (color scheme is the same as the previous graph) shows the momentum in the Y direction of both balls and the total momentum in the Y direction. This graph shows that the total momentum in the Y direction is continually decreasing.


 
 Graphs of Change of Energy During Motion

 
  This graph shows potential (blue and green) , kinetic (red and green) and total energy (red) (for both balls. It can be seen that the gravitational potential energy increases and decreases as expected. The kinetic energy distinctly shows the place where the balls collided. The total energy does not seem to be conserved.


 
Movies of Interactive Physics Animations
With gravity and air resistance
 
 
Fixed enlarged view

 

     This video from Interactive Physics shows a simulation of the action we performed. The graphs in this video show that neither momentum in the X nor Y directions are conserved just as it was in the World in Motion video. It also shows that the Y momentum is distinctly altered by outside forces just as in the experiment from above.

    The graphs show the change of energy of the balls during the motion, clearly the total energy is not conserved.

    The Interactive Physics program has the gravity force set in a vertical direction (downwards) with a magnitude that corresponds to normal earth gravity, and air resistance set as normal atmospheric air resistance (for earth).

 



    In order to examine which forces are acting on the basketballs we considered animations without gravity and air resistance.

Without air resistance

 

Fixed enlarged view

    Without air resistance one sees that the velocity in the x-direction is constant before and after the collision, this is not observed in our experiment thus one can conclude that air resistance is present.


 
Without gravity
 
Fixed enlarged view

    Without gravity but with air resistance the velocity in the x and y directions just slowly decrease before and after the collision. This was not true for the velocity in the y-direction in the experiment, which decreased quickly all the time, showing the presence of a downward gravity force.

  


 
Without both gravity and air resistance
 
 
Fixed enlarged view
 

    Here we see the idealized situation of no external forces during the collision process, the velocity in both the x and y direction stays constant after the collision showing the absence of all external forces.