The Physics of Volleyball
           

    Forces, acceleration, gravity, projectile motion, and many other such things make volleyball the game that it is.  Volleyball is a sport that includes many aspects of Physics some of these are very basic concepts while others are more advanced.  Better understanding of these concepts could improve a player’s game.  Physics explains and elucidates the basic fundamentals of volleyball and why one should perform them in such a way.

            Displacement is one of the basic concepts of Volleyball that need be understood for the reason that it is needed to understand later concepts.  There are six players on the court and each one has a designated position.  For example there are; left-side hitters, middle hitters, right-side hitters, and the same pattern follows for the defensive players.  However, because there is a set rotation, a player will not always begin in their set position and they have to move to that place. This is called displacement.  Displacement is defined as the change in position of an object ad can be either positive or negative depending on the starting point and the direction.  The equation to represent displacement is d=d2-d1.D is the total movement between positions.  The first floor position would be d1 and the second would be d2.  Beyond the fact that players have frequent displacement, the ball itself has displacement.  In fact this happens constantly as it moves from one player to another and from one side of the net to the other.

            Now that the ideas of displacement are understood velocity and acceleration can be found.  Average velocity and average acceleration are complimentary of each other and are both important to the concept of volleyball.  Velocity is defined as displacement in a given time.  Once can find velocity by dividing distance by time.  So the equation for velocity is: v=d/t.  It is possible, with this equation, to find how fast the ball moves from one place to another and how fast a player moves to different spots on the court.  A coach always wants their players to be quick on the court.  They mentally assess how much distance they can cover in a short period of time; or technically speaking, their velocity.  Acceleration is the rate of change of velocity.  Players as well as the volleyball have acceleration.  This will be discussed more later.  Acceleration can be used to find the speed of a player whose velocity increases and decreases during a certain amount of time that they are in motion.  Acceleration has both direction and magnitude.  When a player moves forward and speeds up they have positive acceleration.  If a player moves forward and slows down they have negative acceleration.  The formula for average acceleration is A avg= (Vf-Vi)/ (tf-ti).

            Another very basic concept of physics that affects volleyball is gravity.  It affects every aspect of the game; the players, the ball, the net.  If there was not gravity the ball would never come down and there would be no such game.

            To this point, only one-dimensional aspects of volleyball have been discussed.  A volleyball set, served, or passed, however, moves in two dimensions (both up and forward).  This is influenced by the downward pull of gravity and horizontal motion, it is known as projectile motion.  Projectile motion can be defined as free-fall with an initial   horizontal velocity.  These projectiles follow parabolic trajectories.  Ignoring air resistance, the volleyball would travel along a parabola.  Nevertheless, there is air resistance and the volleyball travels along a shorter path.

            The game of volleyball envelops the forces (a force causes a change in the motion of an object) that exist in nature, which are described in Newton’s Laws.  Newton’s First Law says: An object at rest remains at rest and an object in motion continues in motion  with constant velocity unless it experiences a net external force.  This law is also known as the law of inertia.  Examples of this law are seen in many different situations on the court.  If the ball is falling it will continue falling until it hits the ground or is acted upon (passed, set, or hit) by another player or force.  Also, the volleyball net will not move unless it’s hit by a player.  Newton’s Second Law states: The acceleration of an object is directly proportional to the Force and inversely proportional to the mass of the object.  This can be seen in the equation F=ma.  The force a ball is hit with can be found using this law.  Finally, Newton’s Third Law explains: There is an equal and opposite reaction for every action.  A force acting on a body is the result of its interaction with another body, so forces always come in pairs.  In this case, action and reaction are the two opposite forces, or the action-reaction pair.  The force of the volleyball hitting the forearm of the passer would be considered the action; the force of the passer on the ball would be the reaction.  This law explains the mechanism of how one would pass a ball.

            When someone passes (sets, hits, or serves) a volleyball the ball moves in the direction that the passer is aiming (at the setter’s hands).  This statement is very important for two reasons: first because the ball moves when the payer comes in contact with it and secondly because the ball moves in the direction that the player passes it.  This essentially means that the ball moves in the direction that the force has been applied.  This is called work.  Whenever a force causes displacement to an object it is called work.  The ball is constantly being displaced; therefore, work is constantly being done.  The equation that defines work is: W=Fd.  An angle between the force and the direction of displacement (theta) makes the equation: W=Fd(cos(theta)).

            Total work done to accelerate the volleyball from rest to speed, according to the work-energy theorem, is equal to the amount of kinetic energy it undergoes.  Kinetic energy is defined with the equation K=1/2 mv^2.  The energy of the motion of the ball is dependent on its speed and mass.  In order to have a different kinetic energy concerning a specific volleyball, the velocity would have to change, because the mass will always stay constant.  Potential energy is stored energy.  The equation to represent it is: PE=mgh (g being free-fall acceleration).  The amount of potential energy depends on an objects height from a zero level.  A ball being held in the air ready to be served has more potential energy than a ball being held at the waist.  When someone is approaching to hit a volleyball they are instructed to plant and take off quickly.  This has to do with the concepts of potential and kinetic energy.  During the approach the player has kinetic energy (energy of motion).  The idea is to transfer it into potential energy.  The kinetic energy would be less if one came to a stop, and they wouldn’t be able to jump as high.  It is important to remember that potential energy is the product of mass, gravity, and height of the jump.   So the height is what determines how much potential energy can be achieved.  Potential and Kinetic energy are important in many aspects of the game, but especially in the hitting approach. 

            Power is very important in volleyball.  Maximum power is desired to have the most force behind a hit or serve.  Power is the time rate at which work is done.  When pairing this with the concepts of energy, the arm swing comes to mind.  The faster the arm swing, the more power there is behind the ball.  This supports the definition of power.  There are also many different areas where power is used in the sport, however the most obvious is hitting. 

            The net force acting on a particle equals the time rate of change of momentum of the particle.  There are two types of momentum that exist in volleyball.  The first is the emotional momentum and does not relate to physics.  The second can be described by the equation p=mv.  The direction of the momentum will match the direction of its velocity.  A middle hitter will have more momentum than a defensive specialist.  This is because one, she is probably bigger, and two, she is required to move at much higher speeds than a defensive specialist.  From the momentum-impulse theorem, momentum is equal to the force exerted on the ball multiplied by the time the force is exerted.  Therefore, the shorter amount of time the players hand is in contact with the ball, the greater the force applied to the ball will be.  The momentum from the approach is already great, so the force will be great if the time is short.  This is also evidence to support why the arm swing should be fast.  It will lessen the amount of time that the hand is in contact with the ball.

            Momentum is conserved in collisions.  Collisions are very important because they happen all the time in volleyball.  There are three types of collisions.  The first is a perfectly inelastic collision where two objects stick together and move with the same velocity after colliding.  The second is an elastic collision where the total momentum and total kinetic energy remain constant.  The third is an inelastic collision where two objects deform during the collision making the total kinetic energy decrease and the objects move separately after the collision.  Inelastic collisions occur during volleyball.  When the ball hits the player’s forearm the ball and the arm momentarily deform or dent before the ball bounces off the arm.  This happens anytime the ball is touched.

            In conclusion, all of these ideas can be incorporated to evaluate some of the fundamentals of volleyball.  First of all is the dig (pass of any kind).  If one were to attend a volleyball practice or game they might hear a coach telling their players to absorb or cushion a hard hit.  It is also true that they need to shrug their shoulders more and really use their hips for slower hits and serves.  Cushioning a hard driven hit increases the time of contact, which in turn, decreases the force applied to the ball because for the fact that force and time are inversely proportional in the impulse momentum theorem.  A slower incoming ball demands a greater force to get to the same target.  The player shrugging their arms more and getting under the ball and using their hips to pass produces the desired results.  Some tips include balancing ones weight on the balls of their feet in ready position.  The center of gravity is low and a little forward; using this stature will allow the player to move in any direction with ease.  Relaxing the arms and absorbing the power of a hard hit is another vital basic.  Discussed earlier were ways to attain maximum power when hitting the ball.  Now from a defensive standpoint, it is important to relax and stay low allowing for cushion and more surface time with the volleyball.  In the large scheme of things this lessens the kinetic energy and power of the hit, which makes it easier for the setter to make a play.

            Secondly, these concepts can help someone master a serve.  The first basic idea is to contact the ball high, above the head, with the arm extended and in front of the serving shoulder.  Starting like this will set the server up to reach maximum power and accuracy.   The player then needs to accelerate their arm and rotate their shoulders into contact, hitting through the center of the ball.  Physically speaking this deals wit many various topics including: acceleration, rotation, center of mass, projectile motion, and even the spin of the ball from rotating the shoulders into the serve.  Contact on the ball needs to be short and controlled.  Again, this allows for maximum power when considering time interval and the momentum impulse theory.

            It is safe to say that the majority of people that play or watch volleyball enjoy the hitting aspect of the sport most.  Although it is not readily observed or contemplated, hitting is based on physics.  For instance, before the player can attack the ball they need to watch the set and read it’s trajectory, speed, and placement in order to calculate where the approach should begin and how fast or slow it will need to be.  Does the player sit and contemplate these things on the court, no.  However, the brain sorts these factors out to help ones timing.  The equation v=d/t (velocity), can help one process how much time their approach should take according to the ball speed and the distance it will travel. When the hitting approach is taught there is a lot of emphasis on moving continually through the footwork so that there is acceleration in to the plant and take-off.  This is important for maximum energy and power.  Also, one needs to plant and take off quickly.  The shorter the time interval with the ground during the “lift-off,” the higher the jump will be.  Maximum speed can be acquired by rotating the hips, shoulders, and arm into the hit.  When hitting the ball it is essential to transfer the maximum amount of momentum from the player’s body to the ball.  From the momentum-impulse theorem, momentum is equal to the force exerted on the ball multiplied by the time the force is exerted.  For that reason, the shorter amount of time you r hand is in contact with the ball the greater the force on the ball will be.  To get the most force, the ball should be contacted with a whip-like motion.  This is also known as the wrist snap.

            Although Physics is not something we would readily think about or explore when considering volleyball, it is obvious the game would not even exist without such knowledge.  Using the concepts of Physics one can create a much better understanding of the game of volleyball.

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Moellendorf, Suzanne.  The Physics of Volleyball.  1999.  Yahoo Search 10/5/03.