### Weava Collection - Research on Volleyball Physics (ball, Volleyball, force, time, ball lands)

#### The Physics of Spiking - Physics of Volleyball

• When spiking the ball, you want to apply a very large impulse to the ball so that the ball will have a very large velocity when it is hit to the other side. You want to make the ball’s contact with your hand as long as possible. The more time your hand is in contact with the ball, the faster velocity you will give it. The reason you would follow through is so that you can maximize the time your hand has contact with the ball. This is true when looking at the equations: F*(delta)t = Impulse, M*(delta)v = momentum F*(delta)t = M*(delta)v. The equations show that momentum = impulse, therefore the greater impulse you give the ball the greater momentum the ball will have, which will cause it to have a faster velocity.  When your arm approaches the ball for a spike you want to obtain a large momentum so that you can have a large impulse on the ball, This will cause the ball to have a fast velocity when it approaches your opponent. Therefore, to increase your momentum (momentum=m*(delta)v), since you can’t change your mass, you must increase your velocity. Once you have increased you momentum the impulse you have when smacking the ball will increase and your spike will fly very fast.

#### Volleyball (ball) - Wikipedia

• Indoor volleyballs are designed for the indoor version of the sport, and beach volleyballs for the beach game. Indoor volleyballs may be solid white or a combination of two or three different easily distinguishable colors. They are made in two versions: the youth version is slightly smaller and weighs much less than an adult volleyball and than the standard version to accommodate youth's use. Beach volleyballs are slightly larger than standard indoor balls, have a rougher external texture, and a lower internal pressure. They can be brightly colored or solid white. The very first volleyballs were made from leather paneling over a rubber carcass.

#### Newton's Three Laws of Motion for Volleyball | LIVESTRONG.COM

• If the floor didn’t “push back,” athletes wouldn’t be able to leave the ground.

#### Physics Of Volleyball

• The airborne time of the volleyball can be reduced even more by putting top-spin on the volleyball. This causes the ball to experience an aerodynamic force known as the magnus effect, which "pushes" the ball downward so that it lands faster. This complicates the physics analysis. The figure below illustrates the magnus effect.
• The variables a and b can be solved for in terms of the parameters La, Lb, ho, and H. They can be solved using two simultaneous equations based on the coordinates of points B and C, relative to the coordinate system xy (with origin at point A). The coordinates of point B (relative to xy) is (La , H—ho) The coordinates of point C (relative to xy) is (La+Lb , -ho) Where:
• This is the equation of a parabola in terms of x and y. This equation has the general form:
• To set up this physics analysis we must first define the different variables in the problem. The schematic below shows a top view of a volleyball court, with labels given as shown.
• The coordinate system xy is defined with the positive x and y axes pointing in the directions shown. For convenience, the origin of this coordinate system is at point A.
• To set up this physics analysis we must first define the different variables in the problem. The schematic below shows a top view of a volleyball court, with labels given as shown.
• In addition, serving the ball at a cross-court angle α does not change the time the ball spends in the air (for a given d, ho, and H). It only affects the horizontal speed of the ball (Vcosθ). So, the greater the angle α, the greater the ball speed. This can be advantageous since a higher serve velocity V can make it more difficult for the opposing team to return the shot. The analysis shown previously allows us to predict the primary kinematic behaviour of a volleyball serve, subject to the assumption that air drag and aerodynamic effects can be ignored. However, these effects can in fact be significant and must be accounted for in order to make the model prediction as accurate as possible. In th
• Where: La is the distance from the serve location (behind the end line) to the net, along the direction the volleyball is served Lb is the arbitrary distance from the net to where the ball lands on the other side of the court, along the direction the volleyball is served d is the distance beyond the net where the ball lands α is the angle the volleyball trajectory makes with the side line
• The physics behind this analysis is of a kinematic nature, since we are only concerned with the motion of the ball. This optimization problem is an interesting application of projectile motion. To simplify this analysis we shall assume that air resistance and aerodynamic effects acting on the volleyball can be ignored. From the equations for projectile motion, we have
• Points (1) and (2) make sense since a shallower trajectory means the ball reaches a lower maximum height hmax, which means the ball spends less time in the air. However, if the ball lands close to the net (with small Lb), then the ball requires a high arc. This means that the ball is airborne for a longer period of time. Point (3) makes sense since serving the ball at an ho as large as possible (with a jump serve), enables the ball to start its downward trajectory sooner (since hmax is reached sooner). This also decreases the time the ball spends in the air. To get an idea of how much time the ball spends in the air, let's say we have d = 9 m, ho = 3.0 m, and H = 2.4 m. The time the ball spends in the air is t = 0.86 seconds. A volleyball player can put the above three points into practice by practicing jump serves which (1) barely get the ball over the net, and (2) land as close as possible to the end line. The picture below shows an example of a jump serve.
• The following schematic shows a view of the volleyball trajectory, between the point of serve and the point at which the volleyball lands on the court.
• Where x and y denotes the position of the ball at any point in its trajectory, and t is time, in seconds. Combine equations (1) and (2) to remove the time variable t and we get
• Where:
• Where: g is the acceleration due to gravity (equal to 9.8 m/s2 on earth) H is the height of the net hmax is the maximum height reached by the ball ho is the initial height of the ball at the serve location V is the initial serve velocity of the ball θ is the initial angle the ball makes with the horizontal (and above it) Point A is the serve location Point B is the location just above the net, through which the ball passes Point C is the location on the court where the ball lands
• Where: La is the distance from the serve location (behind the end line) to the net, along the direction the volleyball is served Lb is the arbitrary distance from the net to where the ball lands on the other side of the court, along the direction the volleyball is served d is the distance beyond the net where the ball lands α is the angle the volleyball trajectory makes with the side line
• (1) Get the ball just over the net (2) Make Lb as large as possible (serve the ball so that it lands near the end line) (3) Make ho as large as possible (with a jump serve)
• The time that the ball is airborne (i.e. the time we wish to minimize) is given by
• The coordinates (x,y) for points B and C can be substituted for x and y in the general parabola equation given by
• We can then solve for a and b in terms of the parameters La, Lb, ho, and H. These can then be used to solve for the initial velocity V and initial angle θ of the volleyball using the following equations:

#### Volleyball and Physics - The Science of Volleyball

•  To assist gravity, you can snap your wrist which adds top spin the skids over the ball as you serve.
• " The acceleration of an object is directly proportional to the net external force acting on the object and inversely proportional to the mass of the object."  How does this relate to Volleyball? : Newton's second law of motion is a mathematical equation that explains the relationship between force, mass, and acceleration. Mass multiplied by acceleration equals net external force. A spiked volleyball creates a net external force that stings your hands when you stop it. But your hands hurt even more when you stop a ball hit by a different, stronger opponent. The harder-hit ball's higher acceleration rate results in a stronger net external force.
• To every action there is an equal and opposite reaction."  How does this relate to Volleyball? : Newton's third law explains that every action creates a force that is met by an equal reaction force from the opposite direction. When two objects interact, they exert a force on each other. The action force of a spiked ball meets the reaction force of a player's block. A team scores a point when the action force of a spiked ball meets the reaction force of the opposing team's court. The hard floor has more force than the soft ball, so the ball bounces off the court to equalize the reaction of the impact.
• When spiking, you exert a downward force on the ball so that it falls rapidly on the opponent's side of the court, making it very difficult for your opponent to return the ball. Gravity works in your favor when you spike, because it also exerts a downward force that makes the ball fall to the court floor. For this reason you do not necessarily have to exert tremendous downward force to spike effectively, because gravitational force is also acting on the ball in the same direction.
• Gravitational force, or the force of attraction between an object and the Earth, has an impact on every element of Volleyball. Whether you are serving, bumping, or spiking, gravity will affect every interaction you have with the ball.
• To account for the force of gravity, simply follow through with your forearm when bumping, to exert force on the ball, over a longer period of time. This will cause the ball to go higher and ensure that the target player has time to prepare herself beneath the ball.
• volleyball shot by dividing the distance your ball traveled by the amount of time it took to get there
• As gravity pulls the ball to the ground, it accelerates
• When digging a volleyball, you are exerting a sharply upward force to prevent it from hitting the ground. However, gravity is exerting a downward force on the ball, and if you do not account for this you will not hit the ball high enough to prevent it from hitting the ground. To account for this, bend your knees low to generate force with your legs, when digging. This will ensure that you hit the ball high enough for your teammates to get in position.
• upward and forward force
• " An object at rest will stay at rest, and an object in motion will stay in motion unless acted upon by an unbalanced force."   How does this affect Volleyball? : Newton's first law of motion affects every volleyball player who botches a serve and sends the ball snacking into the net. Every player who blocks a hard-hit ball from an opposing player feels the law's effect on her stinging arms. The server's hand, the net, and the blocker's forearms acted as an unbalanced force that stopped, or changed, the direction of the ball, the object in motion.

#### Importance of Science in Volleyball | SiOWfa15: Science in Our World: Certainty and Controversy

• . Velocity is the speed of the movement, and it is calculated by using the equation velocity = displacement/time
• There are several other scientific components that are present in volleyball such as work and velocity. Work is defined as the displacement of an object due to force. The corresponding equation being work = force * distance.

#### Biomechanical Principles of a Volleyball Spike

• The airborne time of the volleyball can be reduced by putting top-spin on the volleyball. This causes the ball to experience an aerodynamic force known as the Magnus effect, which “pushes” the ball downward so that it lands faster (Linnell, Wu, Baudin, & Gervais , 2007) it also reduces the time the opposing team has in deciding how to return the ball. The figure below illustrates the Magnus effect.
• As the ball spins, friction between the ball and air causes the air to react to the direction of spin of the ball. As the ball undergoes top-spin (shown as clockwise rotation in the figure 2), it causes the velocity of the air around the top half of the ball to become less than the air velocity around the bottom half of the ball (Linnell, Wu, Baudin, & Gervais, 2007). This is due to the tangential velocity of the ball. The top half turns in the opposite direction to the airflow, and the ball in the bottom half turns in the same direction as the airflow. This causes a net downward force (F) to act on the ball. Interesting flight paths can be made with volleyballs due to the surface of the ball being uneven and a varying surface roughness from the panels during the flight (Blazevich, 2010). This force is useful for reducing the balls airborne time decreasing reaction time for opposing team.