Download Chapter 5 The Science of Soccer

Science of Soccer Reading
Bouncing of the Soccer Ball
(Courtesy NASA)
1910 soccer ball [ii] 1950 soccer ball [ii] 2004 Euro Cup ball [ii]
In the late 1980s, the leather casing ball was replaced by totally synthetic ball in soccer competitions. The
covering material of the totally synthetic ball is synthetic leather made from polymer. For high quality ball, the
casing is made of the synthetic leather panels stitched together through pre-punched holes by waxed threads.
The bladder of a totally synthetic ball is usually latex or butyl bladder. The ball is then inflated by pumping air
into its bladder through a tiny hole on the casing. The totally synthetic ball could resist water absorption and
reliably maintain its shape.
How Things Work
Air pressure
Air is consisted of a number of tiny particles called air molecules. By
definition, pressure is the average amount of force exerted on unit
area of a surface by a fluid. Thus air pressure tells us how much
force the air molecules pushed on a fixed region of an object's
surface that is surrounded by the air. Air molecules are not
stationary and they move in random directions with a typical speed
greater than that of a jumbo jet. Due to the random motion, the
molecules continually bombard with each other.
Moreover, the air molecules would hit and thereby exert force on the
surface of any object exposed in the air which gives rise to the air
pressure.
In the "Laws of the game", "pressure" stands for the air pressure
inside the ball. And "atmosphere at sea level" refers to the amount
of force that the air in the Earth's atmosphere is pressing against us
at the altitude of 0m, which is equal to about 10 newtons per square
centimeter. For a surface of 1 square meters large, the force is about
100000 newtons which is equal to the weight of a bus!
The pressure of the soccer ball defined in the
"Laws of the game" is unexpectedly low. In fact,
the ball would collapse if its inside pressure is
smaller than one atmosphere. And the ball is not
hard enough even at a pressure of 1.1
atmosphere. The true meaning of the rule is a
pressure difference between the inside and
outside of the ball.
Figure explaining the extra pressure inside the
soccer ball.
How to make a ball with extra air pressure inside? The extra air pressure is attained by pumping extra air
molecules into the ball. Then there would be more air molecules in each unit volume of space inside the
ball. As a result, the number of air molecules pushing the casing of the ball outward would be more than
that pushing inward for each unit area of the ball's surface. Such imbalance of force leads to the pressure
difference between the inside and outside of the ball.
Obviously, a good soccer ball should not be too heavy to kick, or so light that it will not carry while it
should not be too large or too small to control. In fact, the weight and size of the soccer ball defined by
the "Laws of the game" agree closely with the requirements of a good soccer ball found by trial and.
How to make a ball with extra air pressure inside? The extra air pressure is attained by pumping extra air
molecules into the ball. Then there would be more air molecules in each unit volume of space inside the
ball. As a result, the number of air molecules pushing the casing of the ball outward would be more than
that pushing inward for each unit area of the ball's surface. Such imbalance of force leads to the pressure
difference between the inside and outside of the ball.
Bouncing of ball
If a soccer ball is dropped on a hard surface, it will bounce back to a height lower than its initial position.
Such kind of motion is called the bouncing of the soccer ball, which plays an important role in the motion
of the ball. Let us study the mechanism of the bouncing of the ball in details.
In fact, the mechanism of the bouncing of different
kinds of spherical balls are similar and thus we can
study the bouncing of a spherical ball instead of
soccer ball only. However, different types of balls
have different bounciness (different bouncing
abilities), as shown in the above chart. For
example, the baseball is less bouncy than the
soccer ball, i. e. the baseball will bounce back to a
much lower position than the soccer ball if they are
dropped from the same height. Why some balls are
bouncy while some others are not so bouncy? It is
determined by the elasticity of the ball. A more
elastic ball has more bounciness.
The relative bounciness of different
types of balls [iii]
Elasticity of the ball
The elasticity of an object means the tendency of the object to
return to its equilibrium shape, the natural shape of the object with
no net force applied on it, when it is being deformed. And the force
for the object to restore to its equilibrium shape is called the
restoring force, which is always directed in opposite to the
deformation of the object
Almost all real rigid body are elastic, i. e. having certain extent of
elasticity. A trivial example of an elastic object is the spring. You
probably have the experience that a spring would tend to restore
to its original size when you stretch it to be longer.
The restoring force Fs on a spring
in case of different extension
Scientist found that, providing the deformation is not too large, the relationship between the distortion
and the restoring force is given by the Hooke's law:
"The restoring force exerted by an elastic object is proportional to how far it has been distorted
from its equilibrium shape."
Note that the Hooke's law no longer holds if the object is distorted too much that it has been permanently
deformed.
Work must be done in order to distort an elastic object. Therefore, if you pull a spring outward so that it
become longer, some energy must have been transferred from yourself to the spring. The energy stored
in an distorted object due to its deformation is called the elastic potential energy
So, when talking about the elasticity of the ball, we are indeed talking about the spring-like behavior of
the ball. In other words, we are considering the tendency of the ball to return to its original spherical
shape when it is being squeezed.
Where does the elasticity of the ball come from? The elasticity of a solid ball arises from the elasticity of
the constituting material which is due to the inter-atomic or intermolecular force inside. In contrast, for
air-filled ball like soccer ball, its elasticity is resulted from the extra air pressure inside the ball.
at happens to a ball after you dropped it above a hard floor? The gravity pulls the ball toward the ground
and thus the ball falls leading to the lost of its gravitational potential energy. By the law of conservation of
energy, the ball must gain kinetic energy and so it falls towards the ground with an increasing speed.
Subsequently, the ball hits the hard floor with a high speed. (Note that the ball always moves with the
downward acceleration of g = 9.8 m/s2 as it falls.)
(Note that here "E.P.E." stands for the elastic
potential energy.)
The path of a bouncing tennis ball
Chart of energy conversion in the ball from falling
to rebound.
The net effect of the bouncing of the ball is that the kinetic energy before the impact must be larger than
that after the impact. That's why it is impossible for a ball to be perfectly elastic, i. e. retaining all the
kinetic energy before the impact. In fact, the loss of the kinetic energy would be smaller for a more elastic
ball. Thus the elasticity of a ball can be measured by the ratio of the speed of the ball before and after the
impact which is called the coefficient of restitution e:
Note that the coefficient of restitution is larger for a more elastic ball. The coefficient of restitution would
be equal to one for a perfectly elastic ball bouncing on a hard surface while it is equal to almost zero for a
putty ball. For a typical soccer ball hitting on a hard floor, the coefficient of restitution is about 0.8 and
thus its speed would be reduced by 20% after the impact.
It can be shown that the coefficient of restitution is also proportional to the ratio of the drop height to the
rebound height:
As a result, a ball with smaller coefficient of
restitution rebounds to lower height in successive
bounces and a shorter time is required for the
ball to stop (see below figure). For example,
grass reduces the coefficient of restitution of a
soccer ball since the bending of blades causes
further loss of its kinetic energy. Therefore, it
would take a shorter time for the soccer ball to
stop if it is kicked on grass instead of hard floor
The path of the bouncing ball for different
coefficient of restitution (C.O.R.) where e1 > e
Glossary
Elasticity:
The property of an object by which it tends to resume its original size and shape after being deformed by
a force.
Mechanical Elastic potential energy:
The energy stored by the forces within an distorted elastic object.
Gravitational potential energy:
Energy associated with the position of a mass in the gravitational field. The gravitational potential energy
of an object on the surface of the earth equals its weight (the force of gravity exerted by the object) times
its height above the ground.
Inertia:
A property of matter by which it remains at rest or in uniform motion in the same straight line unless
acted upon by some outside force.
Isolated system:
A type of system in which matter and energy are not exchanged with the surroundings; a closed system.
Mechanical Kinetic energy:
The type of energy associated with moving objects; the energy of motion. Kinetic energy is equal to the
mass of the moving object times the square of the object's velocity, multiplied by 0.5.
Momentum:
Synonym of linear momentum. The product of the mass and the velocity of a particle.
Newton's 3rd law of motion:
For every force that one object exerts on a second object, there is an equal but oppositely directed force
that the second object exerts on the first object.
Pressure:
The average amount of force a fluid exerts on unit area of a surface.
Restoring force:
A force that acts to return an object to its equilibrium shape. A restoring force is directed toward the
position the object occupies when it's in its equilibrium shape.
Mechanical Work:
The mechanical means of transferring energy. Work is defined to be the force exerted on an object times
the distance that object travels in the direction of the force.