By James Mcdaniel – May 18, 2019
When a basketball is bounced on a wooden floor all we see is a ball moving up and down physicists on the other hand see a stream of equations that attempt to make logical and empirical sense of the whole floor-and-ball situation.
One such physicist was Sir Isaac Newton. In fact, when he looked at a bouncing ball, it led him to propose a law we still use today to determine how bouncy a particular object is: the law of restitution.
When one object comes in physical contact with another object a lot of stuff happens: certain forces come into play, velocities of the objects are affected and energy is converted from one form to another.
Let’s consider the most basic example bouncing a basketball on a rigid floor. When you drop the basketball from a given height you probably just see the ball dropping to the floor and bouncing up back towards your hands.
On the surface, this looks simple enough, but there are a number of physical phenomena at play.
When the ball is held at a certain height above the ground, it has potential energy but as it’s dropped that potential energy is converted into kinetic energy just before the ball touches the floor it still has kinetic energy.
But the moment the ball touches the floor a fraction of its kinetic energy is lost in the form of sound or heat this is why the ball makes a sound and also gets heated ever so slightly.
When it’s bounced on a hard surface this is also why the ball loses some of its height with every subsequent bounce you may have noticed that a basketball bounces very well but a plastic ball isn’t as good and if you’re to bounce a lead ball it would hardly bounce.
At all rubber is more elastic than plastic which is in turn more bouncy than lead every object has a different way of reacting while interacting with another object given that how do we compare any two objects in terms of their bounciness for this we use a term called the coefficient of restitution.
The coefficient of restitution of a material tells you how it interacts with other objects it indicates the elasticity of the collision of a given object with another it’s a dimensionless quantity whose value lies between zero and one.
If an object has a high coefficient of restitution it is considered quite bouncy and if it has a low coefficient of restitution.
It won’t be as bouncy the coefficient of restitution is an integral part of newton’s law of restitution which states that wind two objects collide their speeds after the collision depend on the material from which they are made mathematically the coefficient of restitution can be expressed as the ratio of relative speed between the two objects after the collision and the relative speed between the two objects before the collision.
A collision where no kinetic energy is lost is called a perfectly elastic collision and for such a collision to occur the value of the coefficient of restitution would be equal to one such a collision would be the bounciest reaction.
An object could possibly give however a perfectly elastic collision is impossible in the real world as some energy is always lost during the collision and released in the form of heat or summoned.
On the other side of spectrum is a perfectly inelastic collision wherein the two objects stick together and move together after the collision in this case the coefficient of restitution would be zero.
Most real-life collisions are somewhere between these two extremes sports equipment companies pay a lot of attention to the coefficient of restitution of their products that are supposed to bounce or be physically deformed in some way or another in fact sporting authorities in some countries even specify an acceptable value range for the coefficient of restitution of balls and other sporting equipment all-in-all the coefficient of restitution is an indicator of the general bounciness or elasticity of an object therefore next time you find yourself conflicted about choosing between two brands of tennis balls at a sports shop check their coefficient of restitution values and you will be able to make a better bouncier decision