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Name: Jake
Status: student
Grade: 6-8
Location: FL
Country: USA
Date: Winter 2009-2010


Question:
How do the density and chemical makeup of a ball affect its bounce?


Replies:
Wow, Jake. This might sound simple, but it is a really complicated question to answer! When a ball bounces, its kinetic energy (energy of motion) is converted into potential energy by deforming the ball. If you look at a rubber ball when it hits a solid surface, it deforms a lot (there are lots of slow-motion videos available online)! Then, the energy used to deform the ball is converted back to kinetic energy as the ball returns to its original shape.

Basically, the chemical makeup of the ball determines how much it can be deformed, and how much of the original kinetic energy is converted back to kinetic energy. This is called the "elasticity" of the ball (the term elasticity has other meanings -- I'm over-simplifying a bit). An "elastic" collision means all (or nearly all) of the energy is returned back to kinetic (motion) form. An "inelastic" collision means the energy is dissipated by some other means.

Balls made of elastic materials like rubber or air-filled leather (basketballs, footballs, baseballs, golf balls, etc.) will bounce back because the material can "stretch" or "deform" (storing the kinetic energy) and then "unstretch" or "re-form" releasing that energy back into kinetic form. A ball made of, say, mud, can deform, but cannot store and re-convert that energy, and so it will not bounce as high (and if it is really wet mud, it may not bounce at all). If a ball does a poor job of converting the deformation energy back into kinetic energy, it will not bounce well (like an under-inflated basketball).

The density of the ball really does not play a strong, direct role. The mass of the ball (which is related to density) along with velocity determines its kinetic energy when falling or being thrown. If the energy is too great for the materials in the ball to absorb, the ball might break/pop/collapse when impacting something rather than bouncing as expected.

Hope this helps,
Burr Zimmerman


Jake,

This looks like a very simple question but the answer to it is quite complex.

Let's think of what makes anything, a ball, "bounce". In the simplest terms, when something like a ball hits a wall, the ball gives its energy to the wall. The wall will either absorb the energy (convert it to kinetic energy or heat) or send it back to the ball. If the energy is returned to the ball, the ball will either convert that energy to heat or kinetic energy. If the ball converts the energy mainly to kinetic energy, how well the ball is held together will control whether the ball bounces or goes splat.

So, let us think of 4 types of balls: a ball of steel, a ball of rubber, a ball of snow, and a ball of thick syrup. When a steel ball hits a wall, the energy is returned to the ball, and because the steel ball is very stiff, the molecules do not move away from their current location very much, so the steel ball moves as a complete unit away from the wall. The energy is converted to kinetic energy of the whole ball. A rubber ball on the other hand will flex. It is not as hard as steel. But since the rubber holds together the energy is still converted to a kinetic energy for the whole ball. A ball of snow will also flex, but because the particles in the ball is held very loosely, the particles all fly in different directions and the ball disintegrates into many smaller pieces. The energy is converted to kinetic energy of all the smaller pieces of snow. Finally the ball of thick syrup will also flex, but because the particles are held together but can move around within the ball, the ball does not disintegrate like the snow ball, but it does not bounce like the rubber ball either. The energy makes all the particles move around faster, the temperature of the ball goes up, but the mass of the syrup ball does not bounce - the energy is not converted to a kinetic energy for the whole ball. It is converted to energy for individual particles with no particular direction.

So, the short answer (too late right?) is that what happens to the ball depends on how well it is holding itself together.

Greg (Roberto Gregorius)
Canisius College



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