Re: Why does the surface affect the ball bounce height

The question: Why does the surface affect the ball bounce height? I did a project on investigating the factors which will affect the bounce height of a basketball. I have found out that temperature, pressure and dropping on different surfaces will affect the height. One thing i don't understand was the theory behind why will the surface of the ground affect the bounce height of the ball. The different surfaces were grass, pebble concrete, outside basketball court and also brick. The brick seem to give the height rebound whereas the grass gives the lowest.

The succinct answer is that it has to do with the "coefficient of restitution", but that's not really an answer as much as it is a classification of the phenomenon. The underlying cause of the differences in surfaces is the amount of energy that is "wasted" in deforming the surface.

You can find detailed information about "coefficient of restitution" by using any of the usual Internet search engines to search on the subject. If you do so you will find, among others, these good sites:
at Wolfram
at Wikipedia
at Hypertextbook
at Univ. of Sydney

The reason that some surfaces are better at rebounding objects colliding with them is, as mentioned two paragraphs ago, whether or not the surface "wastes" energy. Collisions tend to produce sound and heat. Materials that are hard and brittle, like concrete and metals, tend to lose more energy during the collision to sound than to heat, and materials that are soft and squishy, like soft ground and grass, tend to lose more energy to heat than to sound, but usually the harder material allows more of the collision energy to return to the colliding object. When the molecules of a material can interact with each other without sliding, and can therefore return to their original positions after a collision, less energy is lost from the collision, which is the case of harder, rather than softer, materials.

Why is the loss of energy important? Collisions come in three varieties: elastic, partially inelastic, and totally inelastic. Again, do an Internet search and you will find, among others, these sites:
Elastic at Hyperphysics
Inelastic at Hyperphysics
at Wikipedia
Collisions that are elastic don't lose any of the kinetic energy of the objects to heat and sound (or other losses). In the real world that we live in there are no such things as elastic collisions, but on the subatomic scale collisions between particles (electrons on electrons, protons on protons, for instance) are elastic. (If one wants to classify the gravitational interaction between bodies that don't actually touch, such as moons or asteroids in motion around planets or stars, as "collisions", then those interactions are almost elastic, with only minor losses to "tidal interactions".) Because energy is "wasted" in collisions between macroscopic bodies, the relative velocities after collision are less than the relative velocities before collison and, therefore, by definition the coefficient of restitution of the collision is less than one. For truly elastic collisions the C.O.R. is 1.0, while for totally inelastic collisions the C.O.R. is 0.0 (which makes sense because the objects remain in contact). Other collisions (partially inelastic) have C.O.R. between 1.0 and 0.0.

Some representative coefficients of restitution:
billiard cushions: 0.72 (see Billiards Digest) [Patience is required for this site. It does eventually work, but sometimes the delays are large. It is the best site I've been able to find for this information, though, so I am giving the URL even though it is not well behaved.]
basketball on hardwood floor: 0.75 (see Physics at Central Michigan)
volleyball on hardwood floor: 0.75 (see Physics at Central Michigan)
volleyball on grass: 0.40 (see Physics at Central Michigan)
leather basketball on hard linoleum with concrete underneath: 0.81 (see blog maverick)
synthetic basketball on hard linoleum with concrete underneath: 0.79 (see blog maverick)

Consistent with the idea that energy is "wasted" in the collision for softer and malleable materials, the lowest coefficient of restitution above is for volleyball on grass, while the highest C.O.R. is for a leather basketball on a hard (with concrete beneath) linoleum floor. As you may have noticed, the object doing the colliding has something to do with the C.O.R., as evidenced by the fact that a leather basketball obtains a higher C.O.R. on the same surface than a synthetic basketball, for instance. (Of course the state of inflation of the ball also has an effect on the C.O.R. You can find some previous answers in our archives about this by using our search engine to search on "ball bounce".)

John Link, MadSci Physicist