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|These two (apparently) similar balls are bounced.|
One ball bounces significantly higher than the other.
The "hard" (smart) ball is made up of polybutadiene to which an unusually large amount of sulfer has been added (up to 15 parts of sulfur per 100 parts of polybutadiene). There is extensive cross-linking involved in this polymer, so it dissipates very little energy in the form of heat when it bounces.
The "soft" (stupid) ball is a block co-polymer, such as poly(styrene-butadiene) or poly(vinyl-butadiene). It has very little significant resiliance. It should be noted that poly(styrene-butadiene) is used for automobile tires, which absorb some of the energy associated with the bumps along the highway.
An NSF funded Project