Properties of Rubber: Resilience & Applications

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Do you know why it's important for rubber to be resilient?
and does anybody have an example of an object that is made out of rubber which must be resilient?
and does anybody know why it's important why tires and children's play grounds are made from resilient materials?
Many thanks,
 
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Resilient means that they retain their original shape after being deformed.

For a tire (which are no longer made from rubber!) you want a deformation where "the rubber meets the road" ... this improves your stopping ability ... and keeps the vehicle from slipping on turns, etc. But you also want it to "return to round" or you will have a bumpy ride.
 
Vulcanised Rubber

What implications of physics does vulcanised rubber have?
Basically, what are the risks and benefits of vulcanised rubber?
Many thanks,