Wider Tire = More Grip, right??? Hmm...

I'm having a debate with my physics teacher. I contend that, all other variables being equal, a wider tire will produce greater grip in the form of lateral g forces. He disagrees, stating that race cars run wider tires in order to promote cooling of the tire and are therefore able to use softer compound rubber. I can accept that, but has also stated that the size of the contact patch has nothing to do with the "grip" produced. Discuss.

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