Why do racing tires (slicks) provide more traction with the road? Google: By eliminating any grooves cut into the tread, such tires provide the largest possible contact patch to the road, and maximize traction for any given tire dimension.
My understanding is that the friction force between any two object does not depend on the area in contact. So there should be the same friction force between the tire and the ground whether the tire is smooth or not. How does this relate to traction and tractive forces?
Does it mean that for two identical cars A and B. If A has slicks and B has treaded tires. The engines are of equal power. They will have the same friction with the road but because A has better traction it will accelerate at a higher rate?
 A: One thing everyone seems to have forgotten is the "tar" in tarmac. There is more than just friction on a race track there is also adhesion. drag strips will typically have fresh tar at the beginning and be very tacky. think of it like the tires being glued to the track both by the tar and the melted "rubber" material of the tires. the more surface area for the glue, the stronger the adhesion.
A: The claim that frictional force does not depend on area of contact is not, in general, true. 
It is a good enough approximation for many cases that it can be used for many real world calculation and even more back-of-the-envelope estimates, but it fails under several circumstances.
Conditions for failure of the not-area-dependent approximation include (but are not limited to):


*

*Either surface suffers permanent deformation

*Either surface deforms through a linear distance comparable to the size of the contact patch.

*Either material is stressed beyond it's linear deformation limit.


The most common day-to-day situation where the Physics 101 model for friction breaks down is tire-on-road friction, and especially when softer rubbers are used in the tire surface.
To get a sense of the complexity of tire-on-road friction, find some paper on the matter and just read the abstract. It's a live problem despite a lot of money pushing to understand it.
