Why don't they use normal air in race car

Many race car teams use nitrogen instead of air in their tires
because nitrogen has a much more consistent rate of expansion and
contraction compared to the usual air. Often, a half pound of
pressure will radically affect traction and handling. With track and
tire temperatures varying over the duration of a race, the consistency of nitrogen is needed. Nitrogen pressure is more consistent than
normal air pressure, because air typically contains varying amounts
of moisture due to changes in the relative humidity on race day.
Water causes air to be inconsistent in its rate of expansion and
contraction. So, a humid race in the southeast United States or a dry
race in the desert western United States could make for
unpredictable tire pressures if "dry" nitrogen were not used.

Nitrogen is also used in the high-pressure tires on large and small
aircraft.

Where does the rubber of the tire go that wears
out from driving on the road ? What effect does this "rubbed
off" rubber have on the environment?

We can see rubbed off rubber patches wherever cars skid - skid
marks are everywhere. The rubber tends to stick to the road, or
gradually blow off as dust. I do not honestly think anyone has ever
thought about the environmental effects of rubber dust, but I could
be wrong. A much bigger problem is what to do with the tires after
the tread wears off. And the exhaust gasses from cars probably have
a bigger environmental impact than rubber dust.

At what temperature does a car tire melt and at
what temperature does asphalt melt?

Neither tire rubber nor asphalt "melt" in the usual sense of the term.
They soften over a range of temperature depending upon the
composition. Asphalt will 'flow' if it is hot enough but that is not
usually considered "melting" which is usually confined to cases
where the transition occurs at a sharp temperature.


Is there a formula for how the weight of motor
vehicles effect highways?

It is probably not just the weight of the vehicle that is important but
theweight, number of tires supporting that weight and their total
surface area exposed to the pavement. Therefore, I think that the
pressure exerted bythe tires on the road should be compared with
the yield strength of the asphalt.

Damage done by a given vehicle increases roughly with the fourth
power of its weight. Put another way, if you double the weight of a
vehicle, then the damage it does gets doubled four times. This
means That double the weight causes 16 times the damage.

Spreading the weight over many wheels and many axles greatly
reduces damage caused per pound of vehicle weight. Also, axles
spaced just a few feet apart do less damage than axles located
individually when used on asphalt pavement. On concrete
pavement, the damage is independent of the axle spacing.

Cars do little or no pavement damage in comparison to large trucks.
It takes approximately 12,000 cars to do the same damage as a
single 80,000 pound 18-wheel truck. Engineers who design
pavement typically ignore the number of cars and only concern
themselves about the number of trucks.