## My Initial Variation of this Question

If a car passes by every 4 minutes on a highway the cars on the highway increase the roads temperature from wheel friction, by this equation 40mph *0.001* car number=i. The tire friction of these cars warm the road from 0 degrees to 5 degrees Celsius. How many cars have to pass in order to warm the road to 5 degrees Celsius. Keep in mind that between the cars the surface of the road cools this is represented by the fallowing equation: T=i^0.25/4 T= temperature 0<i=5.

**My thoughts on this problem**

This initial question was very inaccurate, rough, and unrefined in it's explanation of how to properly do the math for this problem. Initially I did not even use correct ways to calculate heat capacity of materials and rate of heat gain.

## Heating Roads With the Friction of Cars

This question was inspired by my many experiences of snow melting off of a road just where the tire marks were on the road. I knew that this phenomenon was often caused by the friction and pressure of the tires on the road warming it just slightly above 0 degrees celsius. So it came about that I would use this question of mine to try and discover how I could implement this wonder of mine and implement it into a mathematical question.

You can find the answer using the following equationmass of the portion of road * the capacitance of the asphalt *change in temperature=#of cars

or m*c*t=C

The capacitance of asphalt is .91o joule per gram degree celsius. The section of road that we will be evaluating in this equation is 10 feet by 1 foot by 3 inches. On average asphalt is 145 lbs per cubic foot.

or m*c*t=C

The capacitance of asphalt is .91o joule per gram degree celsius. The section of road that we will be evaluating in this equation is 10 feet by 1 foot by 3 inches. On average asphalt is 145 lbs per cubic foot.

**My thoughts on this problem**

I now realize that in this problem that some components were rushed and needed to be refined. A benefit of my first rough draft was that I developed the idea of heat loss in the road between cars.