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.
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.
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.