A truck of mass M has 4 wheels. The surface area of the metal disc in each wheel is A. When brakes are applied the brake shoe in each wheel rubs against the metal disc. This produces heat. We will assume that this heat is used to heat the disc in the wheel only. Each disc has mass m and is made of material of specific heat capacity s. One day the truck was going downhill on a road inclined at angle `theta` to the horizontal. To maintain a constant speed v the driver had to apply brakes. The only other dissipative force, apart from the brake force, on the truck is the air resistance force that is equal to F. Assume no heating of discs due to air friction.
(a) Find the initial rate of rise of temperature of each metal disc after the brakes are applied.
(b) Find the final temperature (T) of the disc assuming that it is a black body and it loses heat only through radia- tion. Take the atmospheric temperature to be `T_(0)`

Answer

(a) `(dT)/(dt)=((Mgsintheta-F)/(4m.s))v`
(b) `T=[((Mgsintheta-F)v)/(sigmaA)+T_(0)^(4)]^(1//4)`