# Problem: When a car brakes, a brake pad is pushed firmly against a disk, which allows the wheels to slow down. The effectiveness of brakes is limited by something known as “fade” – a rapid drop in friction. In a typical brake pad, the friction surface should remain below 450°C to prevent fade. For all problems, assume that the air temperature is 23°C. (a) For a brake pad 1.65 cm thick, with an area of 53 cm  2 and a thermal conductivity of 12 W/mK, what is the maximum heat current through the pad that won't cause fade? Assume that the same amount of heat leaks out of the sides of the pad as goes straight through it.         (b) For a disk 1.1 cm thick, with an area of 268 cm  2 and a thermal conductivity of 43.5 W/mK, what is the maximum heat current through the disk that won't cause fade? Assume that the amount of heat leaks out of the sides of the disk as goes straight through it.         (c) For a 2000 kg car going 30 m/s, what is the shortest stopping distance the car can achieve without inducing fade? Assume that the car has 4 uniform brakes.

###### Problem Details

When a car brakes, a brake pad is pushed firmly against a disk, which allows the wheels to slow down. The effectiveness of brakes is limited by something known as “fade” – a rapid drop in friction. In a typical brake pad, the friction surface should remain below 450°C to prevent fade. For all problems, assume that the air temperature is 23°C.

(a) For a brake pad 1.65 cm thick, with an area of 53 cm  2 and a thermal conductivity of 12 W/mK, what is the maximum heat current through the pad that won't cause fade? Assume that the same amount of heat leaks out of the sides of the pad as goes straight through it.

(b) For a disk 1.1 cm thick, with an area of 268 cm  2 and a thermal conductivity of 43.5 W/mK, what is the maximum heat current through the disk that won't cause fade? Assume that the amount of heat leaks out of the sides of the disk as goes straight through it.

(c) For a 2000 kg car going 30 m/s, what is the shortest stopping distance the car can achieve without inducing fade? Assume that the car has 4 uniform brakes.