Automotive Disk Brakes
The driver of a 1200-kg automobile traveling at 100 km/h applies the brakes and brings the vehicle to a complete stop. The vehicle has front and rear disk brakes, and the braking system is balanced so that the front set provides 75% of the total braking capacity. Through friction between the brake pads and the rotors, the brakes convert the automobile’s kinetic energy into heat (Figure 7.9). If the two front 7-kg brake rotors are initially at a temperature of 25^°C , how hot are they after the vehicle stops? The specific heat of cast iron is c = 0.43 kJ/(kg .^°C).
Approach
As the vehicle comes to a stop, a portion of its initial kinetic energy is lost through air drag, the rolling resistance of the tires, and the wear of the brake pads, but we will neglect those extraneous factors at the first level of approximation. The automobile’s kinetic energy [Equation (7.3)]
U_{k}=\frac{1}{2} m v^2 (7.3)
decreases as work is performed on it, and the heat produced will cause the temperature of the brake rotors to
increase. That temperature rise can be found by applying Equation (7.7).
Q = mc(T - T_ 0) (7.7)