Question

A 1200 kg car traveling at 60 mph quickly brakes to a halt. The kinetic energy of the car is converted to thermal energy of the disk brakes. The brake disks (one per wheel) are iron disks with a mass of 4.0 kg. Part A: Estimate the temperature rise in each disk as the car stops.

Answer 1

The temperature rise in each brake disk is estimated to be 16.96 °C.

Step-by-step explanation:

To estimate the temperature rise in each brake disk, we need to calculate the change in gravitational potential energy of the car as it brakes. The car's kinetic energy is equal to its initial gravitational potential energy, so we can use the equation KE = 0.5mv^2 to find the initial kinetic energy. Converting the car's velocity from mph to m/s, we find KE = 0.5 * 1200 kg * (26.8 m/s)^2 = 429,696 J.

Since the brake disks retain 10% of the car's kinetic energy, each brake disk receives 10% of 429,696 J, which is 42,970 J. The specific heat capacity of iron is 800 J/(kg·°C), and the mass of each brake disk is 4.0 kg. Using the equation Q = mcΔT, we can find the temperature increase (ΔT) in each brake disk: 42,970 J = 4.0 kg * 800 J/(kg·°C) * ΔT. Solving for ΔT, we get ΔT = 42,970 J / (4.0 kg * 800 J/(kg·°C)) = 16.96 °C.