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Question

An automobile of mass m=1500 kg is traveling at a speed of 90 km/hour on a level highway when its brakes are applied. It slows uniformly to a stop, without skidding, after traveling a distance of 55.0 meters.

(a) How much heat, in calories, must have been absorbed by the brake system of the auto in order to stop it?

(b) If virtually all of the heat is absorbed in the auto's four brake disks, and if each disk is made of steel and has a mass of 4.5 kg, by how much (on average) does the temperature of each disk rise? (Be sure to show your method clearly.)

P.S. If you know how to find the answer in Joules that alright, I know how to convert. :)

Answer 1

a.) To find the heat, we first need to find the frictional force that stops the car.
F = ma

Find a:
vf^2 = vi^2 + 2ad
0 = (90 km/h * 1000 m/km * 1 h/3600s)^2 + 2a * 55m
0 = 625 + 110a
110a = -625
a = 5.6818 m/s^2

F = ma = 1500 kg * 5.6818 m/s^2 = 8522.7 N of frictional force

To find the energy converted to heat, multiply the frictional force by the distance travelled: 8522.7 N * 55m = 468.7 kJ

b.) 468.7 kJ of heat energy is transferred into 4 disks of mass 4.5kg, or 1 object weight 18 kg. To find the temperature, you need to find the specific heat capacity of the steel (given in J/(kg·K), and plug it into:
ΔT = H / (specific heat * mass)