Temperature of disc brake

Question

A disc brake is 15 C. What is final temperature of the 1.2kg brake when it stops a 2000kg car initially at 20m/s?

Answer 1

To answer this question, we need to also know the material the disc brake is made of. You will need to look up its specific heat. The kinetic energy of the car must be fully converted to the temperature rise of the brake material.

m = mass of brake in kg (given)

c = specific heat of the brake material (look it up in units of joules/(kg°C))

T₀ = initial temperature of brake (given)

T = final temperature of brake = ? (what we want to solve for)

M = mass of car in kg (given)

v = initial speed of car in m/s (given)

Energy conservation requires that

Mv²/2 = mc(T - T₀) ⇒

T = T₀ + Mv²/(2mc)

Plug in all the numbers and get T in °C.