Question

An automobile has a mass of 1 500 kg, and its aluminum brakes have an overall mass of 6.00 kg. (a) Assume all the mechanical energy that transforms into internal energy when the car stops is deposited in the brakes and no energy is transferred out of the brakes by heat.The brakes are originally at ${20.0}^{0}C$. How many times can the car be stopped from 25.0 m/s before the brakes start to melt? (b) Identify some effects ignored in part(a) that are important in a more realistic assessment of the warming of the brakes.

Answer 1

(a) Let n represent the number of stops. Follow the energy:
$nK=mc\Delta T$

$n\left[\frac{1}{2}\right(1500kg\left)\right(25.0m/s^2\left)\right]$
$=\left(6.00kg\right)\left(900J/kg{.}^{0}C\right)({660}^{0}C-{20.0}^{0}C)$
$n=\frac{3.46\times {10}^{6}J}{4.69\times {10}^{5}J}=7.37$
Thus 7 stops can happen before melting begins.

(b) As the car stops it transforms part of its kinetic energy into internal Energy due to air resistance. As soon as the brakes rise above the air temperature they transfer energy by heat into the air, and transfer it very fast if they attain a high temperature