An automobile has a mass of 1,400 kg, and its aluminum brakes have an overall ma

Question

An automobile has a mass of 1,400 kg, and its aluminum brakes have an overall mass of 7.00 kg.
Assuming all the internal energy transformed by friction when the car stops is deposited in the brakes and neglecting energy transfer, how many times could the car be braked to rest starting from 29.0 m/s before the brakes would begin to melt? (Assume an initial temperature of 20.0°C. Count only the number of times the car can come to a complete stop without the brakes melting in the process. The melting point of aluminum is 660°C, and the specific heat of aluminum is 900 J/(kg · °C).)
Use 3.97 x 10^5 for latent heat of aluminum.

Explanation / Answer

Energy to get the brake start melting = mbrakeC(Tmelt-Tamb) = 7*900*(660-20) = 4032 kJ

Energy to get the car completely stop = 0.5mv2 (change all kinetic energy to friction)

= 0.5*1400*292 = 588.7 kJ

Since we neglect energy transfer, each time when we apply brake all energy accumulates in the brake,

# of times the car could be braked = 4032 / 588.7 = 6.85 --> Answer 6

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