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).)

Explanation / Answer

energy required to melt 7Kg aluminium is 7L where L is specific latent heat. You will need to get this from a table. Google gave me 398,000 J/Kg. Thus, energy required to melt it will be 398,000 x 7 = 2786000 Kinetic energy of car is 0.5 x 1400 x 29^2 = 588700 J. When we stop this car, this energy is transfered to the brakes as mentioned by question. When we stop the car n times, the total energy will be 588700n. Thus, brakes will melt when 588700n = 2786000 n = 4.73 or 4

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