On a downhill stretch of the road, a driver applies the brakes of his car so tha
ID: 2014335 • Letter: O
Question
On a downhill stretch of the road, a driver applies the brakes of his car so that he coasts at constant speed. We are interested in the temperature rise of the brakes. Assume the brakes are made of steel and all of the heat generated by friction is absorbed by the brakes. The hill has a height of 100 m, the car has a mass (including brakes) of 900 kg, the total mass of all brakes is 20 kg, and the specific heat of steel is 450 J/(kg ?C).a) Draw a sketch of the problem and collect the available information.
b) Write down the conservation law that allows you to solve this problem.
c) Using the conservation law, the assumption of the problem, and g = 10 m/s2, calculate the heat absorbed by the brakes. (Answer: Q = 9x105 J)
d) Calculate the temperature increase of the brakes and the final temperature, assuming the initial temperature was 20?C.
e) In the calculation, we assumed that all of the heat generated during braking is absorbed by the brakes. In reality, some of the heat is transferred to the environment. Considering this, do you expect the final temperature of the brakes to be higher or lower than calculated?
Explanation / Answer
(b) Total energy of the system at height 100 m from ground is mgh Potential energy of the system at ground is zero Total energy of the system at ground is Q (c) From conservation of energy mgh = Q Q = 900kg*10 m/s^2*100m = 9.0x105 J (d) The heat obsorbed by breaks is Q = mc T T = Q / mc Tf - Ti = Q / mc Tf = Ti + Q /mc = 20oC + (9.0x105 J) /(20 kg)(450 J/kg,K) = 120oC (e) Yes the temperature of the brekes to be lower than calculated.Related Questions
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