You can warm your hands on a cool day by rubbing them togther because almost all

Question

You can warm your hands on a cool day by rubbing them togther because almost all the work done by friction is turned into thermal energy in your hands. This works with almost anything rubbing together. Consider how this applies to a 1000kg car with a braking system that consists largely of 12kg of steel.

a) The driver applies the brakes when the car has velocity 30m/s and brings the car to a stop. Assume that half the kinetic energy of the car goas into heating up the brake mechanism. By how much does the temperature of the brakes increase?

b) If the driver uses the brakes to control the descent of the car from a tall hill or a mountain a substantial portion of the gravitational potential energy can end up in the brake mechanism. Assume the same car starts at the top of a pass 1000m above the valley floor, and that the driver applies the brakes liberally during the decent transforming 20% of the gravitational potential into heat added to the brakes. By how much does the temperature of the brakes increase?

Explanation / Answer

KE = m*v*v/2 = 450 kJ

Heat = 1/2 KE = 225 kJ

Specific heat of steel = 490 J/kg.K

Temp rise = Heat / m*S = 38.26 K

b) When only 20% GPE (gravitational PE) is converted to heat

GPE = m*g*h = 1000*9.8*1000 = 9800 kJ

Heat = 20% of GPE = 1960 kJ

Temp change = 333.3 K

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