8. A car going down a long, steep incline can cause its brakes to fail by the dr

Question

8. A car going down a long, steep incline can cause its brakes to fail by the driver over-using them. This is called "riding your brakes" and it occurs because the brakes work by creating enormous friction forces which then do a large amount of negative work on the car, transferring the car's kinetic energy into thermal energy (heat) in the brakes. Brake systems can only dissipate heat so quickly. For a car which has a mass of 2100 kg, the brakes can reliably accept 50 kW of power. Find the maximum speed this car can descend a 6° incline without over-heating its brakes if friction from the brakes is the only force other than gravity acting on the car

Explanation / Answer

8. given mass of car, m = 2100 kg

power accepted y brakes, P = 50 kW

let friction applied by brakes on each tire be f

then

let maximum speed of the car be v

then

it has to remain at constant speed

power delivered to it by the potential energy = Pc

Pc = m*g*vsin(theta)

theta = 6 deg

so

Pc = 50 kW ( for no chang ein speed)

2100*g*v*sin(6) = 50,000

v = 23.2191938 m/s

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