Wet road - braking distance · Physics Brawl 2015 #FoL.5

Physics · mechanics

Problem

How much does the shortest braking distance increase when it rains, if we do not want the car to skid? The car is moving at a speed of v=90km⋅h−1v = 90\text{km}\cdot\text{h}^{-1}, the coefficient of friction between a dry road and the tires is f1=0.55f_1 = 0.55 and it changes to f2=0.30f_2 = 0.30 in wet conditions. The weight of the car is m=1500kgm = 1500\text{kg} and the acceleration due to gravity is g=9.81m⋅s−2g = 9.81\text{m}\cdot\text{s}^{-2}. Consider only kinetic energy of the car's translational motion.
Intuitive explanation

Braking distance depends on how much friction force can slow the car down—and rain reduces that friction dramatically. Since the car's kinetic energy 12mv2\frac{1}{2}mv^2 must be dissipated by friction work (f⋅m⋅g⋅df \cdot m \cdot g \cdot d), a lower coefficient means you need a longer distance to stop safely. Calculate the braking distance for both dry and wet conditions, then find the difference.

Intuitive explanation

Braking distance depends on how much friction force can slow the car down—and rain reduces that friction dramatically. Since the car's kinetic energy 12mv2\frac{1}{2}mv^2 must be dissipated by friction work (f⋅m⋅g⋅df \cdot m \cdot g \cdot d), a lower coefficient means you need a longer distance to stop safely. Calculate the braking distance for both dry and wet conditions, then find the difference.

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