Question

The four values of f correspond to the coefficient of friction for four road and tire conditions: an icy road, a very good road with great tires, an asphalt road with fair tires, and a wet road with fair tires. Match the coefficients of friction to the appropriate conditions by looking at the braking distance required.

Answer 1

The four values of f are given in part a of the question as

f= 0.30, 0.50, 0.70, 0.90

The answers to the question are

i. icy road, f = 0.3

ii. Very good road with great tires, f = 0.9

iii. Asphalt road with fair tires, f = 0.7

iv. Wet road with fair tires, f = 0.5

Explanation:

The braking distance is given by

`d = (v^2)/(2g(f+G))` Where

d = Braking distance

f = Coefficient of friction

G = Constant = Grade of the road and

g = Acceleration due to gravity = 32.19 ft/s²

Where v = 60 mph we have

`d = (7744)/(64.4f+0.02) ft`

Therefore for

f = 0.3, d = 400.41 ft

f = 0.5, d = 240.35 ft

f = 0.7, d = 171.71 ft

f = 0.9, d = 133.56 ft

From the breaking distance required we have

i. icy road, f = 0.3

ii. Very good road with great tires, f = 0.9

iii. Asphalt road with fair tires, f = 0.7

iv. Wet road with fair tires, f = 0.5