A curved road of radius 20 m is banked for vehicles travelling at 36 km/h. If the static friction coefficient between road and tyres is 0.4, find the range of safe speeds so the vehicle neither slides down nor skids up the bank. (Take g = 10 m/s².)

14.7 km/h to 54 km/h
0 km/h to 36 km/h
20 km/h to 50 km/h
10 km/h to 60 km/h

Correct answer: 14.7 km/h to 54 km/h

Solution

Design speed 36 km/h = 10 m/s gives tan(theta) = 100/200 = 0.5; substituting mu = 0.4 yields v_min about 4.1 m/s (14.7 km/h) and v_max about 15 m/s (54 km/h).

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