What is the fastest safe speed around this bend?

Question

Your 1600 kg car moves around a level curve in the road with a 50 m radius. The coefficient of static friction between the tires and the road is 0.8.

Answer 1

r =50 m, μ_s = 0.8

Centripetal force (F_c) is provided by

static friction (μ_smg) between

the tires and the road.

Centripetal Force and Static Friction

F_c = mv²/r = μ_smg

Centripetal Acceleration

a_c = v²/r = μ_sg

Maximum Safe Speed

v² = μ_sgr

v = 19.8 m/s = 72.3 km/hr = 44.3 mi/hr