Answer to Question #78149 in Mechanics | Relativity for Prerana

Question

A
level road has a turn of radius of curvature
100 m. Calculate the maximum speed with
which a car can travel around the turn
without going off the road. It is given that
the road is dry and the coefficient of static
friction is 0-81.

Answer 1

When the car travels around the turn, the force of static friction provides the necessary centripetal force:
F_c=F_s,
(mv^2)/R=μ_s N,
(mv^2)/R=μ_s mg,
v^2/R=μ_s g.
From this formula, we can find the maximum speed with which a car can travel around the turn without going off the road:
v=√(μ_s Rg)=√(0.81∙100 m∙9.8 m/s^2 )=28.2 m/s.