Problem 3 Engineers often bank highway curves to reduce the vehicle’s reliance on friction while navigating turns. If the bank is angled properly, the posted speed limit is effective in both wet and dry weather. For a curve of radius 13 0m and a speed limit of 100 km/hr, what is the minimum bank angle such that a reliance on friction is not necessary?
in vertical, N cos(theta) - m g = 0
N cos(theta) = m g ....(i)
in horizontal, N sin(theta) = m v^2 / r .... (ii)
(ii)/(i) => tan(theta) = v^2 / r g
v= 100 km/h = 100 x 1000 / 3600 m/s = 27.8 m/s
theta = tan^-1(27.8^2 / (13 x9.8))
= 80 deg
Problem 3 Engineers often bank highway curves to reduce the vehicle’s reliance on friction while navigating...
highway curves are often banked, so the normal force provides the centripetal force and cars don’t have to rely on friction. After having responded to an emergency call in the middle of a snowstorm, an ambulance is speeding back towards the hospital along a slippery curved road. Your job is to inform the ambulance driver of the maximum speed at which he can travel around this curve without slipping up the bank. You are told that the curve has a...