In the design of a highway, among many other considerations, the design of curve
ID: 1592935 • Letter: I
Question
In the design of a highway, among many other considerations, the design of curves is limited by the maximum acceleration a car can (or should) undergo before the tires lose their grip.
A) If this limit is 0.25g (25% of 9.80 m/s2), what is the limit on the radius for the curve of the road for a maximum constant speed of 33.5 m/s (about 75 mph)? Include in your answer the proper inequality.
B) If a car while negotiating a curve with the radius limit calculated in part a is simultaneously accelerating at a rate of 1.50 m/s2, at what speed would the total acceleration exceed the maximum limit of 0.25g?
Explanation / Answer
A) maximum centripetal acceleration, a_rad = v_max^2/r
r = v_max^2/a_rad
= 33.5^2/(0.25*9.8)
= 458 m
B) a_tan = 1.5 m/s^2
a_total = 0.25*9.8
= 2.45 m/s^2
a_rad = ?
we know, a_total^2 = a_tan^2 + a_rad^2
==> a_rad = sqrt(a_total^2 - a_tan^2)
= sqrt(2.45^2 - 1.5^2)
= 1.937 m/s^2
now Apply, a_rad = v^2/r
==> v = sqrt(a_rad*r)
= sqrt(1.937*458)
= 29.9 m/s