An engineer is designing a new on-ramp for a highway. because of space limitations, the on-ramp can have a radius no larger than 60 meters. the on-ramp is not banked and we assume that the vehicle will travel at a constant speed.

(a) what kind of acceleration will the car experience as it travels through the on-ramp?
(b) if the engineers want to design the ramp so that a car of mass 1000 kg can travel a maximum speed of 20 m/s, what coefficient of friction is required?
(c) explain why banking the track makes it easier to drive through the on-ramp at higher speed.

a) acceleration is centripetal , b)  μ = 0.68

Explanation:

For this exercise we will use Newton's second law, let's take a vertical and horizontal reference system.

Y Axis

       N- W = 0

       N = mg

X axis

       fr = ma

a) With going at a constant speed circle this acceleration is centripetal

b) the acceleration formula is

        a = v² / r

        fr = μ N

        fr = μ m g

        μ m g = m v² / R

        μ = v² / R g

        μ = 20² / (60 9.8)

        μ = 0.68

c) when tilting the ramp part of the normal force is in the radial direction, therefore less friction force is needed to remain in the curve, which allows it to be taken at a higher speed