Question

If a roadway is banked (super elevated), a car can round the corner at a higher speed than an unbanked curve. What is the maximum speed a 1200kg car could navigate through an 85m radius turn banked at 16.7° if the maximum value of m_s=0.875?

Answer 1

Here, mass of the car, m = 1200 kg

Banked angle, = 16.7 deg

Radius of the curve, r = 85 m

Suppose, v = maximum speed of the car

Drawing the free-body-diagram we find that the normal reaction on the car, N = m*g*cos -------------------------------(i)

Centripetal force towards the center of the curve = m*v^2/r

This must be equal to -

m*v^2/r = N*sin + *N*cos --------------------------------------------------(ii)

For the stability of the car -

Total force in the Y - direction = 0

=> N*cos -  *N*sin - m*g = 0 --------------------------------------------(iii)

Solving equation (i), (ii) and (iii), we find that -

v = sqrt [{r*g*(sin + *cos)} / {cos - *sin}]

plugin the value of the variables -

v = sqrt [{85*9.8*(sin16.7 +0.875*cos16.7)} / {cos16.7 - 0.875*sin16.7}]

= sqrt [{833*(0.29 + 0.84)} / {0.96 - 0.25}]

= sqrt [{941.29} / {0.71}]

= 36.41 m/s

Therefore, the maximum speed of the car = 34.61 m/s (Answer)