Question

b. A racing car of 1000kg moves round a banked track at a
constant speed of 108kmh ?. Assuming the total reaction at the
wheels is normal to the track and the horizontal radius of the
track is 100m, calculate the angle of the inclination of the track
to the horizontal and reaction at the wheels.​

Answer 1

Given :

Mass = 1000 kg

Speed = 108 km/hr

Radius of circular path = 100m

To Find :

Angle of inclination of the circular track.

Solution :

❒ Banking of tracks (roads) : The minimum velocity with which a vehicle (in the absence of friction) can negotiate a circular road of radius r and banked at an angle θ is given by

• v² = r × g × tan θ

First of all we need to convert unit of velocity into m/s$.$

We know that, 1 km/hr = 5/18 m/s

∴ 108 km/hr = 108 × 5/18 = 30 m/s

By substituting the given values;

➙ v² = r × g × tan θ

➙ 30² = 100 × 10 × tan θ

➙ 900 = 1000 × tan θ

➙ tan θ = 9/10

➙ tan θ = 0.9

➙ θ = tan‾¹ (0.9)