The Open Door Web Site : IB Physics : Banking of a Road Surface

The Open Door Web Site

Mechanics

Banking of a Road Surface

Moving in a Straight line on a Horizontal Surface

Turning on a Horizontal Surface

The normal reaction, R, has no component acting towards the centre of the circular path.

Therefore the required centripetal acceleration is provided by the force of friction, F_f, between the wheel and the road.

If the force of friction is not strong enough, the vehicle will skid.

Turning on a Banked Surface

The normal reaction, R, now has a component acting towards the centre of the circular path.

If the angle, q, is just right, the correct centripetal acceleration can be provided by the horizontal component of the normal reaction.

This means that, even if there is very little force of friction the vehicle can still go round the curve with no tendency to skid.

Angle of Banking

The magnitude of the horizontal component of the normal reaction is

R_H = Rsinq

This force causes the centripetal acceleration, so, the magnitude of R_H is also given by

equation 1

So,

Rsinq =

equation 2

The vertical forces acting on the vehicle are in equilibrium.

Therefore, considering magnitudes only

Rcosq = mg

Dividing equation 1 by equation 2 gives:

tanq =

This equation allows us to calculate the angle q needed for a vehicle to go round the curve at a given speed, v, without any tendency to skid.