Question

If the coefficient of friction between tyres and the road is 0.6, what is the angle of banking for a highway curve of 500 m radius designed to accommodate cars travelling at 180 km/h?

• A. 45°
• B. 56.30°
• C. 47.56°
• D. 26.56°

Hint:

For banking curves, always use the formula involving the speed, radius, and coefficient of friction to calculate the angle of banking.

Answer 1

The Correct Option is B

Step 1: Use the formula for the angle of banking.
For a vehicle moving in a curve, the banking angle \(\theta\) can be calculated using the following formula: \[ \tan \theta = \frac{v^2}{g r} + \mu \] where:
\( v \) is the speed of the car in m/s,
\( g \) is the acceleration due to gravity (9.8 m/s²),
\( r \) is the radius of the curve in meters,
\( \mu \) is the coefficient of friction between the tyres and the road.
Step 2: Convert the speed of the car to m/s.
The speed given is 180 km/h. We need to convert this to meters per second: \[ v = 180 \, \text{km/h} = 180 \times \frac{1000}{3600} = 50 \, \text{m/s} \]
Step 3: Substitute the known values into the formula.
Now, substitute the known values into the formula for \(\tan \theta\): \[ \tan \theta = \frac{(50)^2}{9.8 \times 500} + 0.6 \] \[ \tan \theta = \frac{2500}{4900} + 0.6 = 0.5102 + 0.6 = 1.1102 \]
Step 4: Calculate the angle \(\theta\).
To find the angle \(\theta\), we take the inverse tangent (\(\tan^{-1}\)) of 1.1102: \[ \theta = \tan^{-1}(1.1102) \approx 56.30° \] Thus, the angle of banking is \( 56.30^\circ \).