Question

A train runs along an unbanked circular track of radius 30 m at a speed of 54 km/h.
The mass of the train is 10^6 kg. What provides the centripetal force required for this
purpose -The engine or the rails? What is the angle of banking required to prevent?

wearing out of the rail?

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Answer 1

Answer:

• $36.87^{o}$

Explanation:

• Radius of circular track = 30 m

• Speed of train = $54\frac{km}{h}=\frac{54\times1000}{3600}=15m/s$

• Mass of train = 10⁶ kg

• The centripetal force is provided by the lateral thrust of the rail on the wheel.

$\boxed{tan\theta=\dfrac{v^2}{r\:g}}$

$\implies\:\:\frac{(15)^2}{30\times10}$

$\implies\:\:\frac{225}{300}$

$\implies\:\:0.75$

$\theta = tan^{-1}(0.75)$

$\implies\:\:36.87^{o}$

$\therefore$ The angle of banking is about 36.87°