A body is moving on a frictionless curved path of radius of 1.8 km wit

1.	A body is moving on a frictionless curved path of radius of 1.8 km with a speed of 30 ms-1. Find the banking angle required.
Answer» The centripetal force required to keep the body in circular motion is \(\frac{mv^2}{r}\) Here, v = 30 ms^-1 r = \(\frac {1.8 \times 10^3m}{2}\) = 0.9 10³ = 900m N cos θ = mg and \(\frac{mv^2}{r}\) = N sinθ \(\frac{mv^2}{r}\) = \(\frac{mg}{cos \theta}\) sinθ ⇒ tan θ = \(\frac {v^2}{rg}\) ⇒ θ = tan^{-1 \(\frac {30^2}{900 \times 10}\)} ⇒ θ = tan^-1 (0.1) = 5.71°.

A body is moving on a frictionless curved path of radius of 1.8 km with a speed of 30 ms-1. Find the banking angle required.

Answer»

The centripetal force required to keep the body in circular motion is \(\frac{mv^2}{r}\)

Here, v = 30 ms^-1

r = \(\frac {1.8 \times 10^3m}{2}\)

= 0.9 10³ = 900m

N cos θ = mg

and \(\frac{mv^2}{r}\) = N sinθ

\(\frac{mv^2}{r}\) = \(\frac{mg}{cos \theta}\) sinθ

⇒ tan θ = \(\frac {v^2}{rg}\)

⇒ θ = tan^{-1 \(\frac {30^2}{900 \times 10}\)}

⇒ θ = tan^-1 (0.1) = 5.71°.