Question

Why does a cyclist lean inward when moving along the curved path determine the angle through which a cyclist bends from the vertical while negotiating a curve calculate the angle through which a cyclist bend from the vertical when he crosses a circular path of 3.4 in circumference in √22s. take g=9.8​

Answer 1

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Any cyclist while travelling through a banked curved road tends to lean inwards so that, he can dedicate a component of Normal Reaction towards Centripetal force.

This would help on safe turning at high speeds. Otherwise the centrifugal force would tend to move the cyclist outwards .

Let the angle be θ as shown in the attached photo.

We know that :

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \large{ \red{ \tan( \theta) = \frac{ {v}^{2} }{rg}}}}$

Considering the circumference to be

3.4 metres, we can say :

∴ 2πr = 3.4

=> r = 3.4/(2π)

=> r = 0.54 metres ........(1)

Now for velocity be v

∴ v = 3.4/(√22)

=> v = 0.724 m/s ..........(2)

Putting the value of 1 and 2 in equation :

$\tan( \theta) = \dfrac{ {v}^{2} }{rg}$

$= > \tan( \theta) = \dfrac{ {(0.724)}^{2} }{(0.54 \times 9.8)}$

$= > \tan( \theta) = 0.099$

$= > \theta = 5.65 \degree$

So final answer :

Angle is 5.65°