Question

determine the angle through which the cyclist bends from the vertical while negotiating a curve.​

Answer 1

Explanation:

A cyclist bends inwards while turning around a curve in order to negotiate the effects of slipping which would occur otherwise. Now, the leaning action of the cyclist provides the necessary centripetal force required for following a curved path.

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Answer 2

The angle through which the cyclist bends from the vertical while negotiating a curve is $tan^{-1}(\dfrac{v^2}{rg})$.

Explanation:

Let $\theta$ is the angle between horizontal surface and the road. The net force acting on cyclist is balanced by the centripetal force that is required to turn the vehicle.

The vertical component is balanced by the force of gravity acting on the cyclist such that,

$N\ cos\theta=mg$

m is the mass of cyclist

g is the acceleration due to gravity

$N=\dfrac{mg}{cos\theta}$........(1)

In vertical direction,

$F_{net}=F_{centripetal}=N\ sin\theta$

Using equation (1) in above equation,

$F_{net}=F_{centripetal}=N\ sin\theta=mg\ tan\theta$

The centripetal force is given by, $F_{centripetal}=\dfrac{mv^2}{r}$

So, $mg\ tan\theta=\dfrac{mv^2}{r}$

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

$\theta=tan^{-1}(\dfrac{v^2}{rg})$

Therefore, the angle through which the cyclist bends from the vertical while negotiating a curve is $tan^{-1}(\dfrac{v^2}{rg})$.

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A Banked turn

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