Question

A cyclist is riding at speed of 10m/s take turn on a horizontal circular road of radius 10 under root 3 m without skidding .what is his angle inclination to the vertical.
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Answer 1

Given :

Velocity of cyclist = 10m/s

Radius of circular path = 10√3m

To Find :

Angle of inclination of cyclist to the vertical.

Solution :

❖ Bending of a cyclist : In order to take a circular turn of radius r with speed v, the cyclist should bend himself through an angle θ from the vertical such that

$\dag\:\underline{\boxed{\bf{\purple{tan\theta=\dfrac{v^2}{rg}}}}}$

By substituting the given values;

$\sf:\implies\:tan\theta=\dfrac{(10)^2}{(10\sqrt3)(10)}$

$\sf:\implies\:tan\theta=\dfrac{100}{100\sqrt3}$

$\sf:\implies\:tan\theta=\dfrac{1}{\sqrt3}$

$\sf:\implies\:\theta=tan^{-1}\dfrac{1}{\sqrt3}$

$:\implies\:\underline{\boxed{\bf{\gray{\theta=30^{\circ}}}}}$

Knowledge BoosteR :

• For frictional force relative motion between two bodies or surfaces is not necessary. In fact, contact between two bodies or surfaces is necessary.
• Centripetal force is not a new kind of force. The material force such as tension, gravitational force, electrical force, friction etc., may act as the centripetal force in any circular motion.

Answer 2

Given :

Velocity of cyclist = 10m/s

Radius of circular path = 10√3m

To Find :

Angle of inclination of cyclist to the vertical.

Solution :

❖ Bending of a cyclist : In order to take a circular turn of radius r with speed v, the cyclist should bend himself through an angle θ from the vertical such that

$\dag\:\underline{\boxed{\bf{\purple{tan\theta=\dfrac{v^2}{rg}}}}}$

By substituting the given values;

$\sf:\implies\:tan\theta=\dfrac{(10)^2}{(10\sqrt3)(10)}$

$\sf:\implies\:tan\theta=\dfrac{100}{100\sqrt3}$

$\sf:\implies\:tan\theta=\dfrac{1}{\sqrt3}$

$\sf:\implies\:\theta=tan^{-1}\dfrac{1}{\sqrt3}$

$:\implies\:\underline{\boxed{\bf{\gray{\theta=30^{\circ}}}}}$

Knowledge BoosteR :

For frictional force relative motion between two bodies or surfaces is not necessary. In fact, contact between two bodies or surfaces is necessary.

Centripetal force is not a new kind of force. The material force such as tension, gravitational force, electrical force, friction etc., may act as the centripetal force in any circular motion.