Question

What is the centripetal force experienced by a bike of weight $800\text{N}$ moving at a velocity $v\text{m/s}$ and bending with an angle of ${60}^{\circ }$ with the ground?

• A. $462.43\text{N}$
• B. $400\text{N}$
• C. $692.8\text{N}$
• D. $565.68\text{N}$

Answer 1

The correct option is A $462.43\text{N}$

Given that bike is bending at an angle of ${60}^{\circ }$ from the ground.
$\therefore$ Angle with the vertical, $\theta ={90}^{\circ }-{60}^{\circ }={30}^{\circ }$


From the FBD,
$R$ is the total reaction force.

$R\cos \theta =mg=800\text{N}-\left(1\right)$
and Centripetal force $F_c=R\sin \theta -\left(2\right)$

Dividing (2) by (1),
$\tan \theta =\frac{F_c}{800}=\tan {30}^{\circ }$
$\Rightarrow F_c=\frac{800}{\sqrt{3}}=461.88\text{N}$