Given:
The required frictional force to turn on a road is,
[tex]F[/tex]while the bicycle is moving at a speed of
[tex]v[/tex]To find:
The frictional force required to make the same turn at a speed of 2v
Explanation:
The required frictional force should be equal to the centrifugal force. So, we can write,
[tex]F=\frac{mv^2}{r}[/tex]Now, for the speed 2v, the frictional force is,
[tex]\begin{gathered} F^{\prime}=\frac{m(2v)^2}{r} \\ =\frac{m\times4v^2}{r} \\ =\frac{4mv^2}{r} \\ =4F \end{gathered}[/tex]Hence, the required force is 4F.