Question

You are shown a photo of a car driven on a vertical inside wall of a huge cylinder of radius $50m$. The coefficient of static friction between the car tires and the cylinder is ${\mu }_s=0.8$. The minimum speed $\text{(in m/s)}$ at which the car can be driven like that is $5x$. Find $x$.

Answer 1

Draw a FBD of given situation.



Find the value of $x$.

From the FBD.
$f=\mu N=mg\dots \left(i\right)$
$N=\frac{m{v}^2}{r}$
Put the value of $N$ in equation $\dots \left(i\right)$
$\mu N=mg\Rightarrow \frac{\mu m{v}^2}{r}=mg$
$\Rightarrow v=\sqrt{\frac{gr}{\mu }}=25m/s$

Final Answer: $5$