Question

You may have seen in a circus a motorcyclist driving in vertical loops inside a death well (a hollow spherical chamber with holes, so the spectators can watch from outside). Explain clearly why the motorcyclist does not drop down when he is at the uppermost point, with no support from below. What is the minimum speed required at the uppermost position to perform a vertical loop if the radius of the chamber is $25m$?

Answer 1

When the motorcyclist is at the highest point of the death - well, the normal reaction R on the motorcyclist by the ceiling of the chamber acts downwards. His weight mg also act downwards.
$F_{net}=m{a}_c\Rightarrow R+mg=\frac{m{v}^2}{r}$
Here v is the speed of the motorcyclist and m is the mass of does not fall down. The minimum speed required to perform a vertical loop is given by equation (1) when $R=0$.
Therefore,

$mg=\frac{m{v_{min}}^2}{r}or{v_{min}}^2=gror{v}_{min}=\sqrt{gr}=\sqrt{9.8\times 25m/s}=15.65m/s$.
So, the minimum speed, at the top, required to perform a vertical loop is 15.65 m/s.