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 of death well with no support from below What is the minimum speed required at the uppermost position to perfrom a vertical loop if the radius of the chamber is 25 m ?

Explanation

When the motorcyclist is at the highest point of te death-well, the normal reaction R on the motorcyclist by the ceiling of the chamber acts downwards. His weight mg also acts downwards. These two forces are balanced by the outward centrifugal force acting on him.
`therefore` R + mg = `(mv^(2))/(r ) " "`......(i)
r = radius of the circle
Here v is the speed of the motorcyclist and m is the mass of the motorcyclist (including the mass the motor cycle). Because of the balancing of the forces, the motorcyclist does not fall down. The minimum speed required to perform a vertical loop is given by equation (i), when R = 0
`therefore` mg = `(mv^(2)"min")/(r ) " or " v_("min")^(2) = ` gr
or `v_("min") = sqrt(gr) = sqrt(9.8 xx 25) ms^(-1) = 15.65 ms^(-1)`
So, the minimum speed at the top required to perform a vertical loop is 15.65 `ms^(–1)`.