You may have seen in a circus a motorcyclist driving in vertical loops inside a ‘deathwell’ (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 25 m?

Question

You may have seen in a circus a motorcyclist driving in vertical loops inside a ‘deathwell’ (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 25 m?

Philoid · Accepted Answer

Given:

Radius of vertical loop, R = 25 m

A motor-cyclist should not fall from the top most position of the vertical loop provided that the weight of motorcycle and the normal reactions are balanced by the centrifugal force.

Using Newton’s second law of motion we can write,

F = ma_c

Where,

a_c = Centripetal acceleration

F = Normal force + weight of motorcycle

F = F_N + F_W

F_N + F_W = mv²/R

F_N + mg = mv²/R …(1)

If we consider for the minimum speed the normal force becomes equivalent to Zero.

F_N = 0

We can rewrite equation (1) as,

mg = mv_min² /R

i.e.

V_min = (Rg)^1/2

V_min = (25 m× 10ms^-2)^1/2

V_min = 15.8 ms^-1