Question 5.38:
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 25 m?
Solution:
In a death-well, a motorcyclist does not fall at the top point of a vertical loop because both the force of normal reaction and the weight of the motorcyclist act downward and are balanced by the centripetal force. This situation is shown in the following figure.
In a death-well, a motorcyclist does not fall at the top point of a vertical loop because both the force of normal reaction and the weight of the motorcyclist act downward and are balanced by the centripetal force. This situation is shown in the following figure.

The net force acting on the motorcyclist is the sum of the normal force (FN) and the force due to gravity (Fg = mg).
The equation of motion for the centripetal acceleration ac, can be written as:
Fnet = mac
FN + Fg = mac
FN + mg = mv2 / r
Normal reaction is provided by the speed of the motorcyclist. At the minimum speed (vmin), FN = 0
mg = mvmin2 / r
∴ vmin = √rg
= √25 X 10 = 15.8 m/s
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