Laws of Motion
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Question : 38
Total: 40
You may have seen in a circus a motorcyclist driving in a 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:
When the motorcyclist is at the highest point of the death well , the normal reaction R on him 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.
∴ R + m g =
. . . ( i )
wherev
Because of the balancing of two forces, the motorcyclist does not fall down.
The minimum speed required to perform a vertical loop is given by equation
(i) whenR = 0
i.e.m g =
v 2 min = g r
v min = √ g r . . . ( i i )
r = g = 10 m s – 2
∴ from (ii)
v min = √ 10 × 25
= 15.81 m s − 1 = 16 m s − 1
where
Because of the balancing of two forces, the motorcyclist does not fall down.
The minimum speed required to perform a vertical loop is given by equation
(i) when
i.e.
∴ from (ii)
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