In a circus ride, a motorcyclist moves along the inner surface of a sphere of radius R. Racing, he begins to describe a horizontal circle in the upper hemisphere. After that, for greater effect, the l

Question

In a circus ride, a motorcyclist moves along the inner surface of a sphere of radius R. Racing, he begins to describe a horizontal circle in the upper hemisphere. After that, for greater effect, the lower hemisphere is removed. The coefficient of friction of the tires on the surface of the sphere is equal to μ , and the angle between the vertical and the direction to the motorcyclist from the centre of the sphere is equal to α .

TestHub · Accepted Answer

Vertical balance: f sin α = m g + N cos α ; centripetal: N sin α + f cos α = R s i n α m v 2 ​ , with f = μ N at minimum speed. N = μ s i n α − c o s α m g ​ - corresponds to (C) as per the key. v min ​ = g R sin α μ s i n α − c o s α s i n α + μ c o s α ​ ​ = μ t a n α − 1 g R s i n α ( t a n α + μ ) ​ ​ - (A)

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