Question

A motor cyclist (to be treated
as a point mass) is to undertake horizontal
circles inside the cylindrical wall of a well
of inner radius 4 m. Coefficient of static
friction between the tyres and the wall is
0.4. Calculate the minimum speed and
frequency necessary to perform this stunt.
(Use g = 10 m/s2
)

Answer 1

Answer:

Explanation:

here is the answer

Answer 2

Answer:

The minimum speed is 10m/s and the frequency necessary to perform the stunt is 0.4Hz respectively.

Explanation:

The minimum speed of the cyclist is given as,

$v=\sqrt{\frac{rg}{\mu} }$              (1)

Where,

v=minimum velocity of the cyclist

r=radius of the cylindrical well

g=acceleration due to gravity=10m/s²

μ=minimum  friction between the tires and the wall

From the question we have,

r=4m

μ=0.4

By substituting the values in equation (1) we get;

$v=\sqrt{\frac{4\times 10}{0.4} }=\sqrt{100} =10m/s$            (2)

The minimum frequency(f) required is given as,

$f=\frac{v}{2\pi r}$        (3)

By substituting the value of v and r in equation (3) we get;

$f=\frac{10}{2\times \pi \times 4}=0.4Hz$             (∵π=3.14)

Hence, the minimum speed is 10m/s and the frequency necessary to perform the stunt is 0.4Hz respectively.