The corner of a motor racing track is banked at an angle of 30°. If the coefficient of friction between the tyre and track is 3 /2 , the ratio of the maximum speed at which car can take the turn wit

Question

The corner of a motor racing track is banked at an angle of 30°. If the coefficient of friction between the tyre and track is 3 ​ /2 , the ratio of the maximum speed at which car can take the turn with the corresponding speed of car if there is no friction is α ​ : β . where α and β are smallest integers. Find the value of α + β .

TestHub · Accepted Answer

In case of maximum speed, friction will act down the plane, and its value will be maximum.

Now, $N cos θ = mg + f sin θ$ ............(2)

$f cos θ + N sin θ = \frac{mv _{m a x}^{2}}{R}$ .........(3)

On solving $v_{m a x} = \frac{( s i n θ + μ c o s θ )}{( c o s θ - μ s i n θ )} Rg$

Now if friction is absent :

$N sin θ = \frac{m v ^{2}}{R}$ ........(4)

$N cos θ = mg$ ............(5)

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