A toy car of mass 10 k g is moving with constant speed on a circular track of radius 10 3 m banked at an angle of 3 0 ∘ . The coefficient of friction between the wheels of the car and the track is 3

Question

A toy car of mass 10 k g is moving with constant speed on a circular track of radius 10 3 ​ m banked at an angle of 3 0 ∘ . The coefficient of friction between the wheels of the car and the track is 3 1 ​ . When the car moves on this track with maximum safe constant speed, the normal reaction (in N) between the car and the track is N . Find the numerical value of N 3 ​ .

TestHub · Accepted Answer

Since the car is moving with maximum safe speed, therefore, friction will be at its minimum value and will act down the plane.

From F.B.D. of car :

$N cos 3 0^{\circ} = f sin 3 0^{\circ} + Mg$ ...........(1)

$f = μ N$ ............(20

$\frac{N 3}{2} - μ N \times \frac{1}{2} = 10 \times 10$

$\frac{N 3}{2} - \frac{N}{2 3} = 100 \Rightarrow N = 1003 \Rightarrow N 3 = 300$

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