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A circular road of radius 20 m is banked at an angle whose tangent is…
Question
A circular road of radius 20 m is banked at an angle whose tangent is 3/4. The coefficient of friction between the tyres and the road is 0.50. Taking g = 10 m/s^2, find the maximum speed (in m/s) at which a car can negotiate the curve without skidding outward.
✓ Verified answer: 20checked by our engine — not a guess
Step-by-step solution
For a banked road with friction, the maximum speed satisfies v_max^2 = r g (tan theta + mu)/(1 - mu tan theta).
Here tan theta = 3/4, mu = 1/2: numerator factor (3/4 + 1/2) = 5/4; denominator (1 - (1/2)(3/4)) = 1 - 3/8 = 5/8; ratio = (5/4)/(5/8) = 2.
So v_max^2 = 20*10*2 = 400, giving v_max = 20 m/s.
Final answer20
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