Maximum safe velocity on a banked curved road with friction – Rankers Physics

Uncategorized: Practice Problem & Solution

A car is negotiating a curved road of radius R. The road is banked at an angle (theta). The coefficient of friction between the tyres of the car and the road is (mu_s). The maximum safe velocity on this road is: (2016 - I)
(sqrt{gR frac{mu_s + tantheta}{1 - mu_s tantheta}}\)
(sqrt{gR frac{mu_s + tantheta}{1 - mu_s tantheta}}\)
(sqrt{frac{gmu_s + tantheta}{R(1 - mu_s tantheta)}}\)
(sqrt{frac{gmu_s + tantheta}{R^2(1 - mu_s tantheta)}}\)

Solution Explained:

To solve this problem, we apply the core principles of Uncategorized. Understanding the underlying formula is key to arriving at the correct answer below:

The maximum safe velocity on a banked road with friction is given by the formula (v = sqrt{gR frac{mu_s + tantheta}{1 - mu_s tantheta}}\) by resolving normal and friction forces into horizontal and vertical components. The horizontal components contribute to centripetal force while vertical components balance weight.

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