If a banked curve with radius 80.0 m is banked sufficiently so that no friction

Question

If a banked curve with radius 80.0 m is banked sufficiently so that no friction is required for a car to make the turn without slipping at a speed of 19.4 m/s, (a) then what is the banking angle? (b) What would be the required coefficient of static friction, mu_s, between the road and the car's tires so that a car could make the same radius turn at the same speed, but without banking? A geosynchronous satellite stays above the same point on the Earth's equator by having an orbital period that is exactly 24 h long. At what height above the Earth's surface must such a satellite orbit? The mass of the Earth is m_E = 5.987 times 10^24 kg. The radius of the Earth is 6380 km.

Explanation / Answer

9) (a) For frictionless banked turn, banking angle is given by,

tan = v2/rg

=> = tan-1(v2/rg) = tan-1[19.42 / (80.0 * 9.81)] = 25.6o

(b) = v2/rg = 19.42 / (80.0 * 9.81) = 0.480

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