A car rounds a banked, frictionless curve of radius R = 80\text{ m}. For a design speed of v = 20\text{ m/s}, what is the bank angle? Use g = 9.8\text{ m/s}^2.

27.0° Banking equation: \tan\theta = v^2/(gR) = 400/(9.8 \times 80) = 400/784 \approx 0.5102. So \theta \approx \tan^{-1}(0.5102) \approx 27.0°.

Kinetic and Static Friction

AP Physics 1· difficulty 4/5

R = 80\text{ m}

Explanation

\tan\theta = v^2/(gR) = 400/(9.8 \times 80) = 400/784 \approx 0.5102

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