A circular racetrack of radius 300 m is banked at 15° with friction coefficient 0.2. Find (a) the optimum speed with no tyre friction and (b) the maximum permissible speed.
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A circular racetrack of radius 300 m is banked at 15° with friction coefficient 0.2. Find (a) the optimum speed with no tyre friction and (b) the maximum permissible speed.

G1 Physics · Accepted Answer

Without friction, v(opt)=√(Rg tan15°)≈28 m/s. For the maximum speed, friction acts down the slope; using v(max)²/(Rg)=(sinθ+µcosθ)/(cosθ-µsinθ) with R=300 m, µ=0.2 gives v(max)≈38.19 m/s.