Banked Curve Physics
Example 5.11
A circular racetrack of radius 300 m is banked at an angle of 15°. The coefficient of friction between the wheels and road is 0.2. Find:
- The optimum speed to avoid wear and tear on tires
- The maximum permissible speed to avoid slipping
Given Values
Radius (R) = 300 m
Bank Angle (θ) = 15°
Friction (μ) = 0.2
Gravity (g) = 9.8 m/s²
Optimum Speed
v₀ = √(Rg tanθ)
= √(300×9.8×tan15°)
= 28.1 m/s
Max Speed
vₘₐₓ = √(Rg(μ+tanθ)/(1-μtanθ))
= √(300×9.8×0.466)
= 38.1 m/s
