Taking the Log Curve Turn I

Classical Mechanics Level 3

A race track has a portion that looks like a natural log curve: y = 10 ln ⁡ ( x / 10 ) y=10\ln(x/10) , where the units are in meters.

What is the fastest speed in kph the car can go without slipping off the track?

The coefficient of static friction is μ s = 0.8 \mu_s=0.8 . Use g = 10 m / s 2 g=10m/s^2


The answer is 51.9.

Max Yuen by Max Yuen , 42, USA

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1 solution

Maximum radius of curvature of the given curve is R=15√3 m. Therefore the maximum speed of the car can be √[(15√3)(0.8)(10)]=14.416868 m/s=51.9 km/hr.

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