Question

An 800-kg race car can drive around an unbanked turn with coefficient of static friction between the track and the car's tires of 0.02. The turn has a radius of curvature of 150 m. Air flowing over the car's wing exerts a downward-pointing force of 10 000 N on the car. Calculate the maximum speed without slipping.

Answer 1

Solution :

Given :

m = 800 kg

μ_s = 0.02

r = 150 m

F_air = 10000 N

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From the given diagram :

Here, Normal force acting on the car will be given as : N = F_g + F_air

∴ N = (mg) + F_air

∴ N = (800 kg)(9.81 m/s²) + (10000 N)

∴ N = 7848 N + 10000 N

∴ N = 17848 N

And, Centripetal force is provided by frictional force :

∴ F_C = f_s

∴ m v² / r = μ_s N

∴ (800 kg) v² / (150 m) = (0.02)(17848 N)

∴ v² = 66.93 m²/s²

∴ v = 8.18 m/s

Therefore : The maximum speed without slipping will be 8.18 m/s.