Skid friction

Find the smallest coefficient of skid friction between the car tires and the road so that the car can drive at a 200 m radius at 108 km/h and does not skid.

Result

k =  2.18

Solution:

r=200 m v=108 km/hm/s=108/3.6 m/s=30 m/s g=9.81 m/s2  Fg=mg Fo=mv2/r  Fok=Fg mv2/rk=mg  k=g r/v2=9.81 200/302=10950=2.18r=200 \ \text{m} \ \\ v=108 \ km/h \rightarrow m/s=108 / 3.6 \ m/s=30 \ m/s \ \\ g=9.81 \ \text{m/s}^2 \ \\ \ \\ F_g=mg \ \\ F_o=m v^2 / r \ \\ \ \\ F_o k=F_g \ \\ m v^2 / r k=m g \ \\ \ \\ k=g \cdot \ r / v^2=9.81 \cdot \ 200 / 30^2=\dfrac{ 109 }{ 50 }=2.18



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