Friction with curve

Question

A proud new Jaguar owner drives her car at a speed of 35 m/s into a corner. The coefficients of friction between the road and the tires are 0.70 (static) and 0.40 (kinetic). What is the minimum radius of curvature for the corner in order for the car not to skid?

 

I'm not entirely sure what a skid looks like mathematically.

 

Thank you in advance

Answer 1

Although the car is moving, it is actually the static friction acting perpendicular to the circular path that keeps the car on the circular path.  Solve by setting the centripetal force on the car (going around the circle) equal to the static friction, and get the radius of the circle from that.

 

mv²/r = μ_smg ⇒

 

r = v² / (μ_sg) = (35²) / [0.70(9.8)] m = 178.6 m

 

(By the way, 35 m/s is a pretty high speed, hence the high radius of turning without skidding.)