What is the relationship between speed and radius for a car to avoid skidding?

[Jeann25]

If a certain car, going with speed v, rounds a level curve with a radius R, it is just on the verge of skidding. If its speed is now doubled, the radius of the tightest curve on the same road that it can round without skidding is:

Answer is 4R.. but I don't understand why?

I know the equation is f = mV²/R

 

[andrewchang]

in the equation, the velocity is squared.

if the velocity becomes 2V, when you square it, it becomes 4V^2. to keep the car from skidding, the radius now has to change to 4r

 

[physicsfox]

Also, it is important to understand that the static friction, the source of the net centripetal force, is at its maximum value, and does not change.

 

[Jeann25]

I get it now. Thank you!