Physics question

Question

A 2000. kg car is rounding a curve of radius 200. m on a level road.  At a velocity of 20.0m/s the car starts to slide on the pavement.   What is the static coefficient of friction (µs ) between the tires and the pavement?

Answer 1

A free body diagram looking down on the car from above shows the frictional force is preventing the car from sliding outwards (the same as if this were a rotating object on a string; the frictional force is analogous to tension).

Let μ be the static coefficient of friction, FF be the frictional force, N be the Normal Force, W be the weight, g be the acceleration due to gravity, m be the mass of the car, r be the radius of curvature, and v be the velocity of the car:

F_F = μN and N = W = mg (sum of the forces in the y-direction are zero) so F_F = μW and so μ = F_F/(mg).

F_F = mv²/r so μ = (mv²/r)/(mg) or μ = v²/(rg)

Plugging in the numbers:

μ = v²/(rg)

μ = 20²/(200•9.81)

μ = 400/1962

μ = 0.204

So the static coefficient of friction must be 0.204 when the car starts to slide.