Question

A 950 kg car rounds an unbanked curve at a speed of 25 m/s. If the radius of the curve is 72 m, what is the minimum coefficient of friction between the car and the road required so that the car does not skid?

Answer 1

Compute the car's weight:

W = m g = (950 kg) (9.8 m/s²) = 9310 N

The net vertical force on the car is

∑ F = N - W = 0

so the normal force has magnitude

N = W = 9310 N

Then the friction force that keeps the car from skidding has magnitude F = µ N, where µ is the coefficient of friction, and it's friction that makes up the net horizontal force on the car. By Newton's second law, we have

F = m a

µ N = m v ² / R

µ (9310 N) = (950 kg) (25 m/s)² / (72 m)

µ ≈ 0.89