Question

A 1305 kg test car travels around a flat circular track that is 2.15 km long (circumference). If the coefficient of friction between the car’s tires and the track is 1.20 will the car be able to drive a speed of 55.7 m/s and stay on the track?

Answer 1

The Newton's second law says

$$ma=F=\mu N=\mu mg$$

$$v^2/R=\mu g$$

The critical speed

$$v_c=\sqrt{\mu gR}=\sqrt{1.20*9.8*2150}=159\:\rm m/s$$

Because $v<v_c$ , so the car be able to drive a speed of 55.7 m/s and stay on the track.