Question

1. A 1500 kg car rounds a curve of radius 75 m at a speed of 25 m/s. The curve is banked at an angle of 22° to the horizontal. Calculate:

a) The magnitude of the frictional force

b) The coefficient of static friction

Answer 1

The forces acting on the wheel:

$$F_\text{net}=f\cos\theta+N\sin\theta,\\\space\\ N\cos\theta-mg-f\sin\theta=0,\\\space\\ F_\text{net}=m\frac{v^2}{R}.\\\space\\ m\frac{v^2}{R}=f\cos\theta+N\sin\theta,\\ f=26600\text{ N}.\\ N=32500\text{ N}.$$

b) The coefficient of friction is

$$\mu=\frac fN=0.819.$$