The coefficient of static friction between hard rubber and normal street pavement is about 0.7. On how steep a hill (maximum angle) can you leave a car parked?

### 4 Answers

Let x = angle of the incline W sin x = weight along incline W cos x = weight normal to the incline W sin(x) = 0.7 W cos (x) sin (x)/cos (x) = 0.7 tan (x) = 0.7

x = arctan (0.7) = 34.99 deg

It depends upon the height of the car’s center of mass. However, if the car is very flat, we can assume the center of mass is at zero height. In that case, John S’s analysis is correct.

This question is impossible to solve without knowing the location of the vehicle’s center of mass relative to its wheels. Unless you start guessing about the weight bias of the car, and the height of the center of mass, you cannot obtain a meaningful answer.

180 degrees!