The co efficient of static friction between hard rubber of the tyres and the normal street pavement is about 0.8 . Calculate the maximum angle on a hill , that you can leave a car parked ?

To calculate the maximum angle on a hill that a car can be parked without rolling, we need to consider the forces acting on the car.

The force of gravity acting on the car can be broken down into two components: one parallel to the hill (mg sinθ) and one perpendicular to the hill (mg cosθ), where m is the mass of the car, g is the acceleration due to gravity, and θ is the angle of the hill.

The maximum angle at which the car will not roll can be determined by setting the force of static friction equal to the component of the force of gravity parallel to the hill:

μs * N = mg sinθ

Where μs is the coefficient of static friction and N is the normal force acting on the car (equal to mg cosθ).

Substitute N = mg cosθ into the equation:

μs * mg cosθ = mg sinθ

Simplify the equation:

μs = tanθ

Now, substitute the given coefficient of static friction (μs = 0.8) into the equation:

0.8 = tanθ

Take the inverse tangent of both sides to solve for θ:

θ = tan^(-1)(0.8) ≈ 38.66 degrees

Therefore, the maximum angle on a hill that you can leave a car parked without it rolling is approximately 38.66 degrees.