The coefficient of static friction between hard rubber and normal street pavement is about 0.42. On how steep a hill (maximum angle) can you leave a car parked?
29.2
To determine the maximum angle, or steepness, of the hill on which a car can be parked without rolling down, we need to consider the balance between the force of gravity and the maximum static friction force.
The force of gravity acting on the car can be calculated using the equation:
Force of gravity = mass of the car * gravitational acceleration
Next, we need to determine the maximum static friction force, which is given by:
Maximum static friction force = coefficient of static friction * normal force
The normal force is the force exerted by the ground on the car perpendicular to the surface. On a level ground, the normal force is equal to the force of gravity. However, on a sloping surface, the normal force changes. It can be calculated using the equation:
Normal force = mass of the car * gravitational acceleration * cos(angle)
Where angle is the inclination or angle of the hill.
Now, for the car to be parked without rolling down, the maximum static friction force should equal the force of gravity acting in the downhill direction:
Force of gravity = Maximum static friction force
mass of the car * gravitational acceleration = coefficient of static friction * mass of the car * gravitational acceleration * cos(angle)
mass of the car cancels out from both sides of the equation, leaving:
gravitational acceleration = coefficient of static friction * gravitational acceleration * cos(angle)
Now, we can solve for the angle:
cos(angle) = 1 / coefficient of static friction
Take the inverse cosine (arccos) of both sides:
angle = arccos(1 / coefficient of static friction)
Substituting the given coefficient of static friction of 0.42 into the equation:
angle = arccos(1 / 0.42)
Using a calculator, the angle is approximately 65.9 degrees.
Therefore, a car can be parked on a hill with a maximum angle of approximately 65.9 degrees without rolling down, assuming the coefficient of static friction between hard rubber and the street pavement is 0.42.