The coefficient of static friction between hard rubber and normal street pavement is about 0.68. On how steep a hill (maximum angle) can you leave a car parked?
inv tan of 0.68
Ah, the age-old question: how steep can you park a car on a hill without it getting too frisky and rolling away like a daredevil on a skateboard?
Well, my friend, the answer lies within the coefficient of static friction between hard rubber tires and normal street pavement. At a coeff
To determine the maximum angle of a hill on which a car can be parked without rolling down due to static friction, we can use the coefficient of static friction and the concept of equilibrium.
The maximum angle can be found using the equation:
μs = tan(θ)
Where:
μs = coefficient of static friction
θ = maximum angle of the hill
Rearranging the equation to solve for θ:
θ = arctan(μs)
Given that the coefficient of static friction between hard rubber and normal street pavement, μs, is 0.68, we can substitute it into the equation:
θ = arctan(0.68)
Using a calculator, we find:
θ ≈ 34.99 degrees
Therefore, the maximum angle at which you can leave a car parked on a hill with hard rubber tires on normal street pavement is approximately 34.99 degrees.
To determine the maximum angle at which a car can be parked on a hill without sliding, we need to consider the concept of static friction. Static friction is the force that opposes the motion of an object when it is at rest. The maximum angle at which a car can be parked without sliding depends on the coefficient of static friction between the tires and the pavement.
Static friction can be calculated using the equation:
F_static = μ_static * N
Where:
F_static is the static friction force
μ_static is the coefficient of static friction
N is the normal force
In the case of a car parked on a hill, the weight of the car acts vertically downward, and we can split it into two components: one perpendicular to the surface of the hill (normal force), and the other parallel to the surface of the hill (gravitational force).
The normal force (N) is given by:
N = mg * cos(θ)
Where:
m is the mass of the car
g is the acceleration due to gravity (approximately 9.8 m/s^2)
θ is the angle of inclination of the hill
The maximum angle at which the car can be parked without sliding is when the force parallel to the hill (gravitational force component) is equal to the maximum static friction force:
F_gravity = μ_static * N
mg * sin(θ) = μ_static * mg * cos(θ)
Canceling out the mass (m) and rearranging the equation, we get:
tan(θ) = μ_static
Finally, we can solve for the angle (θ) using the inverse tangent (arctan) function:
θ = arctan(μ_static)
Substituting the given coefficient of static friction of 0.68 into the equation:
θ = arctan(0.68)
Calculating this value, we find that the maximum angle at which the car can be parked on the hill without sliding is approximately 34.6 degrees.