As a car rounds the top of a hill at a speed of 29.03 m/s, it very briefly loses contact with the pavement. This section of the road has an approximately circular shape (see figure). Find the radius r.
To find the radius r of the circular section of the road, we can make use of the concept of centripetal force.
The centripetal force acting on the car as it moves around the circular section is provided by the gravitational force, which is given by the weight of the car. When the car loses contact with the pavement briefly, the normal force acting on the car becomes zero, resulting in zero contact force.
For the car to maintain contact with the road, the centrifugal force (equal to the weight of the car) must be less than or equal to the maximum static friction force. This condition can be expressed as:
m * v^2 / r ≤ μ * m * g
Where:
m = mass of the car
v = velocity of the car
r = radius of the circular section
μ = coefficient of static friction between tires and road
g = acceleration due to gravity
Since the mass of the car cancels out, we can rewrite the equation as:
v^2 / r ≤ μ * g
Now we can plug in the given values:
v = 29.03 m/s
μ (coefficient of static friction) is not given, so we need to find it.
To find the coefficient of static friction, we need more information about the car or the road.