As a car rounds the top of a hill at a speed of 27.53 m/s, it very briefly loses contact with the pavement. This section of the road has an approximately circular shape. Find the radius r?
v^2/r=g
solve for radius r.
To find the radius of the circular section of the road, we can use the concept of centripetal force.
When the car loses contact with the pavement, the only force acting on it is the gravitational force. This force can be equated to the centripetal force required to keep the car moving in a circular path.
The gravitational force acting on the car is given by the formula:
F_gravity = m * g
where m is the mass of the car and g is the acceleration due to gravity.
The centripetal force acting on the car is given by the formula:
F_centripetal = (m * v^2) / r
where v is the speed of the car and r is the radius of the circular path.
Setting the gravitational force equal to the centripetal force, we have:
m * g = (m * v^2) / r
Canceling out the mass term, we get:
g = v^2 / r
Solving for the radius r, we have:
r = v^2 / g
Substituting the given values, we have:
r = (27.53 m/s)^2 / (9.8 m/s^2)
Calculating the value, we get:
r ≈ 75.03 meters
Therefore, the radius of the circular section of the road is approximately 75.03 meters.