a plane is flying in a horizontal circle at 99.5 m/s. The 92.6 kg pilot does not want his radial acceleration to exceed 9.25g. What is the minimum radius of the circular path. The acceleration of gravity is 9.8 m/s^2.
To find the minimum radius of the circular path, we need to consider the forces acting on the pilot and the relationship between the centripetal acceleration and radial acceleration.
First, let's find the radial acceleration. The radial acceleration is the acceleration towards the center of the circular path and can be calculated using the formula:
Radial acceleration = (Centripetal force) / (mass of the pilot)
We can calculate the centripetal force using the formula:
Centripetal force = (mass of the pilot) * (centripetal acceleration)
Given that the plane is flying at a speed of 99.5 m/s and the acceleration due to gravity is 9.8 m/s^2, the centripetal acceleration can be calculated using the formula:
Centripetal acceleration = (velocity)^2 / (radius)
To convert the acceleration from "g" to m/s^2, we multiply by the acceleration due to gravity (9.8 m/s^2).
Now, let's solve the equation step by step:
1. Convert the desired maximum radial acceleration from "g" to m/s^2:
Maximum radial acceleration = 9.25g * (9.8 m/s^2)
2. Calculate the centripetal acceleration from the given speed:
Centripetal acceleration = (99.5 m/s)^2 / radius
3. Set the maximum radial acceleration equal to the centripetal acceleration and solve for the radius:
Maximum radial acceleration = (92.6 kg) * (Centripetal acceleration)
or,
9.25g * (9.8 m/s^2) = (92.6 kg) * [(99.5 m/s)^2 / radius]
4. Solve for the radius:
radius = [(92.6 kg) * (99.5 m/s)^2] / [9.25g * (9.8 m/s^2)]
Plugging in the given values, we can calculate the minimum radius of the circular path.