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.
radial acceleration=v^2/r
r>v^2/a=92.6^2/(9.25*9.8)=94.59m
v^2 / r ≤ 9.25g
r ≥ v^2 / 9.25g
To find the minimum radius of the circular path, we can start by calculating the maximum radial acceleration allowed.
The radial acceleration can be calculated using the formula:
a_r = v^2 / r
Where:
a_r is the radial acceleration
v is the velocity of the plane
r is the radius of the circular path
In this case, the velocity of the plane is given as 99.5 m/s.
Now, let's find the maximum radial acceleration allowed by multiplying the gravitational acceleration by 9.25:
a_max = 9.25 * (9.8 m/s^2)
Next, we can rearrange the formula for radial acceleration to solve for the radius:
r = v^2 / a_r
Substituting the known values:
r = (99.5 m/s)^2 / (9.25 * 9.8 m/s^2)
Calculating this expression will give us the minimum radius of the circular path.