An airplane is flying in a horizontal circle at a
speed of 105 m/s. The 76.0 kg pilot does not
want the centripetal acceleration to exceed
6.35 times free-fall acceleration.
a) Find the minimum radius of the plane’s
path.
Answer in units of m.
(105^2)/(6.35*9.8)= yo answer
6.35g<=v^2/r
calculate r.
177.16
Why did the airplane go to therapy?
Because it had too many issues with turning.
Now, let's calculate the minimum radius for the plane's path. We can start by calculating the maximum centripetal acceleration the pilot can tolerate. The equation for centripetal acceleration is:
a = v^2 / r
where:
a = centripetal acceleration
v = velocity
r = radius of the circle
In this case, we want to find the minimum radius, so we can rearrange the equation to solve for r:
r = v^2 / a
Now we substitute the given values into the equation:
v = 105 m/s
a = 6.35 times the acceleration due to gravity (g)
Since the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the maximum centripetal acceleration:
a_max = 6.35 * 9.8 m/s^2
Finally, we can substitute the values and solve for the minimum radius:
r = (105 m/s)^2 / (6.35 * 9.8 m/s^2)
I'm going to crunch the numbers and find the answer for you.
To find the minimum radius of the airplane's path, we need to calculate the centripetal acceleration and then set it equal to 6.35 times the acceleration due to gravity (free-fall acceleration).
Centripetal acceleration is given by the equation:
a = v^2 / r
Where:
a = centripetal acceleration
v = velocity of the airplane
r = radius of the airplane's path
In this case, the centripetal acceleration should not exceed 6.35 times the free-fall acceleration, which is 9.8 m/s^2 (assuming we are on Earth).
So, we have the inequality:
a <= 6.35 * 9.8
Substituting the formula for centripetal acceleration, we get:
v^2 / r <= 6.35 * 9.8
We know the velocity of the airplane is 105 m/s, so substituting that value, we get:
105^2 / r <= 6.35 * 9.8
To find the minimum radius, we need to rearrange the inequality to isolate r. Let's multiply both sides by r:
105^2 <= 6.35 * 9.8 * r
Now, divide both sides by (6.35 * 9.8):
(105^2) / (6.35 * 9.8) <= r
Calculating this expression, we find:
r >= 198.4404713
Therefore, the minimum radius of the plane's path is 198.440 m (rounded to three decimal places).