Why is the normal force included in this plane's minimum radius problem?

[sakura741]

Hi all,

Homework Statement

My problem is exactly the same as the one here: https://www.physicsforums.com/showthread.php?p=2377784

In the solution that Vykan12 provides (which results in the correct answer according to the textbook), however, there is a normal force included in the equation. I don't understand why this is so? From what I can tell, the question is about the plane, not the pilot.

Homework Equations

The Attempt at a Solution

 

[ehild]

It is about the pilot,

What is the minimum radius of the plane's circular path if the pilot's acceleration at the lowest point is not to exceed 7.0g.

but he moves together with the plane. No need to calculate with the normal force. The pilot moves along a circular path, what is his acceleration in terms of the speed and radius of circle?

ehild

 

[sakura741]

It is about the pilot, but he moves together with the plane. No need to calculate with the normal force. The pilot moves along a circular path, what is his acceleration in terms of the speed and radius of circle?

ehild

So there IS no normal force, meaning that the answer is indeed 3.8 x 10^2 m and not 3.3 x 10^2?

 

[ehild]

No, 330 m was the correct answer. ehild

 

[sakura741]

I don't understand. This is how I solved it:

m=82 kg
v=150 m/s
a=7.0g

Fa is the 'upward force'

Fc = Fa - Fg
mv^2/r = ma - mg
v^2/r = a - g
v^2/(a-g) = r
r=v^2/(7g-g)
r=v^2/6g
r = (150m/s)^2/(6x9.8m^2/s^2)
=3.83 x 10^2 m

How do I get 330 m without using the force of normal, as is done in the solution in the link?

 

[ehild]

What do you call Fa? Is that not the normal force?

The acceleration of the plane (and the pilot) flying at constant speed v along a circle of radius R is equal to the centripetal acceleration. The acceleration can not exceed 7g. Fcp<7g. What is the problem?

ehild

 

[sakura741]

Sorry, I don't understand?

Edit: Nevermind, I think I got it. Is the equation simply:

a = v^2/r?

 

[ehild]

Sorry, I don't understand?

Edit: Nevermind, I think I got it. Is the equation simply:

a = v^2/r?

Yes, it is that simple.

ehild

 

[sakura741]

Okay, but I am wondering, why is it that the force of gravity does that not factor into the equation?

 

[ehild]

Okay, but I am wondering, why is it that the force of gravity does that not factor into the equation?

"The pilot's acceleration can not exceed 7g"

The acceleration is a=v²/R. The acceleration is 70 m/s². It is simple logic that if a=b and b=c then a=c.


If the question was "The pilot feels 7g, what is the radius of the circle" then gravity would come in:
The pilot moves along a circle. The forces are gravity and normal force N (from the seat). So Fcp=N-mg. The pilot feels the normal force from the seat: N = 7mg.

ehild

 

[sakura741]

Ah, okay. Thanks so much for your help!

 

[ehild]

You are welcome.

ehild