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

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Homework Help Overview

The discussion revolves around a problem concerning the minimum radius of a plane's circular path, specifically focusing on the forces acting on the pilot during this motion. Participants are examining the role of the normal force in relation to the pilot's acceleration, which should not exceed 7.0g.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Some participants explore the necessity of including the normal force in the calculations, questioning its relevance to the pilot's acceleration. Others suggest that the pilot's acceleration can be analyzed without directly calculating the normal force.

Discussion Status

The discussion is ongoing, with participants expressing confusion about the role of gravity and normal force in the context of circular motion. Some guidance has been provided regarding the relationship between acceleration, speed, and radius, but there remains a lack of consensus on the necessity of the normal force in the calculations.

Contextual Notes

Participants are working under the constraints of a homework problem, which may limit the information available for discussion. There is an emphasis on understanding the forces involved in circular motion without arriving at a definitive solution.

sakura741
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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

 
Physics news on Phys.org
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
 
ehild said:
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?
 
No, 330 m was the correct answer. ehild
 
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?
 
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
 
Sorry, I don't understand?

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

a = v^2/r?
 
Last edited:
sakura741 said:
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
 
Okay, but I am wondering, why is it that the force of gravity does that not factor into the equation?
 
  • #10
sakura741 said:
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
 
  • #11
Ah, okay. Thanks so much for your help!
 
  • #12
You are welcome.

ehild
 

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