1. Feb 27, 2013

### sakura741

Hi all,

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

3. The attempt at a solution

2. Feb 27, 2013

### ehild

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

3. Feb 27, 2013

### sakura741

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?

4. Feb 27, 2013

### ehild

No, 330 m was the correct answer.

ehild

5. Feb 28, 2013

### 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?

6. Feb 28, 2013

### 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

7. Feb 28, 2013

### sakura741

Sorry, I don't understand?

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

a = v^2/r?

Last edited: Feb 28, 2013
8. Feb 28, 2013

### ehild

Yes, it is that simple.

ehild

9. Feb 28, 2013

### sakura741

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

10. Feb 28, 2013

### ehild

"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. Mar 1, 2013

### sakura741

Ah, okay. Thanks so much for your help!

12. Mar 1, 2013

### ehild

You are welcome.

ehild