What Are the Unknown Variables in a Circular Arc Pilot Dynamics Problem?

[Infamous911]

Homework Statement

A pilot of mass 50 kg comes out of a vertical dive in a circular arc such that her upward acceleration is 6g.

(a) What is the magnitude of the force exerted by the airplane seat on the pilot at the bottom of the arc?

(b) If the speed of the plane is 390 km/h, what is the radius of the circular arc?

Homework Equations

Fc = (mv^2)/r
(v^2/r)=a

The Attempt at a Solution

(a)
Fc = 50(6)(9.8)
Fc = 2940

(b)
2940 = (50(360^2))/r
r=2586.735

Apparently these answers are wrong and I have no idea why.

 

[HallsofIvy]

Homework Statement

A pilot of mass 50 kg comes out of a vertical dive in a circular arc such that her upward acceleration is 6g.

(a) What is the magnitude of the force exerted by the airplane seat on the pilot at the bottom of the arc?

(b) If the speed of the plane is 390 km/h, what is the radius of the circular arc?

Homework Equations

Fc = (mv^2)/r
(v^2/r)=a

The Attempt at a Solution

(a)
Fc = 50(6)(9.8)
Fc = 2940

There would be 1 g, or 9.8 times mass, force even if the pilot were flying in a straight line. If the upward acceleration is 6g, then the force will be 50(7)(9.8), adding that original 1g.

(b)
2940 = (50(360^2))/r
r=2586.735

Where did "360" come from? Did you mean to use 390?

Apparently these answers are wrong and I have no idea why.

 

[berkeman]

Homework Statement

A pilot of mass 50 kg comes out of a vertical dive in a circular arc such that her upward acceleration is 6g.

(a) What is the magnitude of the force exerted by the airplane seat on the pilot at the bottom of the arc?

(b) If the speed of the plane is 390 km/h, what is the radius of the circular arc?

Homework Equations

Fc = (mv^2)/r
(v^2/r)=a

The Attempt at a Solution

(a)
Fc = 50(6)(9.8)
Fc = 2940

(b)
2940 = (50(360^2))/r
r=2586.735

Apparently these answers are wrong and I have no idea why.

The first answer looks right to me. Are you sure it's wrong?

In (b), you first have a typo for the speed, and second, you have not converted the speed from km/hr to m/s. You need to work in a consistent set of units, usually the SI/mks system.

 

[berkeman]

Ah, good point about adding in the extra 1g for level flight, Halls. I thought about it but reasoned incorrectly.

 

[Infamous911]

Ok so I have solved (a) with a solution of 3430 N, thanks.

I'm still having problems with (b) though.

390 km/h = 108.333 m/s

3430=(50(108.333^2))/r
r=171.079

This isn't the correct answer apparently (I put in my answer into an online form and it tells me if it's right or wrong).

 

[Infamous911]

Nevermind, I figured out that it should instead be just:

a=v^2/r
6(9.8)=108.333^2/r
r=199.592

 

[berkeman]

You're Infamous! Good work.