Radius of largest possible loop of an Airplane.

[HRubss]

Homework Statement

A 2250 kg airplane makes a loop the loop (vertical circle) at a speed of 320 km/hour. Find (a) the radius of the largest circular loop possible and (b) The force on the plane at the bottom of this loop.

Homework Equations

F = m*a
Centripetal Force = m * (v²)/r
"Critical Speed" = Sqrt ( r*g) (I'm not sure if that's the proper term)
1/2 *m*v² = 1/2*m*v²

The Attempt at a Solution

Since no height was given in the problem, I set the altitude of the plane at 0 so it shouldn't have any potential energy at the bottom of the loop. Using the conservation of energy and 0 potential energy, I have the 3rd equation. I also know that the "critical speed" is equal to the square root of the radius * gravitation force so I substitute that into my final kinetic energy's velocity and solve for the radius. I'm not sure if this is correct and I know that the normal force is dependent on the finding the correct radius, I don't attempt part b just yet.

 

[mfb]

The problem statement is a bit weird because (a) airplanes have thrust and (b) airplanes have wings. It is unclear what you are supposed to assume. No thrust and no drag (=conservation of energy is useful)? Constant speed? "Feet down" feeling at the top (=the critical speed applies)? Or nearly zero speed at the top?
Assuming no thrust, no drag, and "feet down" feeling: At which height does the airplane need this critical speed (or, asked differently: where is this the limiting factor)? You can plug that into an equation for the conservation of energy and solve for r.

 

[CWatters]

I agree question is a bit problematical.

I would assume that the pilot maintains a constant speed.
I probably wouldn't assume the pilot experiences positive g ("feet down" feeling) at the top because I think that implies a loop of bigger radius is possible.

 

[haruspex]

My guess is you are supposed to pretend that the airplane is not capable of flying upside down for an extended period, i.e. that it can generate no lift when inverted. So at the top of the loop it is behaving like a wingless rocket, or even a projectile.

 

[mfb]

I agree question is a bit problematical.

I would assume that the pilot maintains a constant speed.
I probably wouldn't assume the pilot experiences positive g ("feet down" feeling) at the top because I think that implies a loop of bigger radius is possible.

This combination of assumptions doesn't lead to a maximal radius.