Circular motion and banked curve problem

[bigbk92]

I am stumped on this problem. If anyone can help it would be greatly appreciated.

A plane is approaching an airport in a traffic holding pattern. While awaiting its clearence to land, the plane traverses a horizontal circle of radius 2520 meters at constant speed, Each complete turn of the circle delays the scheduled landing by another 2.5 minutes. Assume that the direction of the lift force exerted on the plane by the air is exactally perpendicular to the wing surface. Please determine, to three significant figures, the angle at which the crew must bank the plane with respect to the horizontal, in order to accomplish these turns.

 

[LawrenceC]

Draw a free body diagram of the plane and note the forces acting on it. You should see what needs to be balanced in order for the plane to remain in the pattern.

 

[bigbk92]

From this I can extract the time of a rotation to be 150 seconds. And the radius is given a 2520 meters. So from this I can find radial acceleration as (4pi^2)r/t^2 or 4.42 m/s^2 After that I don't know what to do.

 

[LawrenceC]

"Assume that the direction of the lift force exerted on the plane by the air is exactally perpendicular to the wing surface."

Does this suggest anything to you?

 

[bigbk92]

y components- w downward, normal force up

 

[LawrenceC]

What would happen if the plane were not banked?

 

[bigbk92]

if it were not banked the plane would fly straight.

 

[LawrenceC]

If the plane is banked, what is the direction of the lift force due to aerodynamics?

 

[bigbk92]

the direction would depend on the angle of the embankment

 

[bigbk92]

Nsin@ = ma
Ncos@ = mg
Divide equations and plug in numbers and angle should come to 24.3 degrees, is this correct?

 

[LawrenceC]

That's what I computed. But I am having a problem understanding your notation. I would prefer if you would write one equation that balances the forces. And radially is a good direction to work with.