# Circular motion and banked curve problem

1. Oct 24, 2011

### 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.

2. Oct 24, 2011

### 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.

3. Oct 24, 2011

### 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 dont know what to do.

4. Oct 24, 2011

### 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?

5. Oct 24, 2011

### bigbk92

y components- w downward, normal force up

6. Oct 24, 2011

### LawrenceC

What would happen if the plane were not banked?

7. Oct 24, 2011

### bigbk92

if it were not banked the plane would fly straight.

8. Oct 24, 2011

### LawrenceC

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

9. Oct 24, 2011

### bigbk92

the direction would depend on the angle of the embankment

10. Oct 24, 2011

### bigbk92

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

11. Oct 24, 2011

### 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.