Centripetal Force: Calculating Bank Angle for Plane Circling Airport

[pats6]

Homework Statement

As your plane circles an airport, it moves in a horizontal circle of radius 2100m with a speed of 400km/h. If the lift of the airplane's wings is perpendicular to the wings, at what angle should the plane be banked so that it doesn't tend to slip sideways

Homework Equations

The Attempt at a Solution

 

[LowlyPion]

So what are your thoughts on how to solve it?

 

[pats6]

i do not know i tried to draw a diagram for the problem and when i worked the problem out i got a really small number

 

[pats6]

i know that i need to find the horizontal lift components but I am not sure how

 

[LowlyPion]

If the plane is in equilibrium - flying in a circle - what do you know that must be balanced that will keep it from slipping sideways?

 

[pats6]

I should be able to use arctan(v^2/rg) to give me the angle
when i plug the numbers in i get arctan(400^2/9.8*2100)=90
and that is not the right

 

[LowlyPion]

400km/h = ? m/s?

 

[pats6]

400km/h= 1.1*10^-4
When i plugged it into the equation I got 3.3*10^-11 I don't think this is right because that angle is to small. Can u tell me what I am doing wrong.
arctan((1.1*10^-4)^2/(9.8)(2100)

 

[LowlyPion]

Gee, I get 111 m/s

400,000/3600 = 111.1111

 

[pats6]

ok i used that and i get 90 degrees when i put it in as an answer it is declined I am i still doing something wrong

 

[LowlyPion]

I really think you need to recalculate your tan^-1.