# Airplane wing and forces on it

• ~christina~
In summary, an airplane has a mass of 1.60x10^4 kg and each wing has an area of 40.0m^2. The pressure on the lower wing surface is 7.00x10^4 Pa and the pressure on the upper wing surface is -2,643,200 Pa.
~christina~
Gold Member

## Homework Statement

An airplane has a mass of 1.60x10^4 kg and each wing has an area of 40.0m^2. During level flight the pressure on the lower wing surface is 7.00x10^4 Pa. Determine the pressure on the upper wing surface.

http://img168.imageshack.us/img168/617/41426717vo3.th.jpg

## Homework Equations

$$\sum F= F_L -F_u - F_{mg} = 0$$

## The Attempt at a Solution

My basic problem is that I keep getting a negative number for the pressure which is odd

$$\sum F= F_L -F_u - F_{mg} = 0$$

$$F_u = F_{mg}- F_L$$

P= F/A

$$P_u= Mg - P_L A$$

$$((9.8m/s^2)*(1.60x10^4kg))-((40.0m^2)(7.00x10^4Pa))= P_u$$

$$-2,643,200 = P_u A$$

$$P_u= -66,080 Pa$$ =>

my problem is why is it negative?? is it because it's force is downward??
Plus..the answer that was given (only the answer) was 6.80x10^4 Pa so I must have done something wrong. However I ccalculated it 3 times and I still get the same answer.

Thank you very much =D

Last edited by a moderator:
First of all, your rearranging of the equation has an error:

FL - Fu - Fmg = 0

Now add Fmg to both sides of the equation, and subtract FL from both sides:

- Fu = Fmg - FL

This is not what you arrived at. The discrepancy explains your errant minus sign

Your third equation also makes no sense. You have written:

Pu = Mg - PLA

But Pu is a pressure whereas Mg and PLA are forces. You can't equate a pressure to a force. Your equation is not dimensionally consistent. Does this help?

cepheid said:
First of all, your rearranging of the equation has an error:

FL - Fu - Fmg = 0

Now add Fmg to both sides of the equation, and subtract FL from both sides:

- Fu = Fmg - FL

This is not what you arrived at. The discrepancy explains your errant minus sign

Hm I still get the same answer...just without the negative. 6.60x10^4Pa

cepheid said:
Your third equation also makes no sense. You have written:

Pu = Mg - PLA

But Pu is a pressure whereas Mg and PLA are forces. You can't equate a pressure to a force. Your equation is not dimensionally consistent. Does this help?

I actually forgot to type that in. On paper I did add that in.

I get the same answer as you, too.

catkin said:
I get the same answer as you, too.

okay then, I'm suspecting it might be a typo.

I don't think you understand. This equation that you have:

Pu = Mg - PLA

is WRONG, because the thing on the left-hand side is a pressure, and the quantities on the right-hand side are forces. Therefore your equation is not dimensionally consistent: it is in error and you need to fix it.

Either have all pressures or all forces.

cepheid said:
I don't think you understand. This equation that you have:

Pu = Mg - PLA

is WRONG, because the thing on the left-hand side is a pressure, and the quantities on the right-hand side are forces. Therefore your equation is not dimensionally consistent: it is in error and you need to fix it.

Either have all pressures or all forces.

this is what I have:

$$P_u A= Mg- P_L A$$

(technically now all forces)
I used this in my calculations.

Is its still wrong?

Well, it should be

$$-P_u A= Mg- P_L A$$

because of what we talked about before with the sign error. But other than that, it looks ok.

When I plug in the numbers, I get

$$P_u = 6.6076 \times 10^4 \ \ \textrm{Pa}$$

So if the book says 6.8*10^4, then maybe it IS a typo.

Sorry I misinterpreted what you were saying before about how you used the correct formula on paper, without the typo.

cepheid said:
Well, it should be

$$-P_u A= Mg- P_L A$$

because of what we talked about before with the sign error. But other than that, it looks ok.

When I plug in the numbers, I get

$$P_u = 6.6076 \times 10^4 \ \ \textrm{Pa}$$

So if the book says 6.8*10^4, then maybe it IS a typo.

oh yep and I corrected that..

Okay, thanks

## 1. What is the purpose of an airplane wing?

The main purpose of an airplane wing is to provide lift and support for the aircraft during flight.

## 2. How does an airplane wing create lift?

An airplane wing creates lift through the difference in air pressure above and below the wing. The shape of the wing, also known as an airfoil, allows air to flow faster over the top of the wing, creating lower air pressure and causing the wing to lift upwards.

## 3. What are the four forces acting on an airplane wing?

The four forces acting on an airplane wing are lift, weight, thrust, and drag. Lift and weight act in opposite directions, while thrust and drag act in opposite directions as well.

## 4. How does the angle of attack affect the forces on an airplane wing?

The angle of attack, or the angle at which the wing meets the oncoming air, affects the amount of lift and drag on an airplane wing. As the angle of attack increases, so does the lift, but at a certain point, the lift decreases and drag increases, causing the plane to stall.

## 5. What is the role of flaps and slats on an airplane wing?

Flaps and slats are movable parts on the trailing edge and leading edge of the wing, respectively. They help to increase lift and decrease stall speed during takeoff and landing by changing the shape of the wing.

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