On a particular airplane wing, air flows over the upper surface with a speed of 115 m/s and along the bottom surface with a speed of 90 m/s during flight. If the area of the wing is 140 m^2, what is the lift force on the wing? Air density is 1.29 kg/m3.

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To calculate the lift force on the wing, we need to use the Bernoulli's equation, which relates the pressure difference between the upper and lower surfaces of the wing to the speed of the air flow. Bernoulli's equation states that:

P1 + 0.5 * ρ * v1^2 = P2 + 0.5 * ρ * v2^2

where:
P1 is the pressure on the upper surface of the wing,
P2 is the pressure on the lower surface of the wing,
ρ is the air density, and
v1 and v2 are the velocities of the air flow on the upper and lower surfaces of the wing, respectively.

We can rearrange the equation to solve for the pressure difference (ΔP = P1 - P2):

ΔP = 0.5 * ρ * (v2^2 - v1^2)

Substituting the given values:
ρ = 1.29 kg/m^3
v1 = 115 m/s
v2 = 90 m/s

ΔP = 0.5 * 1.29 kg/m^3 * (90 m/s)^2 - (115 m/s)^2

Now we can calculate ΔP:

ΔP = 0.5 * 1.29 kg/m^3 * (8100 m^2/s^2 - 13225 m^2/s^2)
= 0.5 * 1.29 kg/m^3 * (-5135 m^2/s^2)
= -3313.575 kg/(m*s^2) or -3313.575 Pa

The negative sign indicates that the pressure is higher on the lower surface than the upper surface, which creates the lift force.

Finally, the lift force (F) can be calculated by multiplying the pressure difference (ΔP) by the wing area (A):

F = ΔP * A
= -3313.575 Pa * 140 m^2
= -462899.5 N

Therefore, the lift force on the wing is approximately -462899.5 Newtons.