A plane is in level flight at constant speed and each of its two wings has an area of 40 m². If the speed of the air is 180 km/h over the lower wing surface and 252 km/h over the upper wing surface, the mass of the plane is ___________ kg. (Take air density to be 1 kg m⁻³ and g = 10 ms⁻²) Numerical answer type. Work it out, then open the answer.

Answer: 9600. 180 km/h = 50 m/s, 252 km/h = 70 m/s Δ P = 1/2ρ(vu² - vl²) = 1/2(1)(4900 - 2500) = 1200 Pa Lift on both wings: F = Δ P × 2A = 1200 × 80 = 96000 N mg = F ⇒ m = (96000)/(10) = 9600 kg

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Applications of Bernoulli's Theorem

A plane is in level flight at constant speed and each of its two wings has an area of $40\text{ m}^2$ . If the speed of the air is $180\text{ km/h}$ over the lower wing surface and $252\text{ km/h}$ over the upper wing surface, the mass of the plane is ___________ kg.

(Take air density to be $1\text{ kg m}^{-3}$ and $g = 10\text{ ms}^{-2}$ )

Numerical answer type. Work it out, then open the answer.

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Answer: 9600

$180\text{ km/h} = 50\text{ m/s}$ , $252\text{ km/h} = 70\text{ m/s}$
$\Delta P = \frac{1}{2}\rho(v_u^2 - v_l^2) = \frac{1}{2}(1)(4900 - 2500) = 1200\text{ Pa}$
Lift on both wings: $F = \Delta P \times 2A = 1200 \times 80 = 96000\text{ N}$
$mg = F \Rightarrow m = \frac{96000}{10} = 9600\text{ kg}$

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