The upward lift force L on the wings of an aircraft is calculated using the relationship $$L = \frac{1}{2} \rho v^2 A C_L$$ where: $\rho$ is the density of air $v$ is the speed of the wings through the air $A$ is the area of the wings $C_L$ is the coefficient of lift. The weight of a model aircraft is 80.0N. The area of the wings on the model aircraft is 3.0m². The coefficient of lift for these wings is 1.6. The density of air is 1.29kg/m³. The speed required for the model aircraft to maintain a level flight is A 2.5 m s⁻¹ B 3.6 m s⁻¹ C 5.1 m s⁻¹ D 12.9 m s⁻¹ E 25.8 m s⁻¹

Scottish Highers Physics Unseen Formula/Graph Plotting: The upward lift force L on the w

The upward lift force L on the wings of an aircraft is calculated using the relationship $$L = \frac{1}{2} \rho v^2 A C_L$$ where: $\rho$ is the density of air $v$ is the speed of the wings through the air $A$ is the area of the wings $C_L$ is the coefficient of lift - Scottish Highers Physics - Question 20 - 2015

Question 20

$The-upward-lift-force-L-on-the-wings-of-an-aircraft-is-calculated-using-the-relationship--$$L-=-\frac{1}{2}-\rho-v^2-A-C_L$$--where:--$\rho$-is-the-density-of-air-$v$-is-the-speed-of-the-wings-through-the-air-$A$-is-the-area-of-the-wings-$C_L$-is-the-coefficient-of-lift-Scottish Highers Physics-Question 20-2015.png$

The upward lift force L on the wings of an aircraft is calculated using the relationship $$L = \frac{1}{2} \rho v^2 A C_L$$ where: $\rho$ is the density of air $v... show full transcript

Worked Solution & Example Answer:The upward lift force L on the wings of an aircraft is calculated using the relationship $$L = \frac{1}{2} \rho v^2 A C_L$$ where: $\rho$ is the density of air $v$ is the speed of the wings through the air $A$ is the area of the wings $C_L$ is the coefficient of lift - Scottish Highers Physics - Question 20 - 2015

Step 1

Calculate the Lift Force

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Answer

We know from the problem that the weight of the model aircraft (which equals the lift force for level flight) is 80.0 N. Thus, we can set the lift force equal to this value:

$L = 80.0 \text{ N}$

Step 2

Identify Given Values

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Answer

We have the following values:

$\rho = 1.29 \text{ kg/m}^3$ (density of air)
$A = 3.0 \text{ m}^2$ (area of the wings)
$C_L = 1.6$ (coefficient of lift)
$L = 80.0 \text{ N}$ (lift force)

Step 3

Solve for Speed v

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Answer

Using the lift equation:

$L = \frac{1}{2} \rho v^2 A C_L$

we can rearrange it to solve for speed $v$ :

$v = \sqrt{\frac{2L}{\rho A C_L}}$

Substituting the known values: $v = \sqrt{\frac{2 \times 80.0}{1.29 \times 3.0 \times 1.6}}$

Calculating this gives: $v = \sqrt{\frac{160.0}{6.144}} \approx \sqrt{26.0} \approx 5.1 \text{ m/s}$

Step 4

Choose the Correct Answer

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Answer

Thus, the speed required for the model aircraft to maintain a level flight is:

C 5.1 m s⁻¹

Calculate the Lift Force

Identify Given Values

Solve for Speed v

Choose the Correct Answer

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