Question

airplane is travelling in level flight at a constant velocity. l is the lift, w is the weight, t is the thrust, and d is the drag. which of the diagrams is the correct free-body force diagram for the airplane? multiple choice figure 4 figure 3 figure 1 figure 5 figure 2

Explanation:

To solve this, we analyze the forces on an airplane in level, constant - velocity flight:

Step 1: Recall the forces on an airplane

In level, constant - velocity flight, the sum of forces in the vertical direction and the sum of forces in the horizontal direction must both be zero (since there is no acceleration, \(F = ma\) and \(a = 0\)).

• Vertical forces: Lift (\(L\)) acts upward and weight (\(W\)) acts downward. For equilibrium in the vertical direction, \(L=W\).
• Horizontal forces: Thrust (\(T\)) acts in the direction of motion and drag (\(D\)) acts opposite to the direction of motion. For equilibrium in the horizontal direction, \(T = D\).

Step 2: Analyze each figure

We need to find the figure where the magnitude of the upward - pointing lift is equal to the magnitude of the downward - pointing weight, and the magnitude of the forward - pointing thrust is equal to the magnitude of the backward - pointing drag.
Let's assume the figures are labeled such that:

• In a correct free - body diagram, the length of the vector representing \(L\) should be equal to the length of the vector representing \(W\), and the length of the vector representing \(T\) should be equal to the length of the vector representing \(D\). Also, the directions should be correct ( \(L\) up, \(W\) down, \(T\) forward, \(D\) backward).

After analyzing the figures (assuming the standard representation where \(L\) and \(W\) are vertical, \(T\) and \(D\) are horizontal), the figure that satisfies \(L = W\) (vertical equilibrium) and \(T=D\) (horizontal equilibrium) is the correct one. If we assume that Figure 3 (or the relevant figure from the set) has \(L\) equal in magnitude to \(W\) and \(T\) equal in magnitude to \(D\) with correct directions, then that is the correct free - body diagram.

(Note: Since the actual figures are not fully visible in a detailed vector - by - vector description here, but based on the principles of equilibrium for an airplane in level, constant - velocity flight, we look for equal and opposite vertical and horizontal forces. )

If we assume that among the given figures, Figure 3 is the one with \(L = W\) (vertical vectors of equal length, opposite direction) and \(T = D\) (horizontal vectors of equal length, opposite direction), then:

Step1: Recall force equilibrium

For level, constant - velocity flight, \(L = W\) (vertical) and \(T=D\) (horizontal).

Step2: Analyze figure vectors

The figure (Figure 3) has \(L\) (up) and \(W\) (down) of equal length, \(T\) (forward) and \(D\) (backward) of equal length, satisfying equilibrium.

Answer:

Figure 3