Question

an airplane is traveling 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 diagram for the airplane?

Explanation:

For an airplane in level, constant - velocity flight, the net force in the vertical direction (lift \(L\) and weight \(W\)) and the net force in the horizontal direction (thrust \(T\) and drag \(D\)) must both be zero (Newton's first law, since acceleration is zero). So, \(L = W\) (vertical equilibrium) and \(T=D\) (horizontal equilibrium). We need to find the diagram where the upward lift equals the downward weight and the forward thrust equals the backward drag.

Answer:

To determine the correct free - body diagram, we analyze the force balances:

1. Vertical Force Balance: The lift (\(L\)) acting upward must be equal in magnitude to the weight (\(W\)) acting downward.
2. Horizontal Force Balance: The thrust (\(T\)) acting forward must be equal in magnitude to the drag (\(D\)) acting backward.

Looking at the diagrams (assuming the standard representation where \(L\) is up, \(W\) is down, \(T\) is forward, and \(D\) is backward), the diagram where \(L = W\) (vertical vectors have the same length) and \(T = D\) (horizontal vectors have the same length) is the correct one. If we assume the diagrams are labeled such that in a correct diagram, for example, if Figure 2 (or the relevant figure with \(L\) up, \(W\) down, \(T\) forward, \(D\) backward and equal - length pairs) shows \(L = W\) and \(T = D\), that is the correct free - body diagram.

(Note: Since the actual figure details are a bit unclear from the text - based description, but the key is the force balance. In a typical correct diagram, vertical forces \(L\) (up) and \(W\) (down) are equal, horizontal forces \(T\) (forward) and \(D\) (backward) are equal. So the answer would be the diagram with \(L\) and \(W\) of equal magnitude (vertical) and \(T\) and \(D\) of equal magnitude (horizontal).)