To analyze the statements, we can use Newton's second law of motion, which states that \( F = ma \) (force equals mass times acceleration).
Given that the first airplane is twice as heavy as the second airplane, let's denote the mass of the second airplane as \( m \) and the mass of the first airplane as \( 2m \).
- If both airplanes are using the same engine, they have the same maximum thrust or net force (let's call it \( F \)).
- For the second airplane (mass \( m \)): \[ F = ma \implies a = \frac{F}{m} \]
- For the first airplane (mass \( 2m \)): \[ F = (2m)a' \implies a' = \frac{F}{2m} \]
Since \( a' \) (acceleration of the first airplane) will be half that of \( a \) (acceleration of the second airplane), we can draw conclusions about the statements:
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A. Decreasing the mass of the airplane will result in the airplane accelerating more.
- This is true because a lower mass would produce higher acceleration for the same amount of force.
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B. Increasing the acceleration of the airplane causes the engine to provide less force.
- This is false; to increase acceleration, the required force actually increases if the mass remains constant.
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C. Decreasing the mass of the airplane will result in the airplane accelerating less.
- This is false; decreasing mass results in more acceleration.
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D. Increasing the acceleration of the airplane causes the engine to provide more force.
- This is true; to accelerate more, the engine needs to provide more force (again applying \( F = ma \)).
Thus, the correct statements based on the question are A and D. However, since the question asks for the "correct" statement and presents them in a single point context, the best answer focusing on the effect of mass specifically in context to the airplane's acceleration is:
A. Decreasing the mass of the airplane will result in the airplane accelerating more.
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