To analyze the situation of two airplanes with the same type of engine but different masses, we can apply Newton's second law of motion, which is stated as:
\[ F = ma \]
Where:
- \( F \) is the net force,
- \( m \) is the mass,
- \( a \) is the acceleration.
Given that the first airplane is twice as heavy as the second airplane, we can denote the mass of the second airplane as \( m \) and the mass of the first airplane as \( 2m \).
- If the net force applied by the engine is constant for both airplanes:
- For the second airplane (lighter): \( F = m a_2 \) ⇒ \( a_2 = \frac{F}{m} \)
- For the first airplane (heavier): \( F = 2m a_1 \) ⇒ \( a_1 = \frac{F}{2m} \)
According to these equations:
- The lighter airplane (mass \( m \)) will have greater acceleration (\( a_2 \)) than the heavier airplane (mass \( 2m \)), which will have lower acceleration (\( a_1 \)) because the force is the same, but the mass is different.
Now, looking at the provided statements:
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Decreasing the mass of the airplane will result in the airplane accelerating less. - Incorrect. Decreasing mass would increase acceleration.
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Increasing the acceleration of the airplane causes the engine to provide less force. - Incorrect. Increasing acceleration requires more force if mass remains constant.
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Decreasing the mass of the airplane will result in the airplane accelerating more. - Correct! Less mass with the same force yields greater acceleration.
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Increasing the acceleration of the airplane causes the engine to provide more force. - Correct in a general sense, but the statement is about a direct relation of acceleration to the force provided by the engine which can be misinterpreted.
The correct answer is: Decreasing the mass of the airplane will result in the airplane accelerating more.
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