To analyze the situation, we can apply Newton's Second Law of Motion, which states that \( F = ma \), where \( F \) is the net force, \( m \) is the mass, and \( a \) is the acceleration.
Given that one airplane is twice as heavy as the other, let's denote the mass of the lighter airplane as \( m \) and the mass of the heavier airplane as \( 2m \). If both airplanes are subjected to the same constant net force \( F \), we can derive their accelerations:
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For the lighter airplane: \[ a_1 = \frac{F}{m} \]
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For the heavier airplane: \[ a_2 = \frac{F}{2m} = \frac{1}{2} \cdot \frac{F}{m} = \frac{1}{2} a_1 \]
From this analysis, we see that the lighter airplane (mass \( m \)) will have greater acceleration than the heavier airplane (mass \( 2m \)).
Now, let's evaluate the provided statements based on this understanding:
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Increasing the acceleration of the airplane causes the engine to provide more force. - This is incorrect. Acceleration can be increased by decreasing mass, but for a constant mass, a greater acceleration implies a greater force is needed.
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Decreasing the mass of the airplane will result in the airplane accelerating less. - This is incorrect. A decrease in mass will lead to an increase in acceleration for a constant net force.
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Decreasing the mass of the airplane will result in the airplane accelerating more. - This is correct. A lighter airplane will accelerate more for the same engine force due to its lower mass.
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Increasing the acceleration of the airplane causes the engine to provide less force. - This is incorrect. To achieve greater acceleration, more force would need to be applied (assuming mass is constant).
The correct statement is: Decreasing the mass of the airplane will result in the airplane accelerating more.
9 answers