To answer this question, we can use 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.
- Scenario: We have two airplanes powered by the same type of engine. The first airplane is twice as heavy as the second airplane.
Let's denote:
- The mass of the second airplane as \( m \).
- The mass of the first airplane as \( 2m \).
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Assuming constant net force (same engine):
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For the first airplane, using Newton's second law: \[ F = (2m)a_1 \quad \text{(where \( a_1 \) is the acceleration of the first airplane)} \]
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For the second airplane: \[ F = ma_2 \quad \text{(where \( a_2 \) is the acceleration of the second airplane)} \]
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Since both airplanes have the same force produced by the engine (let's say \( F \)), we can equate both equations to find the acceleration: \[ (2m)a_1 = F \implies a_1 = \frac{F}{2m} \] \[ ma_2 = F \implies a_2 = \frac{F}{m} \]
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Now, examine the relationship between \( a_1 \) and \( a_2 \):
- Since \( a_2 = \frac{F}{m} \) and \( a_1 = \frac{F}{2m} \), it's clear that: \[ a_1 = \frac{1}{2} a_2 \] This means the second airplane (the lighter one) accelerates faster than the first airplane (the heavier one).
Conclusion:
- Decreasing the mass of the airplane will result in the airplane accelerating more.
Therefore, the correct statement is: Decreasing the mass of the airplane will result in the airplane accelerating more.