To analyze the situation, we can use Newton's second law of motion, which states that force equals mass times acceleration (F = ma).
- If the first airplane is twice as heavy as the second airplane, it would have twice the mass (let's denote the mass of the second airplane as 'm' and the first airplane as '2m').
- Assuming the same engine provides a constant net force (let's call it F), we can find the acceleration of each airplane.
For the first airplane: \[ F = (2m) \cdot a_1 \] \[ a_1 = \frac{F}{2m} \]
For the second airplane: \[ F = m \cdot a_2 \] \[ a_2 = \frac{F}{m} \]
From the equations, we can see that:
- The acceleration of the second airplane (a2) will be twice that of the first airplane (a1) because it has half the mass.
Now let's evaluate the provided statements:
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Decreasing the mass of the airplane will result in the airplane accelerating more. - True. A decrease in mass leads to greater acceleration for a given force.
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Increasing the acceleration of the airplane causes the engine to provide less force. - False. Increasing acceleration for a constant mass requires more force, not less, according to F = ma.
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Decreasing the mass of the airplane will result in the airplane accelerating less. - False. Decreasing the mass increases acceleration for a constant force.
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Increasing the acceleration of the airplane causes the engine to provide more force. - True. To achieve greater acceleration, the force must increase, assuming the mass remains constant.
In conclusion, the statements that are correct based on the principles of physics are:
- Decreasing the mass of the airplane will result in the airplane accelerating more.
- Increasing the acceleration of the airplane causes the engine to provide more force.
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