The same type of engine is placed in two different airplanes. The first airplane is twice as heavy as the second airplane. Which statement is correct about the mass of the airplane and its acceleration, assuming a constant net force?(1 point)

Responses

Increasing the acceleration of the airplane causes the engine to provide more force.
Increasing the acceleration of the airplane causes the engine to provide more force.

Decreasing the mass of the airplane will result in the airplane accelerating more.
Decreasing the mass of the airplane will result in the airplane accelerating more.

Decreasing the mass of the airplane will result in the airplane accelerating less.
Decreasing the mass of the airplane will result in the airplane accelerating less.

Increasing the acceleration of the airplane causes the engine to provide less force.

1 answer

To analyze the situation involving the two airplanes with different masses but the same type of engine, we can apply Newton's second law of motion, which states:

\[ F = ma \]

where \( F \) is the net force, \( m \) is the mass, and \( a \) is the acceleration.

Given that the first airplane is twice as heavy as the second airplane, if both airplanes experience the same engine force (assuming constant net force), we can observe the following:

  1. For the heavier airplane (mass = \( 2m \)):

    \[ F = 2m \cdot a_1 \]

  2. For the lighter airplane (mass = \( m \)):

    \[ F = m \cdot a_2 \]

Since the net force \( F \) is constant and equal for both airplanes, we can rewrite these equations as:

  • For the first airplane: \[ a_1 = \frac{F}{2m} \]

  • For the second airplane: \[ a_2 = \frac{F}{m} \]

From this, we can see that:

\[ a_2 = 2a_1 \]

This means that the acceleration of the lighter airplane (mass \( m \)) is twice that of the heavier airplane (mass \( 2m \)). Therefore, decreasing the mass of the airplane (from the heavier to the lighter one) will indeed result in greater acceleration.

Based on this explanation, the correct statement is:

Decreasing the mass of the airplane will result in the airplane accelerating more.