Question

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 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 more force. Increasing the acceleration of the airplane causes the engine to provide more force. Increasing the acceleration of the airplane causes the engine to provide less force. Increasing the acceleration of the airplane causes the engine to provide less force. Decreasing the mass of the airplane will result in the airplane accelerating more.

Answer 1

According to Newton's second law of motion, \( F = ma \), where \( F \) is the net force, \( m \) is the mass, and \( a \) is the acceleration. If the first airplane is twice as heavy as the second airplane, then for a constant net force provided by the engine:

1. The heavier airplane (mass \( 2m \)) will experience less acceleration than the lighter airplane (mass \( m \)) because: \[ a = \frac{F}{m} \]

2. So, for the lighter airplane: \[ a_1 = \frac{F}{m} \]

   And for the heavier airplane: \[ a_2 = \frac{F}{2m} = \frac{a_1}{2} \]

This means that the lighter airplane will accelerate more than the heavier airplane under the same force.

Therefore, the correct statement is: Decreasing the mass of the airplane will result in the airplane accelerating more.