A twin-engine military cargo aircraft with a total mass of 80,000 \text{ kg} is accelerati… — Armed Services Vocational Aptitude Battery (ASVAB)

A twin-engine military cargo aircraft with a total mass of $80,000 \text{ kg}$ is accelerating down a runway for takeoff. Each of the two engines generates $140,000 \text{ N}$ of forward thrust. If the combined forces of rolling friction and aerodynamic drag opposing the aircraft's motion amount to $80,000 \text{ N}$ , what is the forward acceleration of the aircraft in $\text{m/s}^2$ ?

Answer: 2.5 m/s^2

Answer

The forward acceleration of the aircraft is 2.5 m/s².

To accurately determine the acceleration, one must first find the net force acting on the aircraft. The total forward thrust is the sum of both engines (

140,000 \text{ N} \times 2 = 280,000 \text{ N}

). Subtracting the opposing forces of friction and drag (

80,000 \text{ N}

) yields a net forward force of

200,000 \text{ N}

. Dividing this net force by the aircraft's mass of

80,000 \text{ kg}

gives a forward acceleration of

2.5 \text{ m/s}^2

Step-by-Step Solution

Calculate the total forward thrust applied to the aircraft.

2 \times 140,000 \text{ N} = 280,000 \text{ N}

The aircraft has two engines, and the problem provides the thrust generated by each individual engine.

Calculate the net force (

F_{net}

) acting on the aircraft.

F_{net} = 280,000 \text{ N} - 80,000 \text{ N} = 200,000 \text{ N}

Net force is the vector sum of all forces. The opposing forces (drag and friction) must be subtracted from the forward thrust.

Apply Newton's Second Law to calculate the acceleration.

a = \frac{200,000 \text{ N}}{80,000 \text{ kg}} = 2.5 \text{ m/s}^2

According to Newton's Second Law, acceleration equals the net force divided by the mass (

a = \frac{F_{net}}{m}

Key Concept

Newton's Second Law of Motion (

F_{net} = ma

)

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