An arresting gear system is used to stop a 12,000 \text{ kg} aircraft landing on a flight … — Armed Services Vocational Aptitude Battery (ASVAB)

An arresting gear system is used to stop a $12,000 \text{ kg}$ aircraft landing on a flight deck. The aircraft touches down with a velocity of $144 \text{ km/h}$ and is brought to a complete stop in $2.0 \text{ seconds}$ by the arresting wire. Assuming a constant deceleration, what is the magnitude of the average net braking force applied to the aircraft?

A
$600 \text{ N}$
B
$864,000 \text{ N}$
$240,000 \text{ N}$ Answer
D
$2,352,000 \text{ N}$

Answer

The correct magnitude of the net braking force is

240,000 \text{ N}

The correct answer accurately calculates the force by first converting the velocity from km/h to m/s (

144 \text{ km/h} \times \frac{1000 \text{ m}}{3600 \text{ s}} = 40 \text{ m/s}

). It then finds the magnitude of acceleration (

a = \frac{\Delta v}{t} = \frac{40 \text{ m/s}}{2.0 \text{ s}} = 20 \text{ m/s}^2

) and applies Newton's Second Law (

F = m \times a = 12,000 \text{ kg} \times 20 \text{ m/s}^2 = 240,000 \text{ N}

Step-by-Step Solution

Convert the initial velocity from km/h to m/s.

144 \text{ km/h} \times \left(\frac{1000 \text{ m}}{3600 \text{ s}}\right) = 40 \text{ m/s}

Standard SI units (meters and seconds) are required to correctly calculate force in Newtons.

Calculate the magnitude of acceleration (deceleration) using the change in velocity over time.

a = \frac{40 \text{ m/s}}{2.0 \text{ s}} = 20 \text{ m/s}^2

Acceleration is defined as the rate of change of velocity.

Apply Newton's Second Law to find the average net braking force.

F = 12,000 \text{ kg} \times 20 \text{ m/s}^2 = 240,000 \text{ N}

Newton's Second Law states that force equals mass times acceleration (

F = ma

Key Concept

Newton's Second Law (F=ma) and Kinematics

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic