Question

A 12.5 kg black box flight recorder was pulled from an airplane wreckage and provided the following information. The plane was initially moving at a speed of 177.7 m/s as it contacted the ground and came to rest in a distance of 3.20 m. As an investigator of this crash you must determine the
acceleration of the box (/3)
Average net force applied to the box (/3)
work done on the box to bring it to rest (/3)

Answer 1

The acceleration of the box is how quickly it changed its speed from 177.7 m/s to 0 across 3.20 m:

$$a=\bigg|\frac{v_\text{f}^2-v_\text{i}^2}{2d}\bigg|=\bigg|\frac{0-177.7^2}{2\cdot3.2}\bigg|=4934\text{ m/s}^2,$$

which is equivalent to $503.1g$.

The average net force applied to the box can be found by Newton's second law:

$$F=ma=12.5\cdot4934=61675\text{ N}.$$

The work done on the box to bring it to rest can be fount by work-energy theorem: this work is equivalent to the change in kinetic energy:

$$W=KE_2-KE_1,\\ W=0-\frac{mv^2}{2}=0-\frac{12.5\cdot177.7^2}{2}=-197.4\text{ J}.$$