A piece of electronic equipment that is surrounded by packing material is dropped so that it hits the ground with a speed of 4 m/s. After contact, the equipment experiences an acceleration of a = –kx, where k is a constant and x is the compression of the packing material. If the packing material experiences a maximum compression of 20 mm, at which point the box comes to a complete stop, determine the maximum acceleration of the equipment.

400 m/s²

Explanation:

The question asks us to find the acceleration it needs to change a speed of 4 m/s through a time distance of 20 mm.

Given that

v = 4 m/s

d = 20 mm or 20*10^-3 m

First we start by applying the energy formula,

E = ½ * m * v², on substituting, we have

E = ½ * m * 4²

E = ½ * 16m

E = 8m m²/s²

Next, to find the work needed, we use the formula

E = m * f * d

8m = m * f * 0.02

0.02f = 8

f, = 400 m/s²

Thus, it needs an acceleration of 400 m/s²

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