Packages for transporting delicate items (e.g., a laptop or glass) are designed to “absorb...

Packages for transporting delicate items (e.g., a laptop or glass) are designed to “absorb” some of the energy of the impact in order to protect their contents. These energy absorbers can get very complicated (e.g., the mechanics of Styrofoam peanuts can be complex), but we can begin to understand how they work by modeling them as a linear elastic spring of constant k that is placed between the contents (an expensive vase) of mass m and the package P. Assume that the vase’s mass is 3 kg and that the box is dropped from rest from a height of 1.5 m. Treating the vase as a particle and neglecting all forces except for gravity and the spring force, determine the value of the spring constant k so that the maximum displacement of the vase relative to the box is 0.15 m. Assume that the spring relaxes after the box is dropped and that it does not oscillate.

Figure P4.33