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 pretty complicated (e.g., the mechanics of Styrofoam peanuts is not easy), 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 weighs 6 lb and that the box is dropped from a height of 5 ft. Treat the vase as a particle, and neglect all forces except for gravity and the spring force.

Figure P4.20

Plot the maximum displacement of the vase relative to the box and the maximum force on the vase as a function of the linear elastic spring constant k. What do these plots tell you about the problem you would encounter in trying to minimize the force on the vase?