Problem

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 the contents. These energy absorbers can get pretty complicated to model (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. Assuming that m = 3 kg and that the box is dropped from a height of 1.5 m, determine the maximum displacement of the vase relative to the box and the maximum force on the vase if k = 3500 N/m. Treat the vase as a particle and neglect all forces except for gravity and the spring force. Assume that the spring relaxes after the box is dropped and that it does not oscillate.