It is your responsibility to build a support beam that will be utilized to tensionedly hang a hefty weight. The beam is composed of steel with a nominal yield strength of $325$ MPa and has a square cross section. What are the beam's minimal measurements if it has to support $10,000kg$ of weight? Let us assume a safety factor of $4.$

A rectangular piece of molybdenum with dimensions $1cm2cm4cm$ is placed on a mass balance and is found to have a mass of $81\mathrm{.}857$ g $.$

a$)$ Use this data to calculate the density of the sample.

b$)$ Use atomic and crystal structure data obtained from Wikipedia to calculate the theoretical density of molybdenum.

c$)$ Offer a brief explanation as to why these two values might be different.