Final answer:
The compression of the copper cube under the same conditions as the steel cube, which compresses by 50 nm, depends on the ratio of the Young's moduli for copper and steel. Without these specific values, the question cannot be answered numerically.
Step-by-step explanation:
The question involves a copper cube and a steel cube with identical dimensions on which an extremely massive object is placed.
The steel cube compresses by 50 nm under the weight, and the aim is to determine the compression of the copper cube under the same conditions, assuming that the masses of the cubes are negligible compared to the massive object.
The compression of the cubes would depend on the Young's modulus (or modulus of elasticity) for each material, which is a measure of the stiffness of a solid material. It defines the relationship between stress (force per area) and strain (proportional deformation) in a material.
Since we know the steel cube's compression, given the identical nature of the forces applied due to the massive object, we could set up a proportional relationship between the steel and copper compressions based on their Young's moduli, if those values were known.
Let's denote the Young's modulus of steel as E_s and that of copper as E_c. The deformation, or compression, is inversely proportional to the Young's modulus, assuming the same force is applied.
Denote the compressions for steel and copper as Δs and Δc respectively. If we know that Δs = 50 nm under a certain load and assuming the areas of cross-section to be the same for both cubes, we can establish the following relationship given a negligible difference in the applied forces:
(Δs/Δc) = (E_c/E_s)
Without the specific values of Young's moduli for steel and copper, we cannot provide a numerical answer to the compression of the copper cube.
This relationship illustrates that if the modulus of elasticity of copper is less than that of steel, then the copper would compress more than steel under the same force.