Final answer:
To determine if copper is harder than the plastic of a cup, a scratch test can be performed where copper is used to scratch the plastic. If the copper marks the plastic, it's harder; no mark indicates the plastic is harder.
Step-by-step explanation:
To find out whether copper is harder or softer than the plastic used in a plastic cup, you can perform a scratch test. This involves trying to scratch the surface of the plastic cup with a piece of copper. If the copper leaves a mark, it is harder than the plastic. If not, then the plastic is the harder material. As copper is a metal with a relatively well-defined hardness on the Mohs scale, it's expected to be harder than most common plastics which are lower on the scale and tend to be softer. However, the scratch test results might vary based on the type of plastic used in the cup.
It's important to consider the physical and chemical properties of both materials to understand their relative hardness. Unlike measuring thermal conductivity, where a metal spoon heats faster than a plastic spoon, a scratch test directly assesses hardness.