Final answer:
The observed volume of a cube moving relativistically at 0.800c past a space station is calculated by applying special relativity’s length contraction. By finding the Lorentz factor and contracting the length in the direction of motion, the cube’s contracted volume as measured by stationary observers can be determined.
Step-by-step explanation:
The question asks about the volume of a perfect cube as observed by someone on a space station, with the cube moving at a relativistic speed of 0.800c (where c is the speed of light). This scenario falls under the realm of special relativity in physics, a theory developed by Albert Einstein. According to special relativity, objects that are moving at speeds comparable to the speed of light will appear contracted in the direction of motion to a stationary observer. This phenomenon is known as length contraction.
To calculate the observed volume of the cube, we first need to figure out the length contraction factor. The Lorentz factor, γ (gamma), is given by the formula γ = 1/√(1 - v2/c2), where v is the relative velocity. The contracted length l' is then found through l' = l/γ, where l is the proper length (the length of the cube at rest). Since the cube is moving in a direction perpendicular to its sides, only one dimension (the length along the direction of motion) will be contracted. The volume of the cube observed, V', is the product of the contracted length and the square of the side of the cube that is perpendicular to the motion, so V' = l'3.
To give a complete solution, we solve the mathematical problem by applying the formula for length contraction to find the correct contracted dimension and then cube it to find the volume as observed by the space station observers. As requested in the main question, we ignore other parts such as a spaceship or a canister being sent from it and focus solely on the cube's volume from the observers' perspective.