Final answer:
Both you and your friend will have the same gravitational potential energy at the top of the Eiffel Tower as it's dependent on mass and height, despite different methods of ascent. Energy consumption is higher when walking the stairs compared to taking the elevator.
Step-by-step explanation:
When both you and your friend reach the top of the Eiffel Tower, your gravitational potential energy (GPE) will be the same, assuming you have the same mass and are at the same height above the ground. This energy is calculated using the equation GPE = mgh, where m is mass, g is the acceleration due to gravity, and h is height. Despite the method of ascent, whether by elevator or by walking up the stairs, the gravitational potential energy at the top for both of you will be equivalent as it is dependent only on your mass and the height you have reached relative to a reference point.
Energy consumption, however, is a different matter. Walking up the stairs requires more physical effort and thus more energy consumption compared to taking the elevator. While climbing in a zigzag path or spiral staircase requires less effort at any given step compared to going straight up, it results in a longer path and therefore greater energy expenditure overall.