Final answer:
Riding an elevator to the top of a mile-high building would result in a slight decrease in weight due to a weaker gravitational pull at a higher altitude, though this change would be very small and potentially rounded to zero at one significant figure.
Step-by-step explanation:
Calculating the Change in Weight at the Top of a Mile-High Building
Your weight, which is the force due to gravity acting on your mass, would slightly decrease if you were to ride an elevator from street level to the top of a mile-high building. This change is due to the gravitational force being inversely proportional to the square of the distance from the center of the Earth. At a higher altitude, you would be farther away from the Earth's center, thus experiencing a slightly weaker gravitational pull.
Weight Change Calculation
To calculate the change in weight, we could use the formula:
W = mg
Where W is weight, m is mass, and g is the acceleration due to gravity. The value of g will decrease with altitude. For small changes in altitude, however, the change in g and thus in weight can be negligible. If Frank Lloyd Wright's building had been constructed, the exact change in your weight could be calculated by considering the decrease in g at the building's top compared to sea level.
Significance for Engineers
In structural engineering, especially while designing extremely tall buildings like the mile-high proposal by Frank Lloyd Wright, the change in gravitational acceleration (g) with height can be significant. This factor, among many others, needs to be taken into account to ensure the stability and safety of the structure.
To round to one significant figure, more detailed calculations involving the exact height and specific values for g at different altitudes would be necessary, but typically, the weight change would be so small that it could be approximated to zero when rounded to one significant figure at such heights.