In 1956, Frank Lloyd Wright proposed the construction of a mile-high building in Chicago. Suppose the building had been constructed. Ignoring Earth's rotation, find the change in your weight if you were to ride an elevator from the street level, where you weigh 760 N, to the top of the building.

g'=9.8 (rearth/(radearth+1mile))^2

0.791

To find the change in weight when riding an elevator from the street level to the top of the mile-high building, we need to consider the difference in gravitational force at different heights. The force of gravity is given by the equation:

F = mg

Where:
F is the gravitational force (weight)
m is the mass of the object
g is the acceleration due to gravity (approximately 9.8 m/s^2 on Earth)

At any point on Earth's surface, we can calculate our weight by multiplying our mass (which is constant) by the value of acceleration due to gravity (g).

Given that you weigh 760 N at street level, we can divide this value by the acceleration due to gravity (g) to find your mass (m):

m = F / g = 760 N / 9.8 m/s^2 ≈ 77.55 kg

Now, let's consider the change in weight when going to the top of the mile-high building. Since the height of the building is not given, we can assume that it is exactly 1 mile, which is equivalent to approximately 1609 meters.

The force of gravity (F) at the top of the building can be calculated using the same equation:

F = mg

Using the mass (m) we calculated earlier, we can find the new weight (F) at the top of the building:

F = 77.55 kg * 9.8 m/s^2 = 759.99 N (approximately)

Therefore, the change in weight would be the difference between the weight at street level and the weight at the top of the building:

Change in weight = Weight at top - Weight at street level = 759.99 N - 760 N ≈ -0.01 N

So, the change in your weight when riding the elevator to the top of the mile-high building would be approximately -0.01 N.