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 580 N, to the top of the building.

N

Use the inverse square law. You will need to look up the radius of the earth. It is about 3960 miles, as I recall. Square the ratio of the the distances to the center of the Earth at the top and the bottom of the building. Use that factor to compute the weight at the top, and the change. The weight there will be less.

To find the change in weight while riding an elevator from the street level to the top of the mile-high building, we need to consider the change in distance from the center of the Earth. The force of gravity depends on the distance from the center of the Earth, so as you move away from the center of the Earth, your weight will change.

Let's assume that at the street level, the radius of the Earth is denoted by R (approximately 6370 km). Since the mile-high building is in Chicago, the radius will increase by an additional height of 1 mile (about 1.6 km).

To calculate the change in weight, we can use the equation:

F = (G * m1 * m2) / r^2

where F is the force of gravity, G is the gravitational constant (approximately 6.67430 × 10^-11 N * (m/kg)^2), m1 and m2 are the masses, and r is the distance between the two masses.

At the street level, let's assume your mass is m and the mass of the Earth is ME. The force of gravity is given by:

F1 = (G * m * ME) / (R^2)

At the top of the building, the distance from the center of the Earth will be R + 1.6 km. The force of gravity at the top is given by:

F2 = (G * m * ME) / (R + 1.6 km)^2

The change in weight is the difference between the forces at the top and the street level:

Change in weight = F2 - F1

Substituting the values into the equation, we can calculate the change in weight.