In 1956 Frank Lloyd Wright proposed the construction of a mi

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 690 N, to the top of the building.

Solution

The mass at street level by dividing 690/9.8.

F = GMm/r², with r being the radius of the earth plus the 1609.344 meters that are the building.

1 mile = 1.609 km = 1.609*10³ m
Earth radius = 6.378*10⁶ m
Distance to top of building from center of earth = 6.379609*10⁶
Mass = (690 ÷ 9.8)
Mass of earth = 5.9736*10²⁴ g
Universal Gravitational constant = G = 6.67*10^-11 m³ kg^-1s^-2

Universal Gravitational force Equation

F = (G*M1*M2) ÷ r²

F at earth = (6.67*10^-11*(690 ÷ 9.8)*5.9736*10²⁴)÷(6.378*10⁶)²

F at earth = 689.629701057 N


F top = (6.67*10^-11*(690÷9.8)*5.9736*10²⁴)÷(6.379609*10⁶)²

F top building = 689.281882167 N

Difference = 0.34781889 N
% diff = (689.629701057 - 689.281882167) ÷ 689.629701057 = 0.00050435601 %