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 728 N, to the top of the building.

Solution

weight on the street level, w= 728 N

w=m*g=728 N

and

height of the building, h=1 mile =1609.344

wieght at the top of the building is, w\'=m*g\'

w\'/w = g\'/g

w\'=w*(GM/(R+h)^2)/(GM/R^2)

here, radius of the earth, R =6371*10^3 m

w\'=w*(R/(R+h))^2

w\'=728*(6351*10^3/(6351*10^3+1609.344))^2

w\'= 727.63 N

wieght at the top of the building is, w\'=727.63 N