Question

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 867 N, to the top of the building.

Answer 1

Newton's Law of Universal Gravitation:

Newton's law of universal gravitation states that every particle attracts another particle in the universe using a force which is directly proportional to the product of their individual masses and inversely proportional to the square of the distance between the two centers.

The formula for Newtons law of gravitation is given by

Now moving to the calculations,

1 mile=1609.344 mts

Mass of Earth =  

Radius of Earth=6378100 meters

At street level, we weigh 881 N.

Now

Which would mean m= 89.95kg for the person.

So, looking at acceleration due to gravity at the top of the building Radius will be (Rearth+176+1609.344)m.
a= 9.7899 m/s²
Multiply by mass of a single person,

Weight= Fgravity

=880.556N.

The change in Weight is calculated to be =.444225N.