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 469 n, to the top of the building.

The change in your weight if you were to ride an elevator from the street level where you weigh 469N to the top of the building is; -0.237 N

The formula for acceleration here is;

a = GM/r²

Where;

G is gravitational constant = 6.67 × 10⁻¹¹ m³/kg.s²

M is mass of earth = 5.972 × 10²⁴ kg

r is distance from center of earth

Since we are trying to find change in weight, let us first find the change in acceleration with respect to r;

da/dr = -2GM/r³

da =  -(2GM/r³) dr

Thus, change in weight from top to bottom is;

W_top - W_bottom = m(da)

Now, weight at bottom is gotten from the formula;

W_bottom = GmM/r²

Also, W_bottom = m(da) since we are dealing with change in weight.

Thus;

m(da)= -(2GmM/r³) dr

Recall that GmM/r². Thus;

m(da) = -2W_bottom × dr/r

where;

W_bottom = 469 N

r is radius of earth = 6371000 m

dr = 1 mile = 1609.34 m

Thus;

m(da) = -2 × 469 × 1609.34/6371000

m(da) = -0.237 N

Read more about Newton's law of gravitation at; link

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