The person's weight would decrease by about 0.354 Newtons when they reach the top of the building.
Earth's rotation, the change in weight of a person moving from the street level to the top of a mile-high building can be calculated using the following formula:
ΔW = mgΔh/R^2
where:
ΔW is the change in weight
m is the person's mass
g is the acceleration due to gravity at the Earth's surface (approximately 9.81 m/s²)
Δh is the change in height (in this case, 1 mile, or approximately 1609.34 meters)
R is the Earth's radius (approximately 6,371,000 meters)
Plugging in the values, we get:
ΔW = (71.36 kg)(9.81 m/s²)(1609.34 m) / (6,371,000 m)²
ΔW ≈ -0.354 N
Therefore, the person's weight would decrease by about 0.354 Newtons when they reach the top of the building.
This is because the acceleration due to gravity decreases slightly as you move farther away from the center of the Earth.
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 700 N, to the top of the building.
What I did:
radius of earth = r = 6.38x10^6 m
mass of earth = M = 5.97x10^24 kg
mass of person = m = 700N/9.81 = 71.36kg
height of building = h = 1609.34 m
G = 6.67^-11
F = mg(top of building) = (G*m*M)/(r + h)^2 = 697.741 N
mg(top of building)- mg(ground) = 697.741N