In 1956, Frank Lloyd Wright proposed the construction of a mile-high building in
ID: 2097231 • Letter: I
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
Explanation / Answer
By dividing 700/9.8, I got the mass at street level. I then used F = GMm/r^2, with r being the radius of the earth plus the 1609.344 meters that are the building, and when I calculated it, the difference in weight turned 1 mile = 1.609 km = 1.609 *10^3 m Earth radius = 6.378 * 10^6 m Distance to top of building from center of earth = 6.379609 * 10^6 Mass = (700 ÷ 9.8) Mass of earth = 5.9736 * 10^24 g Universal Gravitational constant = G = 6.67 * 10^-11 m^3*m^kg-1*s^-2 Universal Gravitational force Equation F = (G * M1* M2) ÷ r^2 F at earth = (6.67 * 10^-11 * (700 ÷ 9.8) * 5.9736 * 10^24) ÷ (6.378 * 10^6)^2 F at earth = 699.6243 N F top = (6.67 * 10^-11 * (700 ÷ 9.8) * 5.9736 * 10^24) ÷ 6.379609 * 10^6^2 F top building = 699.27147 N Difference = 0.3538 N ( round off to 3 decimal points = 0.354) here is your answer