Asked by sonam

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 532 N, to the top of the building.
Answered by drwls
Use the inverse square law. You will need to look up the radius of the earth. It is about 3960 miles, as I recall. Square the ratio of the the distances to the center of the Earth at the top and the bottom of the building. Use that factor to compute the weight at the top, and the change. The weight there will be less.

Answered by Ms. Sue
Welcome back, DrWLS!

Answered by sonam
At the ground level

weigh = 532 N

W = m*g

at ground g = 9.81 m/sec^2

mass = 532/9.81 = 54.2303 kg

Now at top of the building gravitational accleration will be

g = GM/r^2

so gravitational acceleration is inversely proportional to r^2

g'/g = r^2/r'^2

r = Re = 6.371*10^6 m

1 mile = 1609.34 m

g' = g*(Re/(Re + h))^2

g' = 9.81*(6.371*10^6/(1609.34 + 6.371*10^6))

g' = 9.8075 m/sec^2

your weight will be

W' = m*g'

W' = 54.2303*9.8075

W' = 531.8636 N

Change in weight = 532 - 531.8636

Change in weight = 0.1364 N

CAN ANY ONE HELP WHERE DID I GO WRONG??? BECAUSE IT SAYS THE ANS IS INCORRECT
Answered by Damon
W = k/r^2
dW/dr = -2kr/r^4

dW = - 2 k dr /r^3
====================
532 N = k / 3959^2
so
k = 532 (3959)^2

so
dW=-2 * [532 * 3959^2]* 1/3959^3

dW = -.2687
Answered by Damon
I believe that is indeed Dr WLS ! To be sure, how did we get to Nova Scotia and back ?
There are no AI answers yet. The ability to request AI answers is coming soon!