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.

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  1. 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.

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  2. Welcome back, DrWLS!

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    Ms. Sue
  3. 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


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  4. W = k/r^2
    dW/dr = -2kr/r^4

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

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

    dW = -.2687

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  5. I believe that is indeed Dr WLS ! To be sure, how did we get to Nova Scotia and back ?

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