How Does Height Affect Weight in a Hypothetical Mile-High Building?

[dominus96]

Homework Statement

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 520 N, to the top of the building.

Homework Equations

a = Gm/R^2

The Attempt at a Solution

g = Gm/R^2, so I used 6.67E-11 for G, the mass of the Earth (5.97E24) for m, and the radius of the Earth plus the distance from Earth's surface (1 mile, which is about 1609 meters) for R. I calculated all that and got about 9.77 for g and then found weight and subtracted it from 520, but it was wrong. What's the deal?

 

[borgwal]

You don't need the mass of the Earth, nor the value of G: the fractional change in g (which gives you the fractional change in weight) equals the fractional change in 1/r^2, with r the distance to the center of Earth (so, that number you do need).

The fractional change in g that you get is way too large (rounding errors?).

 

[thomate1]

There could be a few reasons why your answer may be incorrect. Firstly, it's important to note that the equation you used, a = Gm/R^2, gives the acceleration due to gravity, not the actual weight. To find the change in weight, you would need to use the formula F = ma, where F is the force of gravity, m is the mass of the object, and a is the acceleration due to gravity.

Secondly, you may have used the incorrect value for the mass of the Earth. The mass of the Earth is actually 5.97E24 kg, not 5.97E24. This could have affected your final answer.

Lastly, it's possible that the problem is asking for the change in weight due to the building's construction, not just the change in weight from being at a higher altitude. In this case, you would need to take into account the additional mass of the building and its effect on the gravitational force.

It's important to double check your calculations and make sure you are using the correct equations and values. If you are still having trouble, it may be helpful to consult with a teacher or classmate for assistance.