Gravity Problems: Equilateral Triangle and Mile-High Building

[Reti]

Homework Statement

3 single-point objects (M, m and m) forms an equilateral tri-angle with a 4th object in the middle. The sum of the gravitational force on the central object is 0. Represent the force of M in terms of m.



Problem 2: 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 488 N, to the top of the building.

Homework Equations

F = G*(Mm/r^2)
= ma(gravity)
a(gravity) = GM/r^2

The Attempt at a Solution

1. answer says M = m, and yes, it does make sense, but can someone show me

2. my answer was -0.231N, but Wileyplus says it's wrong.

 

[diazona]

How did you do them? (For what it's worth, I agree with M=m and also can confirm that -.231N is wrong)

 

[Reti]

1. i do not know how to do it

2. since ma(g) = 488 N, you can find m by dividing 488 by 9.8.
Then you will realize that the ratio of r = ratio of a(g)
so therefore :

r+1600/r = 9.83/x

x being the new a(g).

then 488 - mx = -.231