Question

Objects with masses of 265 kg and a 565 kg are separated by 0.410 m. At what position (other than infinitely remote ones) can the 53.0 kg object be placed so as to experience a net force of zero?

Answer 1

Call the distance to the balance point (in between the two masses) from the 265 kg object X, and place the 53 kg object there. The distance to the 565 kg mass from the 53 kg mass will then be (0.410 - X). Balance the forces:
G(265)(53)/X^2 = G(565)(53)/(0.410 - X)^2
and solve for X. There will be two roots (since it's a quadratic) but one is spurious (it doesn't make sense physically). If you think about it, you expect it to be closer to the SMALLER mass, since the LARGER mass exerts a LARGER force -- but it falls off at 1/r^2.

Answer 2

then the 53's would cancel?

Answer 3

yes 53's cancel along with the G's
you get a term like -300/265 x^2 - .81 x + .1681 = 0
use a site like http://mste.illinois.edu/exner/ncsa/quad/
scroll down and input coeffiecents and the answer will appear

Answer 4

oh answer is .1681 for x