at what distance from the earth's surface will a mass of 50 kg(490N) be just 481 N? frmula i Fg=Gm1m2/r^2?

Question

please put the whole solution. it it a physics problem Newton's Universal law of gravitation. the given formula is Fg=GM1M2/r^2, please include all convertions. thank you

Answer 1

The earth's mean radius is: 6.37x10^6m. At the surface(r = 6.37x10^6m), 50kg mass is 490N. We want to know at what height h (r = 6.37x10^6m + h), 50kg mass is 481N. Written in math language, we have:
490N = G(m1m2) /(6.37x10^6m)^2............(1)
481N = G(m1m2) /(6.37x10^6m + h)^2......(2)
(1)/(2) we get:
490/481 = {(6.37x10^6m + h)/(6.37x10^6m)}^2
or h = (6.37x10^6m)*[sqrt(490/481) - 1] = 59.3 km
No conversion is needed.