1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Applying Newton's Universal Law of Gravitation

  1. Mar 31, 2016 #1
    1. The problem statement, all variables and given/known data
    This problem only requires to find h, but I want to make sure that I also found Me and g correctly.
    Starting with Newton's Law of Gravitation, determine the height h one person has to go from the surface of the earth in order for that person's weight to be reduced to one-third of his/her weight at the surface of the earth. The only information you have is that the radius of the earth is 6.4X106m. Knowing that the acceleration due to gravity at the surface of the earth is 9.8m/s2, determine the acceleration due to gravity at the point were the weight of the person is reduced to 1/3rd.

    2. Relevant equations
    GMem/r2 = 1/3GMem/Re2
    r2 = 3Re2
    r = √3(6,400,000)
    h = r - Re = 11,085,125.17m - 6,400,000m = 4,685,125.17m
    Me = gRe2/G
    g = G9.0 X 10-9/6.4 X 106

    3. The attempt at a solution
    GMem/r2 = 1/3GMem/Re2 Cross out the GMem, leaving: r2 = 3Re2
    r = √3(6,400,000) = 11,085,125.17m
    h = r - Re = 11,085,125.17m - 6,400,000m = 4,685,125.17m
    6400km X 1000m/1km = 6.4 X 106m
    h = 4,685,125.17m,
    Me = gRe2/G = 9.8m/s2 X (6.4 X 106)2/6.67 X 10-11 = 9.0 X 10-9
    Acceleration due to gravity at the point were the weight of the person is reduced to 1/3rd = g = G9.0 X 10-9/6.4 X 106 = 9.37 X 10-3m/s2
     
    Last edited: Mar 31, 2016
  2. jcsd
  3. Mar 31, 2016 #2
     
    Last edited: Mar 31, 2016
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Applying Newton's Universal Law of Gravitation
Loading...