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Homework Help: Newton's law of universal gravitation

  1. May 13, 2016 #1
    1. The problem statement, all variables and given/known data

    Two 100-kg thrill seekers are diving into a neutron star. The neutron star’s mass is 1.1 solar masses and its radius is 12.0 km. For safety, they tie themselves together with a cord 10m long, so that as Melvin reaches the surface of the neutron star, Fred is 10.0 m behind him. Consequently, the pull of the neutron star on Melvin is very slightly stronger than the pull of the neutron star on Fred. However, due to the connecting cord, the two fellows accelerate towards the neutron at the same rate. By setting up free-body diagrams for both sundivers, find the tension in the connecting cord.

    Answer is 8.45 X 10^10 N

    2. Relevant equations
    ΣF = ma

    3. The attempt at a solution
    Mn = mass of neutron star
    m1 = mass of melvin
    m2= mass of fred
    R= radius of star
    d = length of cord

    Sum of forces on melvin
    (G*Mn*m1)/ R^2 - T = m1a
    Sum of forces on fred
    (G*Mn*m2)/ (R+d)^2 + T = m2a

    m1=m2 so
    m1a = m2a

    (G*Mn*m1)/ R^2 - T = (G*Mn*m2)/ (R+d)^2 + T

    T = (G*Mn*m1)/ 2R^2 - (G*Mn*m2)/ 2(R+d)^2

    Mn converted to kg = 2.19 x 10^30 kg
    R= 1200m
    G= 6.67 x 10^-11
    d = 10m

    Plugging everything in im getting 8.35 x 10^13 N but the answer is 8.45x 10^10 N, what am i doing wrong
  2. jcsd
  3. May 13, 2016 #2


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    Homework Helper
    Gold Member
    2017 Award

    Your method and final formula for T look correct. Check the final calculation where you plug in the numbers.
    Note that the radius is 12 km, which is not equal to 1200 m.
  4. May 13, 2016 #3
    omg i just noticed 12 km is 12000 m not 1200 thanks
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