Results 1 to 2 of 2

Math Help - gravity between 2 objects

  1. #1
    Junior Member
    Joined
    Oct 2006
    Posts
    71

    gravity between 2 objects

    Two spheres having masses M and 2M and radii R and 3R, respectively, are released from rest when the distance between their centers is 12R. How fast will each sphere be moving when they collide? Assume that the two spheres interact only with each other.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by gracy View Post
    Two spheres having masses M and 2M and radii R and 3R, respectively, are released from rest when the distance between their centers is 12R. How fast will each sphere be moving when they collide? Assume that the two spheres interact only with each other.
    There are a number of tackling this. One of the simples utilises the conservation of energy and of linear momentum.

    The two spheres start at a seperation of 12R, and end at a seperation of 4R,
    so the change in potential energy of the system is equal to the work required
    to take the spheres from a seperation of 4R to one of 12R:

    DE=int(r=4R:12R) G _1 m_2/r^2 dr = G m_1 m_2/(6R)

    So as the spheres start from rest this is equal to the sum of their KE's
    when they hit:

    G m_1 m_2/(6R) = (m_1 v_1^2 + m_2 v_2^2)/2.

    The conservation of momentum gives:

    m_1 v_1 = -m_2 v_2.

    Solve these two equations to find v_1 and v_2.

    RonL
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Distributing different objects
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: April 29th 2011, 03:00 AM
  2. heights of objects
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: January 2nd 2010, 01:42 AM
  3. Tensions between three objects
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: September 19th 2009, 05:03 PM
  4. Objects are closer than they appear?
    Posted in the Math Topics Forum
    Replies: 0
    Last Post: November 27th 2008, 09:01 PM
  5. Objects in Equilibrium
    Posted in the Advanced Applied Math Forum
    Replies: 1
    Last Post: October 11th 2008, 12:38 PM

Search Tags


/mathhelpforum @mathhelpforum