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Kinetic energy and momentum

  1. Oct 8, 2005 #1
    Theres some calculations in this problem that I just dont get...

    Start with the equations for initial and final momenta and kinetic energies and derive the

    theoretical equation for the ratio fo [tex]K_f[/tex] to [tex]K_i[/tex]

    [tex]P_i=Mv_i[/tex]
    [tex]P_f=(M+m)v_f[/tex]
    [tex]K_i=1/2Mv_i^2[/tex]
    [tex]K_f=1/2(M+m)V_f^2[/tex]
    [tex]K_f/K_i=1/2(M+m)v_f^2/1/2Mv_i^2=M/(M+m)[/tex] this part I dont get. I only get

    [tex](M+m)/M[/tex] and im assuming that [tex]v_f[/tex] and [tex]v_i[/tex]

    cancel out...

    I basically solved for [tex]M=P_i/v_i[/tex] and [tex](M+m)=P_f/v_f
    [/tex]
    I plug it in to kinetic energy equations and get [tex]K_f/K_i=P_f/P_i[/tex] I guess [tex]

    v_f[/tex] and [tex]v_i[/tex] cancel out? Is this answer correct?
     
  2. jcsd
  3. Oct 8, 2005 #2
    I dont understand the intial question, are two bodies inelastically colliding? Could you be more specific as to the problem please.
     
  4. Oct 8, 2005 #3
    Yes, it is an inelastic collision.

    Also a seperate question is what would the difference between an elastic and inelastic collision?
     
  5. Oct 8, 2005 #4
    the intial and final velocities are not going to be the same, in general. A simple example is a fly hitting a winsheild. Its traveling with its initial speed of lets say 2m/s. It hits the truck, and gets stuck on the winsheild, now its moving at the speed of the truck, maybe 30m/s.
     
    Last edited: Oct 8, 2005
  6. Oct 8, 2005 #5

    jtbell

    User Avatar

    Staff: Mentor

    In an elastic collision, the total kinetic energy is conserved. In an inelastic collision, the total kinetic energy is not conserved.
     
  7. Oct 8, 2005 #6
    I think the most you can do is simplify the ratio as:

    [tex] (1 + \frac{m}{M}) (\frac{V_f}{V_i})^2 [/tex]

    but if you want it in terms of intial and final momentum it will be:

    [tex] ( \frac {M}{M+m})( \frac{ P_f}{P_i})^2 [/tex]
     
    Last edited: Oct 8, 2005
  8. Oct 8, 2005 #7
    In an elastic collision , the initial and kinetic energies remain the same But in inelastic collision , some of the initial KE is lost to the surroundings as other forms of energy like heat/sound , but in both the cases , the Total energy is always conserved.

    BJ
     
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