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Elasticity in collisions

  1. Jun 1, 2009 #1
    1. The problem statement, all variables and given/known data
    a billiard ball of mass of 0.115kg moves with a velocity of 12.5m/s toward a stationary billiard ball of identical mass and strikes it in a head on collision. the first billiard ball comes to a complete stop. determine whether the collision was elastic.


    2. Relevant equations
    Ek1 + Ek2 = Ek1' + Ek2'

    p=mv


    3. The attempt at a solution
    first i calculate the velocity of the steel ball after being struck by the billiard ball...
    mv + mv = mv' + mv'
    0.155kg(12.5m/s) = (0.155kg + 0.155kg)v
    1.94 = 0.31v
    v = 1.94/0.31
    v = 6.26m/s

    then i calculate the total kinetic energy before the collision (only the billiard ball because the steel ball was idle)

    Ek = 1/2mv^2
    Ek = 1/2(0.155)(12.5)^2
    Ek = 12.1J

    then i calculate the total kinetic energy after the collision

    Ek + Ek = Ek' + Ek'
    12.1 + 1/2(0.155)(0)^2 = 1/2(0.155)(0)^2 + 1/2(0.155)v^2
    12.1 = .078v^2
    v^2 = 12.1/0.078
    v^2 = 155
    v = 12.46m/s (but this doesnt make sense...)

    so maybe this:
    Ek = 1/2(0.155 + 0.155)(6.26)^2
    Ek = 0.155(39.20)
    Ek = 6.1J

    - the answer in the back of my textbook is this:
    v=6.32m/s[41.5' counterclockwise from the original direction of the first ball]; the collision is not elastic: Ek = 12.1J; Ek' = 10.2J

    i got the first 2 correct but the third one i dont understand. as well.. i am not sure how to know whether something is considered an elastic collision or not)
     
  2. jcsd
  3. Jun 1, 2009 #2
    Excuse me,
    But I have to disagree with the answer in your textbook.
    assume system is isolated , no external forces, thus momentum conserved,
    m*V+m*U=m*V'+m*U'
    U=0 ,V'=0
    we get that U'=V, 1 ball stops and the other one gets the speed of the other one.
    thus Ek(initial)= mV^2/2 , Ek(final)=m*U'^2/2
    because U'=V
    Ek initial =Ek final...
    Am I understanding Your question wrong??Do they scatter with an angle?? but it's head to head collision?
     
  4. Jun 1, 2009 #3
    ok so are you agreeing with my answers?
    and yes it was a head on collision, so there are no angles to worry about.
     
  5. Jun 1, 2009 #4

    rock.freak667

    User Avatar
    Homework Helper

    Well given what Dweirdo says, it does look like the final velocity of the other ball is 12.5m/s, which would imply that the collision is elastic.

    0.155kg(12.5m/s) = (0.155kg + 0.155kg)v


    you also used this to find v. This implies that you assumed the collision was completely inelastic.
     
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