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2D Elastic Collision

  1. Feb 6, 2016 #1
    1. The problem statement, all variables and given/known data
    Problem: An object of mass m1 elastically collides with an object of mass m2 =(3/2) m1 that is initially at rest. The less massive object has speed v1 and travels at an angle of θ1with its original direction (x-axis) after collision; the more massive object has a speed of v2 = (2/3) v1 and travels at an angle of θ2 after collision. What are the initial speed v0 of the less massive object and the two scattering angles, θ1 and θ2?

    known values ( symbolically at least)
    m1
    m2 = 1.5 m1
    v1f
    v2f = 2/3 v1f

    Finding:
    v0
    θ1
    θ2

    2. Relevant equations
    Momentum Equations:

    Pi=Pf
    KEi=KEf
    Before:
    Px: m1*v0
    Py: 0
    E: 1/2 m1*v0^2
    After:
    Px: m1*v1f*cos(θ1)+3/2 m1 * 2/3 v1f cos(θ2)
    Py: m1*v1f*sin(θ1)-3/2 m1 * 2/3 v1f sin(θ2)
    KE: 1/2 m1* v1f^2+1/2 3/2 m1 (2/3v1f)^2

    Combined:
    (1)KE: v0^2=5/3 v1f^2
    (2)Px: m1v0 = m1*v1f cos(θ1) + m1*v1f cos(θ2)
    (3)Py: m1*v1f sin(θ1) = m1*v1f sin(θ2)


    3. The attempt at a solution
    Equation (3)simplifies to sin(θ1)=sin(θ2)
    (4) θ1=θ2
    plugging (3) into (2)
    (5) v0 = 2*v1f cos(θ1)
    plugging 5 in to 1
    (2 v1f cos(θ1) ) ^2 = 5/3 v1f^2
    solving for θ1 you get θ1=arccos( sqrt(15) / 6 ) which means θ2=arccos( sqrt(15)/6) as well


    From here I am stuck trying to solve for v0. I am also unsure if my value for θ is correct.


    Thanks for the help.
     
    Last edited: Feb 6, 2016
  2. jcsd
  3. Feb 6, 2016 #2
    As the collision is elastic
    Did you use the fact
    That the total kinetic energy before the collision equals the total kinetic energy after the collision?

    Use this




    UchihaClan13
     
  4. Feb 6, 2016 #3
    My bad. I forgot to label this fact carefully in the givens the Ei=Ef was non specific energy but it was intended to be kinetic energy. But yes I did take this into account
     
  5. Feb 6, 2016 #4

    haruspex

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    I agree with your solution for the angle (though I would have expressed it as arccos(√(5/12))).
    Since you are given no numeric values for speeds, it is only possible to find v0 in terms of v1. Does that help?
     
  6. Feb 9, 2016 #5
    That does definitely help knowing I got the angles correct. Is it still not possible to find the original velocities even though we know the relationships between the masses and their final velocities?
     
  7. Feb 9, 2016 #6

    haruspex

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    Are you familiar with dimensional analysis? None of the numerical data you are given has an associated dimension, so it is not possible to come up with a numerical answer for a dimensioned quantity. Even knowing masses would not help. You would need to know at least one quantity involving distance and at least one involving time.
    Just go ahead and find v0 in terms of v1.
     
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