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Mechanics: conservation of momentum problem

  1. Apr 18, 2006 #1
    Here's the problem:

    An atom of mass 2mp with an anitial velocity vo undergos an elastic collision with an atom at rest with mass 3mp. After the collision, the first atoms trajectory deviates 30 degrees from the initial. What angle does the second atom travel from the first atoms initial trajectory?

    I used conservation of momentum to get

    2vo = (3)^(1/2)v1' + 3 cos(θ2) v2'

    and

    v1' = -3 sin(θ2)v2'

    I used conservation of kinetic energy to arrive at

    2(vo)^2 = 2(v1')^2 + 3(v2')^2.

    So there are three equations and three unknowns (θ, v1' and v2').

    After 18 pages of algebra I've decided to ask for some help. Are there trig identies that would help. I am also given θ = -65.2 but only to check with my answer, and working backwards from it didn't help.

    Please, can anyone help?
     
  2. jcsd
  3. Apr 18, 2006 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Try combining these using [itex]\sin^2\theta + \cos^2\theta = 1[/itex]. Combine that result with your equation for conservation of energy to solve for v1' & v2'.
     
  4. Apr 18, 2006 #3
    thanks, i was skeptical of that approach but it worked out after a mess of algebra and a quadratic equation to solve
     
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