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Conservation of momentum, elastic collision, find other mass? help

  1. Nov 18, 2012 #1
    conservation of momentum, elastic collision, find other mass? help!!

    Two titanium spheres approach each other head-on with the same speed and collide elastically After the collision, one of the spheres, whose mass is 300 g, remains at rest.

    What is the mass of the other sphere?

    What i did:

    m1v1 + m2v2 = m1u1 + m2u2
    v1 = 0 b/c at rest

    m2v2 = m1u1 + m2u2

    m2v2 - m2u2 = m1u1

    m2(v2 - u2) = m1u1 ????? This is where I got stuck!

    please help!
     
  2. jcsd
  3. Nov 18, 2012 #2
    Re: conservation of momentum, elastic collision, find other mass? help!!

    What is the relationship between u1 and u2?

    The collision is elastic. What can you say about the relative speeds of approach and separation?
     
  4. Nov 18, 2012 #3
    Re: conservation of momentum, elastic collision, find other mass? help!!

    Momentum is the same so initial speed equals final speed?
     
  5. Nov 18, 2012 #4
    Re: conservation of momentum, elastic collision, find other mass? help!!

    So I looked up the solution and it uses v=2u
    (m1-m2)u = m2(2u)

    So why is it 2u? I know that m1v1 is at rest. Is it because when m1 collides with m2 it gave its speed to m2 so you multiply by 2?
     
  6. Nov 18, 2012 #5

    Doc Al

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    Staff: Mentor

    Re: conservation of momentum, elastic collision, find other mass? help!!

    You applied momentum conservation. What else is conserved in an elastic collision?

    Also, redo your momentum conservation equation. The spheres approach each other with the same speed, thus they move in opposite directions.
     
  7. Nov 18, 2012 #6
    Re: conservation of momentum, elastic collision, find other mass? help!!

    I know that p and ke is comserved. I'm not sure what else.

    m2v2 = m1u1 - m2u2
     
  8. Nov 18, 2012 #7

    Doc Al

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    Staff: Mentor

    Re: conservation of momentum, elastic collision, find other mass? help!!

    Make use of the fact that KE is conserved.

    Better. Note that the speeds of the balls before colliding are the same. Use that fact.
     
  9. Nov 18, 2012 #8
    Re: conservation of momentum, elastic collision, find other mass? help!!

    How can we use ke in this?

    m2v2 = (m1 - m2)u?
     
  10. Nov 18, 2012 #9

    Doc Al

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    Staff: Mentor

    Re: conservation of momentum, elastic collision, find other mass? help!!

    Calculate the KE before and after. Set them equal to each other.

    OK.

    There's a quicker way to solve this (hinted at by Fightfish), but I suggest doing it this way.
     
  11. Nov 18, 2012 #10
    Re: conservation of momentum, elastic collision, find other mass? help!!

    1/2m1vi + 1/2m2vi = 1/2m2vf

    1/2vi(m1 + m2) = 1/2m2vf --> mult each side by two

    vi(m1 + m2) = m2vf ??
     
  12. Nov 18, 2012 #11

    Doc Al

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    Staff: Mentor

    Re: conservation of momentum, elastic collision, find other mass? help!!

    Two things:
    (a) KE = 1/2 mv2, not 1/2 mv.
    (b) Use the same symbols for the speeds that you used in the momentum equation.
     
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