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Find V(f) for two particles resting (and compressing) against a spring.

  1. Jul 10, 2011 #1
    1. The problem statement, all variables and given/known data
    Two particles of mass m1= 2.2 kg and mass m2 = 4.5 kg that are free to move on a horizontal track are initially held at rest so that they compress a spring as shown in the figure below. The spring has a spring constant k = 395 N/m and is compressed 0.15 m. Find the final velocities of the two particles.


    2. Relevant equations

    M1V1=M2V2

    1/2M1V1^2 + 1/2M2V2^2 = 1/2 kx^2


    3. The attempt at a solution

    I am copy/paste a solution for the problem that is exactly what I did but with different numbers.

    Conservation of momentum:
    m1 v1 + m2 v2 = 0 ...(1)

    Conservation of energy:
    m1 v1^2 / 2 + m2 v2^2 / 2 = kx^2 / 2
    m1 v1^2 + m2 v2^2 = kx^2 ...(2)

    From (1):
    v2 = - m1 v1 / m2

    Substituting for v2 in (2):
    m1 v1^2 + m1^2 v1^2 / m2 = kx^2

    m1 m2 v1^2 + m1^2 v1^2 = k m2 x^2
    m1(m1 + m2)v1^2 = k m2 x^2
    v1^2 = k m2 x^2 / [ m1(m1 + m2) ]

    v1 = sqrt{ 395 * 4.4 * 0.11^2 / [ 2.3(2.3 + 4.4) ] }
    v1 = 1.17 m/s to 3 sig. fig.

    Similarly:
    v2^2 = k m1 x^2 / [ m2(m1 + m2) ]

    v2 = sqrt{ 395 * 2.3 * 0.11^2 / [ 4.4(2.3 + 4.4) ] }
    v2 = 0.611 m/s to 3 sig. fig.


    I did this and my answer is incorrect.


    I ALSO tried:

    0.5*k*x^2 = 0.5*m1*v1^2
    0.5*k*x^2 = 0.5*m2*v2^2

    and THAT was incorrect. I'm in the dark here.


    By the way, this is my first post, though I've been browsing PF all semester! Thanks for all the previous help =)
     
  2. jcsd
  3. Jul 10, 2011 #2
    Oh, I forgot to speak of the figure:

    0~~~O Two figures are compressing a spring .15 m.
     
  4. Jul 10, 2011 #3
    Your algebra looks good to me. Check the part where you plug in values, though.
     
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