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Velocity Of An Object Accelerated By A Spring

  1. Nov 5, 2008 #1
    1. The problem statement, all variables and given/known data
    I'm pulling my hair out over this problem. A spring with a force constant of k is compressed x meters. An object of mass m is placed against the spring. The spring is then released. At what velocity is the object moving at the instant that is ceases to touch the spring?

    2. Relevant equations

    3. The attempt at a solution
    I'm really unsure. All of my solutions don't seem realistic.
  2. jcsd
  3. Nov 5, 2008 #2
    Using Energy:
    E=0.5kx^2=Kinetic Energy=0.5mv^2.

    solve for v=((k/m)^1/2)*x
    where x is initial displacement of spring.

    Using F
    F=-kx x is negative therefore

    a=dv/dx*dx/dt = dv/dx*v
    vdv=(kxdx)/m integrate
    0.5v^2=0.5k/m x^2
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