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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
    E=0.5kx^2

    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
    F=kx=ma

    a=dv/dx*dx/dt = dv/dx*v
    vdv=(kxdx)/m integrate
    0.5v^2=0.5k/m x^2
    v=((k/m)^1/2)*x
     
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