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Easy Energy Conservation Problem causing me trouble

  1. Oct 13, 2004 #1
    Problem:
    A 3.30kg block is dropped from a height of 5.70m onto a spring of spring constant 3806 N/m. When the block is momentarily at rest, the spring has compressed by 32.0 cm. Find the speed of the block when the compression of the spring is 13.5cm.

    How I approached it:
    Calculate the the elastic energy when the spring is compressed 32.0cm. Then subtract the elastic energy when the spring is compressed 13.5cm. Then that energy would be the current kinetic energy, and I determined velocity from that. However, this is not giving me the correct answer.

    Calculations:
    Elastic Energy at 32.0cm
    E = .5kx^2 = .5*3806*.32^2 = 194.8672 J

    Elastic Energy at 13.5cm
    E = .5kx^2 = .5*3806*.135^2 = 34.682 J

    Subtract the potential energy remaining
    194.8672 - 34.682 = 160.185 J

    Find velocity
    Ke = .5mv^2
    160.185 = .5*3.30*v^2
    v = 9.85 m/s

    Where am I going wrong? Thanks in advance
     
  2. jcsd
  3. Oct 13, 2004 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Don't forget to include gravitational PE in your energy calculations.
     
  4. Oct 14, 2004 #3
    Doesn't all of the gravitational potential energy become elastic potential energy when the spring is compressed 25 cm?
     
  5. Oct 14, 2004 #4
    Ah, never mind to my last post, I see where the potential energy comes into play because not all of the elastic energy is converted into kenitic energy, and some becomes potential energy. Thank you for the help.
     
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