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Simple Spring Problem

  1. Oct 16, 2006 #1
    A 6 kg mass slides to the right on a surface
    having a coeffcient of friction 0.78 as shown
    in the figure. The mass has a speed of 8 m/s
    when contact is made with a spring that has
    a spring constant 147 N/m. The mass comes
    to rest after the spring has been compressed
    a distance d. The mass is then forced toward
    the left by the spring and continues to move
    in that direction beyond the unstretched posi-
    tion. Finally the mass comes to rest a distance
    D to the left of the unstretched spring.
    The acceleration of gravity is 9.8 m/s^2.
    Find the compressed distance d. Answer in
    units of m. Also find Vf and D.

    im thinking i would use W=(1/2)kx^2 with k=147 N/m and x being the distance i need to find. i dont know what to set W equal to.

    http://pics.bbzzdd.com/users/turtle/spring.JPG
     
  2. jcsd
  3. Oct 17, 2006 #2
    clue: In this question, you need to apply your knowledge on energy conservation. Yes, you do need your elastic potential energy as your spring is compressed by the mass. But what else? When your mass is moving, what kind of energy does it possess? Will there be any energy loss due to friction? Equate the energy that causes the mass to move forward to the energy that causes the mass to slow down in its directed motion and you should be able to solve for ur d.
     
    Last edited: Oct 17, 2006
  4. Oct 18, 2006 #3
    would it be kinetic energy - energy lost to friction = 1/2kx^2 ?

    (1/2mv^2) - (m_k*9.8*m) = 1/2kx^2

    i solved for x and got 1.41 which was wrong.

    where did i go wrong?
     
  5. Oct 18, 2006 #4

    OlderDan

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    You left something out. It would help you to check your equation for consistent dimensions. Two of your terms have dimensions of energy. One does not.
     
  6. Oct 18, 2006 #5
    Ditto Dan. If you don't get the correct answer, the first thing you should check is your units. If they don't check, then you are missing a value, and if you are sharp, you can figure out what term, and then what unit to look for.
     
  7. Oct 19, 2006 #6
    Don't go careless now. Your steps are right. You are simply losing a value in finding ur energy due to friction.
     
    Last edited: Oct 19, 2006
  8. Oct 19, 2006 #7
    ok i finally got it and found that the spring compresses 1.334 meters. now to find the final velocity i thought i would use 1/2mv^2=1/2kx^2 solve for v and it was also wrong. im not having too much luck on this problem...
     
  9. Oct 19, 2006 #8

    OlderDan

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    When the spring is fully compressed, all remaining energy is stored in the spring. When the mass comes to rest, all that energy has been dissipated by friction. In the end, there is no velocity, and since firction is doing work during the compression and restoration, the velocity of the mass is less than 8m/s when the spring is restored.

    If you have incorporated all the friction work correctly, make sure you are finding the distance moved from the restored spring position, not the distance moved from the compressed position.
     
    Last edited: Oct 19, 2006
  10. Oct 19, 2006 #9
    im sorry, i still dont get it at all. i have tried this problem so many ways and looked in my text book and the internet for over an hour. i either need it explained where an idiot can get it, or an equation.
     
  11. Oct 19, 2006 #10

    OlderDan

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    You got the correct value for the compression of the spring by fixing your equation to read

    (1/2mv^2) - (m_k*9.8*m)x = 1/2kx^2

    That x that was added to the second term makes that term the work done by friction during the compression. As the spring is restored, it gives its stored potential energy to the mass, except for some energy lost to friction. The mass acquires kinetic energy which is eventually lost to friction. You do not need to know how much kinetic energy the mass acquired, because it is all lost to friction in the end. All you need to know is that the energy that had been stored in the spring is ultimately all converted to heat as friction does work on the mass. All you need to do is set the spring energy when compressed equal to the work done by friction and solve for the distance the mass has to move for this much work to be done. D is the distance the friction force acts minus the compression distance of the spring.
     
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