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Spring problem using work energy theorem

  1. Mar 3, 2017 #1
    1. The problem statement, all variables and given/known data
    A 2.90 kg block on a horizontal floor is attached to a horizontal spring that is initially compressed 0.0360 m . The spring has force constant 860 N/m . The coefficient of kinetic friction between the floor and the block is 0.35 . The block and spring are released from rest and the block slides along the floor.

    What is the speed of the block when it has moved a distance of 0.0200 m from its initial position? (At this point the spring is compressed 0.0160 m)

    2. Relevant equations
    I'm using the equation Work( of the nonconservative forces) = Eb - Ea where Eb equals the final kinetic energy plus the final potential energy and Ea equals the initial kinetic energy plus the initial potential energy. I'm calculating kinetic energy using (1/2)mv^2 and for potential energy (1/2)kx^2.


    3. The attempt at a solution
    My attempt at it:

    The work done by friction should equal (mass)(gravity)(coefficient of friction)(displacement) which would equal 2.9(9.8)(0.35)(0.02)

    Now for the other side of the equation:

    (1/2)(m)vf^2 + (1/2)k(x2)^2 - ( (1/2)(m)vi^2 + 1/2k(x1)^2 )

    So this is what I get:

    2.9(9.8)(0.35)(0.02) = (1/2)(2.9)(vf)^2 + (1/2)(860)(0.016) - (1/2)(2.9)(0) - (1/2)(860)(0.036)

    I punched this into wolfram and got 2. something. I know the answer is 0.414, so I must be doing something wrong. I'm just using the equation I learned in class. Any suggestions?
     
    Last edited by a moderator: Mar 3, 2017
  2. jcsd
  3. Mar 3, 2017 #2

    kuruman

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    Is the work done by friction positive or negative?
     
  4. Mar 3, 2017 #3

    haruspex

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    So the friction is adding energy to the block?
     
  5. Mar 3, 2017 #4
    Ah so the work done by friction should be negative, right? That still doesn't give me 0.414 though. What else is wrong?
     
  6. Mar 3, 2017 #5

    haruspex

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    Compare.
     
  7. Mar 3, 2017 #6
    ah man. Even writing out the equations, I still couldn't punch in the numbers right! Thanks so much guys. I made the corrections and got the answer I was looking for!
     
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