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Block on Spring with Friction

  1. Oct 4, 2008 #1
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    A relaxed spring with spring constant k = 50 N/m is stretched a distance di = 63 cm and held there. A block of mass M = 6 kg is attached to the spring. The spring is then released from rest and contracts, dragging the block across a rough horizontal floor until it stops without passing through the relaxed position, at which point the spring is stretched by an amount df = di/10.

    What is the coefficient of kinetic friction µk between the block and the floor?


    I know i need to use the Work-Energy theorem.

    I'm not really sure what i need to do?

    The kinetic energy is 0, but i don't know how to find the work done by friction.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 4, 2008 #2

    Hootenanny

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    Welcome to Physics Forums,

    You're spot on with using the work-energy theorem. What does that theorem state and how can we apply it to this problem?
     
  4. Oct 4, 2008 #3

    Doc Al

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    What's the definition of work?
     
  5. Oct 4, 2008 #4
    Thanks,
    The work-energy theorem is: change in Kinetic Energy=the work done by friction.
    I believe the change in kinetic energy is 0, but its the work done by friction i can't seem to find.

    Work is a force over a distance, correct?
    So would the work done by friction mean its
    (Coefficient of friction-M)(Fnormal)(distance)=Work done by friction?
     
  6. Oct 4, 2008 #5

    Doc Al

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    Make that the change in total mechanical energy (kinetic energy plus spring potential energy).
    Exactly.
     
  7. Oct 4, 2008 #6
    So the kinetic energy = 0
    Work done by friction = M(58.86N)(.567m)
    The potential energy = -Force(x2-x1)???

    I'm not too familiar with potential energy yet. Is this the right formula i need to use?
    If so what is the force i need? Is it F = -50N/m(x)?
    If so what distance will i use, the distance it was initially stretched or the distance it comes to rest at?
     
  8. Oct 4, 2008 #7

    Doc Al

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    Good.
    No. (Look up the formula for the energy stored in a stretched spring. Or derive it yourself.)

    Since the force is not constant, you can't just use FΔx.
     
  9. Oct 4, 2008 #8
    I used Elastic Potential Energy Formula: (1/2)kx^2

    So i set it up like this:
    Work by Friction_______Potential Energy Final____Potential Energy Initial__Kinetic
    M(58.86N)(0.567m) = (1/2)(50N/m)(.063)^2 - (1/2)(50N/m)(.63)^2 + 0

    I solved for M = -.29, but its saying this is the wrong answer and i thought i had it right.
     
  10. Oct 4, 2008 #9

    Doc Al

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    Good.

    The work done by friction is negative, since it opposes the motion.
     
  11. Oct 4, 2008 #10
    I see, i had the right answer it just needed to be positive and have a more exact answer. It was 0.294! Thanks alot for your help. I'm beginning to understand this now. I wish i had you as my teacher, i don't seem to learn too much from the one i have right now. Thanks again.
     
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