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Stretched spring -find coeff of friction

  1. Aug 8, 2007 #1
    stretched spring --find coeff of friction

    1. The problem statement, all variables and given/known data
    A relaxed spring with spring constant k = 70 N/m is stretched a distance di = 66 cm and held there. A block of mass M = 10 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/7

    2. Relevant equations
    7What is the coefficient of kinetic friction µk between the block and the floor?

    3. The attempt at a solution
    This problem is a problem for me.
    i know about spring constants and friction but cant visualize where to start?

    I know:
    M= 10kg
    df = .094m
    Fs = .09 * 70 = 6.3N
    N = 9.8*10= 98N

    dont know
    µk (µk = Fk/N)

    Also i know (obviously) that block stops because µk force must be greater than the spring constant force.

    thanks for any help
  2. jcsd
  3. Aug 8, 2007 #2


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    Staff: Mentor

    Fun problem. I don't know the answer right off the bat, but the way I'd approach a problem like this is to initially break it into understandable segments. Like, you know the initial force on the block from the spring and its mass, so what would be the possible accelerations for the block initially based on the mu values? And if you were going to set up a differential equation for the instantaneous velocity of the block based on the things that you are given, what would that equation look like? And given that instantaneous differential equation, how would you integrate or solve for the motion versus time, based on the mu value? And given that and the answer that you are given for the final V=0 position, how can you then solve for the mu?
  4. Aug 8, 2007 #3


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    Homework Helper

    I'd use the work-energy theorem... The final energy - initial energy = work done by non-conservative forces (ie work done by friction).
  5. Aug 9, 2007 #4
    this is what i did but its wrong sumhow.

    Fsp = -K delta x
    Fk = mu N

    so i equated equations

    -K delta x = mu N

    mu = -K delta s / N

    mu = -70(.094) / (10*9.8)

    mu = .067

  6. Aug 9, 2007 #5


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    That gives the coefficient of static friction, not kinetic.
  7. Aug 9, 2007 #6
    coeff of static and kinetic use same formula dont they?
    Fk = mu*N
    Fs = mu*N
  8. Aug 9, 2007 #7
    oh so whole picture is wrong
    i am looking at it like : equate forces, then when they become equal (and opposit) that is mu-max for static.\
    should be..
  9. Aug 9, 2007 #8


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    There are 2 different mu's... mustatic and mukinetic
  10. Aug 9, 2007 #9
    so is kinetic coeff, --get that from KE=.5mv^2 somehow?
  11. Aug 9, 2007 #10


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    Yes. To get mu-kinetic, you need to use work-energy...
  12. Aug 9, 2007 #11


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    You don't need that... what's the initial mechical energy of the system (includes all kinetic and potential energies)... what's the final mechanical energy of the system... It starts at rest and ends at rest so the kinetic energies are 0. There is kinetic energy in between, but we don't need to worry about that... we just need to worry about the initial and final states...

    work done by friction = final mechanical energy - initial mechanical energy

    From the left hand side you can get mu-kinetic.
    Last edited: Aug 9, 2007
  13. Aug 9, 2007 #12
    OK so i am equating PE of spring with force of spring??

    I know its these 3 equations :

    Fsp = -K delta x
    Fk = muN

    But Fsp and Fk are in in newtons and U is in Joules.
    I want everything in joules to use conserv of energy??

    How can i get both equations in J?
  14. Aug 9, 2007 #13


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    Homework Helper

    Just use the first equation for now... what's the initial energy, and what's the final energy?
  15. Aug 9, 2007 #14


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    Homework Helper

    Work done = Force * distance... which is N*m which is the same as J.
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