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Springs, thermal energy

  1. Nov 5, 2014 #1
    1. The problem statement, all variables and given/known data

    1. A block with mass m = 1.46 kg is attached to a spring with spring constant k = 52.0 N/m and negligible mass. The coefficient of kinetic friction between the block and the table is µk = 0.349. The block is displaced from its equilibrium position to the left by 0.203 m and released from rest. Calculate the block's displacement when it first comes to rest again.

    2. Relevant equations
    Thermal energy=Ff * x
    Us= 0.5kx^2

    3. The attempt at a solution
    Ff= MuN= (1.46 x 9.8)(0.349)=4.99 N
    Us(initial)= 0.5(52)(-0.203^2)
    Us(final)= 0.5(52)Xfinal
    initial thermal and spring energy=final thermal and spring energy
    (4.99)(-0.203)+26(0.203^2)=4.99x +26x^2
    i tried to solve it, plugged it into a quadratic equation but am still getting the wrong answer.

    Any ideas on what im doing wrong? Thanks!
  2. jcsd
  3. Nov 5, 2014 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Instead of calling it thermal energy, call it energy dissipated by friction. Note that x is the distance traveled by the mass.

    OK. Here x is the displacement from equilibrium. Careful with notation!

    Careful! You start and end with pure spring potential energy, the difference being the energy lost to friction.
  4. Nov 5, 2014 #3
    Okay, so now I got:
    4.99 (0.203+x)=26x^2-26(0.203^2)
    plugged everything in and still didn't get the correct answer.
  5. Nov 5, 2014 #4

    Doc Al

    User Avatar

    Staff: Mentor

    The two terms on the right hand side are in the wrong order. You want initial U minus final U.
  6. Nov 5, 2014 #5
    Okay awesome! Thank you very much haha I had been going at this one for a good 45 minutes! I feel pretty confident I understand it now just needed a bit of guidance. Thanks again!
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