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Why am I getting a negative? (Energy conservation)

  1. Dec 9, 2009 #1
    Why am I getting a negative!? (Energy conservation)

    1. The problem statement, all variables and given/known data

    2kg block slides on a rough table with uk = 0.3, just before the block hits the spring V0 = 1.3 m/s. k = 120N/m. How far is the spring compressed?

    2. Relevant equations
    Ki + Us = Kf + Us - Eth


    3. The attempt at a solution

    Okay just before it touches the spring, what energy does it have?

    Ki = 1/2(2)(1.3)^2 = 1.68 J

    1.68J + 0 = 0 + 1/2kx^2 -fx
    0 = 1/2kx^2-mgukx-1.68
    0 = 60x^2 -5.88x - 1.68
    x= 0.22 or x= -0.13

    Why is my answer negative!!???

    The only thing i can think of that intially the spring is not compressed. (x=0) Once you compress the spring, the spring must get smaller, what's smaller than 0? -0.13

    Can anyone clearly explain to me why this is negative!!?
     
  2. jcsd
  3. Dec 9, 2009 #2
    Re: Why am I getting a negative!? (Energy conservation)

    Bump, exams tomorrow hoping for an answer ASAP!
     
  4. Dec 9, 2009 #3
    Re: Why am I getting a negative!? (Energy conservation)

    Should be Ki + Us = Kf + Us + Eth.

    Initial kinetic energy of the block, plus initial potential energy of the spring, equals: final kinetic energy of the block, plus final potential energy of the spring, plus energy expended to friction.

    Then you solve the quadratic equation and you get two solutions, the negative solution is unphysical, the positive solution is your answer.
     
  5. Dec 9, 2009 #4
    Re: Why am I getting a negative!? (Energy conservation)

    Oh I thought of it this way,

    I start with a kinetic energy, and all of this energy is going to be converted into to spring energy, BUT there's friction, so just take away the energy friction consumes.

    Is this wrong?
     
  6. Dec 9, 2009 #5
    Re: Why am I getting a negative!? (Energy conservation)

    Then you have to put the friction term on the left, with the '-' in front of it.
     
  7. Dec 9, 2009 #6
    Re: Why am I getting a negative!? (Energy conservation)

    Thats correct, hopefully I can fix this understanding in my head before tomorrow :S.

    Any tips how to think/understand this better?
     
  8. Dec 9, 2009 #7
    Re: Why am I getting a negative!? (Energy conservation)

    Could it be as simple as saying, regardless of the circumstances of the problem my thermal energy is always going to be on the INITIAL side of my equation(for energy conservation) and it will always be NEGATIVE?
     
  9. Dec 9, 2009 #8
    Re: Why am I getting a negative!? (Energy conservation)

    Bump anyone know if what I stated above is correct?
     
  10. Dec 9, 2009 #9
    Re: Why am I getting a negative!? (Energy conservation)

    lol i was stuck in the same question as well but its kinda easy
    and dont break ur head with this stuff.. just remember the equation u wont have time to think about it on the exam
     
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