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Total mechanical energy

  1. May 17, 2015 #1
    1. The problem statement, all variables and given/known data
    upload_2015-5-17_5-25-1.png

    2. Relevant equations


    3. The attempt at a solution
    So for part a, i just plugged 3 into the equation, got the U(3) = -5.36

    to get mechanical energy, (KE + PE):

    5 J + (-5.36 J)= -0.36 J

    is this correct? what does it mean when the total energy is a negative value? (I have never seen this before)

    and part b) I have no clue how to do this.
     
  2. jcsd
  3. May 17, 2015 #2
    Think about this. If you have an object at a height h, it has gravitational potential energy equal to mgh. If you then drop the object, the force of gravity acts on the object, reducing its potential energy.
     
  4. May 17, 2015 #3

    Orodruin

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    How does the force relate to the potential?
     
  5. May 17, 2015 #4
  6. May 17, 2015 #5
    yes, I sort of understand what you said , but I always thought the decrease in height lowered the potential energy.
     
  7. May 17, 2015 #6
    Wgrav = mgh
    W = F d

    mgh = F d

    ?
     
  8. May 17, 2015 #7
    And why would the height change, if not for the force acting on the object? Since Ug = mgh, how would the gravitational potential energy of an object change if not for the force acting on it?
     
  9. May 17, 2015 #8
    yes. that is true. makes complete sense now

    but isn't height on the y axis? how can I find where the particle is located on the x axis at a given time?
     
  10. May 17, 2015 #9
    So how is the conservative force related to the potential energy in the OP?
     
  11. May 17, 2015 #10
    -dU / dx = F(x) = g

    ?
     
  12. May 17, 2015 #11
    Exactly! Now apply that to the original problem statement. The thing about gravity was just an analogy. Find the opposite of the derivative of the potential energy function listed in the problem statement, and you will have the conservative force as a function of x.
     
  13. May 17, 2015 #12
    dU/dx = 4e-2/x ( x - 2) = F = 0

    ?
     
    Last edited: May 17, 2015
  14. May 17, 2015 #13
    also, can you give me a real life example where the total mechanical energy of a system is negative?
     
  15. May 17, 2015 #14

    Orodruin

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    Energy is only defined up to an additive constant (at least for the purposes of classical mechanics). By redefining the zero level of potential energy, any system can have a negative total energy. The prime example would be anything on Earth bound by gravity (the zero level of gravitational potential energy is usually taken to be at infinite separation).
     
  16. May 17, 2015 #15

    gneill

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    A planet orbiting a star is an example. Objects in bound orbits (circles, ellipses) have negative total mechanical energy associated with them. A body on a hyperbolic trajectory that passes by the Sun only once: approaching, swinging around the Sun, then heading out again never to return, has a positive total mechanical energy. The borderline case where the total mechanical energy is zero corresponds to a parabolic orbit (such as some comets are thought to have) and are also "one time guests" to the solar system.
     
  17. May 17, 2015 #16

    Orodruin

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    Just to be clear here: This is true for the convention of having zero potential at infinite separation as I indicated above. You can always add a constant to the potential.
     
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