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Can potential energy be greater than total energy?

  1. Dec 21, 2015 #1
    I'm working on a homework problem which states:

    "Some object, starting from far down the negative x axis and moving in the positive x direction, experiences a force, the potential energy U of which is modelled by the function U = 2e^(-x^2), where x is in meters and U is in Joules. The total energy E of the object remains constant at E = 1J. Describe the motion of the object."

    The problem isn't worded that well but I take it to mean the potential energy of the object, not of the force.

    Relevant equations:
    E = U + K
    ΔU + ΔK = 0

    I understand everything up until the point where U = 1. I know that the greater the potential energy gets, the lesser the kinetic energy gets due to conservation of energy. Thus, the object will slow down as U gets larger and speed up as U gets smaller. When U is greater a than 1, however, K would have to be negative for E to remain constant, which I know is not possible, so I am confused. Am I overlooking something that has to do with the force applied to the object?

    Thanks in advance for the help.
     
  2. jcsd
  3. Dec 21, 2015 #2

    haruspex

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    Exactly. So what does that tell you about the motion of the object?
     
  4. Dec 21, 2015 #3
    My guess would be that it's not moving, but I'm still not sure how that makes sense in the E = U + K equation.
     
  5. Dec 21, 2015 #4

    haruspex

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    It tells you more than that.
    You wrote, correctly:
    Think about this: if you throw a stone up at 1m/s, what will be its speed when it reaches an altitude of 1km?
     
  6. Dec 21, 2015 #5
    So it never gets there in the first place.
     
  7. Dec 21, 2015 #6

    haruspex

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    Indeed.
     
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