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Why does the work of a constant force is conservative?

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  1. Jan 26, 2016 #1
    1. The problem statement, all variables and given/known data

    Why for a given constant force, in a study reference system, which point of application moves from A to B, the work of the force is conservative?

    2. Relevant equations


    3. The attempt at a solution
    The only thing I know is that if the angle ##(\vec{F},\vec{AB})## is acute ##W_{AB}## is an engine work else, its resilient.
     
  2. jcsd
  3. Jan 26, 2016 #2
    Some constant forces are not conservative, sliding friction, for example.
     
  4. Jan 26, 2016 #3

    ehild

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    Sliding friction is not a constant force. Its magnitude is constant but the direction is opposite to the velocity.
     
  5. Jan 26, 2016 #4
    If the direction of the velocity is constant, then both the magnitude and direction of the sliding friction force vector are constant.

    If the magnitude and direction of a vector are constant, then the vector is constant. Yet, friction is not conservative.

    Another example is the drag force on a falling object that has reached terminal velocity in air. The drag force is constant, but it is not conservative.
     
  6. Jan 26, 2016 #5

    ehild

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    http://www.britannica.com/science/conservative-force

    A function f(x) is not constant function, even in case x has a definite value. Friction depends on the direction of velocity. The work done between points A and B and back to B to A is not zero, because the velocity changes sign in the reverse path.
     
  7. Jan 26, 2016 #6

    ehild

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    The force is conservative, when the the work of the force does not depend on the path between points A and B. Along a closed path, the work is zero. In case of constant force, if the work is positive while the point of application moves from A to B, it is negative when moving back to B to A. Look at the angles between force and displacements (the blue and green vectors in the figure).
    work.png
     
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