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Normal force: Why not conservative?

  1. Feb 2, 2010 #1
    Oh hello there!
    I have a question about the normal force!

    In my mechanics class we are CONSTANTLY told that the normal force is not conservative. I don't doubt this for a second, if you imagine a ball rolling up and down an incline, the normal force is related to the velocity of the ball and the slope of the incline, and as far as I know, conservative forces are related only to position, not velocities.
    There were some mathematics done to show that this was the case, but I am short on time and will not reproduce them here. Anyway, from what I read, the normal force is non-conservative.

    If the normal force is the repulsion of adjacent atoms... the normal force is pretty much just the electric force, right? It's not even 'pretty much' the electric force, as far as I can tell it is ONLY the electric force.
    And the electric force is a field force like gravity, right? Just with a different constant of nature. Gravity is accepted as a conservative force, and because it is similar in nature to the electric force I think that should be conservative too, and by extension, the normal force should be conservative!

    Why not?
  2. jcsd
  3. Feb 2, 2010 #2
    The normal force is not dependent on velocity.Are you sure your teacher is not talking about friction?
    The reason the normal force is not conservative is because it does not really do work. When an object is moving the normal force acts perpendicularly to the path so so it does no work.
  4. Feb 2, 2010 #3
    In my head I'm imagining a block glued to a surface that is free to rotate from an axis some distance away from the block. If the surface rotates 360 degree, it is back where it started, but not before doing some work on the block.

    I'm used to thinking of conservative forces in terms of the curl of their vector fields, but I guess in this respect, normal forces are non-conservative.
  5. Feb 2, 2010 #4
    I do not completely understand your mental image but i do not see how does the normal force does any work here. The work done on the is still made by a force that acts parallel to the glued face between them.
  6. Feb 2, 2010 #5
    A difference between those two pictures (ball in a shallow versus atomic spacings) is that the former assumes rigidity of the bodies, neglecting that when (for a given position in the surface) the normal force varies, so too does the penetration (compressing atomic spacings), and so overlooking a dimension of position-dependence.

    You need to be very careful what your instructor means when saying that the normal force is non-conservative, they're likely excluding the "cause" of the force from the system. It's feels like tunnel vision: they're saying the force (or the tension) exerted (on a mass say) by one end of a spring (if the other end is separately driven) can be non-conservative, while the bigger picture of the same spring is still always conservative.
    Last edited: Feb 2, 2010
  7. Feb 2, 2010 #6


    Staff: Mentor

    The normal frce does no work on the block. The friction force does work.

    Conservative forces are the gradient of their scalar field.

    In any case, you can get a "non-conservative" force by ignoring some of your system's degrees of freedom.
  8. Feb 3, 2010 #7
    Ah, so are you saying that the fact that it is not conservative is only due to the fact that we do not account for the other 'end' of the thing that's causing the normal force? So like, if we accounted for the work done on the earth as a ball rolls up and down an incline, it would turn out that the normal force IS conservative?

    It seems like in that case, there can be no such thing as a non conservative force without ignoring degrees of freedom, as some of you have mentioned.
    Do I have your explanation straight?
  9. Feb 3, 2010 #8
    That's almost reducing it to the global statement that energy is conserved. The (non)conservative force distinction makes more sense when dealing with forces that transfer energy into forms not directly re-accessible through (macroscopic) mechanics, such as heat. But it seems perverse to define the normal force of the table as non-conservative just because it depends (not just on where my hand is but) on how hard I press my hand against it.. It's like division of zero by zero: taking the limit of a spring as its stiffness increases, and then neglecting that it's still a spring. (Kind of like continuing to discuss momentum conservation after assuming the Earth to be immovable.) Or like the statement that magnetic fields do no work (technically true but often decried as confusing/irrelevant): pedagogically dangerous because if not taught well enough then it could actual diminish (rather than improve) understanding for some.
    Last edited: Feb 3, 2010
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