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Question about Friction and gravity

  1. Oct 21, 2007 #1
    Let's say you have an object on the ground. Why do they say that friction is proportional to the normal force instead of saying it's proportional to the force of gravity? I know that they're equal in magnitude, so you get the same answer, but they're opposite in direction. The force of gravity exerted by the Earth on the object pulls the object TOWARD the surface of the ground, whereas the normal force exerted by the ground on the object pushes the object AWAY from the surface of the ground. It makes more sense to me intuitively that the force of friction between two surfaces is proportional to the force that pushes or pulls two surfaces together.
  2. jcsd
  3. Oct 21, 2007 #2

    Doc Al

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    I'm not sure I understand your question.

    The normal force is the force which which the two surfaces push against each other. If gravity and the upward normal force are the only forces acting on the object, and the ground is horizontal, then the normal force will equal (in magnitude) the weight of the object. But that's not always the case. What if someone were stepping on the object? Then the normal force would be greater than the weight of the object.

    And the maximum value for static friction depends on how hard the two surfaces are squeezed together, which may or may not equal the weight of the object.
  4. Oct 21, 2007 #3


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    Note that according to Newton's 3.law, the object pushes back on the surface with a force of the same magnitude as the normal force it experiences.

    Hence, you could say that the magnitude of normal force is a measure of the interaction strength between the two surfaces, in which light it makes some sense on the intuitive level that the frictional force between them also should be stronger whenever the normal force is increased.
  5. Oct 21, 2007 #4


    Staff: Mentor

    A lot of times the normal force has nothing whatsoever to do with weight. Consider your car's brakes. The brake pads generate a large amount of normal force against the drum by pushing with hydraulics. The normal force in this case is many times the weight of the brake pad.
  6. Oct 22, 2007 #5
    also don't forget about inclined planes, you must be dealing with the normal force because if it's an inclined plane you have to take into account the x and y-components.
  7. Oct 22, 2007 #6
    I'm fully aware that weight is not the force we should consider regarding friction in all cases. I mentioned the above for cases in general, whereas I said it should be proportional to mg in my example. Sorry that I was unclear. I did not claim that the force of friction = mu*mg in all cases.

    The purpose of this question was to better understand the theory behind friction. It seems like a dumb question at first, but I think it reveals a lot about the theory behind friction. In the classical sense, friction is an empirical force, so there's not a lot of theory behind it, but I wanted to understand the theory that is there. (I imagine friction has better foundations in QM.)

    I'm simply noting that it would be more intuitive for the frictional force to be proportional to the net force that is pushing one surface TOWARD the other in the direction of the normal of the other surface. TOWARD is the key word. The normal force between two surfaces pushes each surface in the direction AWAY from each other, even if they don't move away from each other (forces are balanced).

    However, I've answered my own question, viz. why friction is theoretically proportional to the normal force, by piecing together explanations from Ohanian's textbook (which is really good, btw). Here's my resolution:

    First I'll establish that the force of friction technically DOES depend on contact area. It's true that friction does not depend on the macroscopic contact area, but it does depend on the microscopic contact area. This is because the frictional force is caused by bonds of atoms between two surfaces, and the more microscopic contact area (actual contact area), the more bonds. The bonds are usually created between two peaks in the surfaces that "touch" each other.

    The role of the normal force in friction is to deform these peaks such that it creates more contact area. With a larger macroscopic area, you have more peaks but less force per peak. With a smaller macroscopic area, you have less peaks but more force per peak. Thus the sum of the deformations, which amount to the contact area, is the same in both cases.

    So yeah, the answer to my question, as stated above, is that the role of the normal force in friction is to deform the peaks between surfaces in which bonds can form between atoms, thus creating a larger contact area and more friction. Hence friction being proportional to N.
  8. Oct 22, 2007 #7
    The gravitational force bulling the object down is only equal to the normal force pushing it up if those are the only forces in the y direction and if the net force is zero.

    For example, if you are in an elevator accelerating upwards, an object in the elevator will have more friction than an object of the same mass outside that is not accelerating.
  9. Oct 22, 2007 #8
    You must have skipped my most recent post.
  10. Oct 24, 2007 #9
    Aww, no feedback on my last post? I started out with a controversial statement in hopes that it would generate discussion :P Could a mod copy/paste it into my original post? I personally find it very helpful / instructive -- much thanks to Ohanian's book.
  11. Oct 25, 2007 #10
    so how exactly does the normal force go about deforming these peaks? i've been wondering about this situation myself for a while now
  12. Oct 25, 2007 #11
    It's like when you take a bit of playdoh, form it into a sharp peak, needle-like, and then press it against the ground. The ground supplies the normal force, which deforms the playdoh so that the "sharp peak" is now a blunt surface, which has more surface area than the sharp peak.
    Last edited by a moderator: Oct 25, 2007
  13. Oct 26, 2007 #12
    you said the friction force is dependant on molecular bonds between molecules of each surface, but does sanding down a surface to make it smoother not generally reduce friction? but this would result in more contact area if anything and should then increase friction in your model. (i'll admit i may not have given this due thought yet)

    my initial image of friction was that it was simply the coulomb repulsion of one peak away from another is it is forced past it, hence making it a much more mechanical situation.
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