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in class we where asked to position a mass (a wooden object on a wood surface) in two ways, so that we have a case where the area of contact with the surface is larger than the initial positioning and then asked if both mass will start moving at the same angle regardless ,knowing that object is at rest in the y direction I got that $$m*g*cos(\theta)=N$$ (the objects are on an inclined plane with angle theta )in the y direction and the positioning of the mass won't change the normal force but the normal force results from the atoms pressing one another and more area means less pressure so I started to wonder how the relationship is still being conserved is it being compensated by the increase in the total number of microscopic contact points between the surfaces?

so my first question is my analysis flawed if yes do correct me . the second being if the analysis is correct what about cases like rubber and rubber materials in contact would not a larger area of contact cause a higher resistance in this case ?

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In the Coulomb model of friction, the maximum static friction force is proportional to the applied load $N$ and independent of the surface area in contact. Thus

$F_{friction} \le \mu N$

where $\mu$ is the coefficient of friction.

The Coulomb model is an empirical model that holds in many circumstances but not all. One circumstance where it does not hold is tyres (especially tyres on drag cars) where adhesion between the tyre and the road surface means that the maximum static friction force becomes dependent on contact area.

The study of friction between surfaces and ways to reduce or increase it as required is called tribology.

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  • $\begingroup$ if I may ask what does an empirical model mean? $\endgroup$
    – lodo
    Commented Feb 24 at 11:49
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    $\begingroup$ @lodo An empirical model is a model based entirely on experimental evidence that is lacking a clear theoretical explanation or mechanism. $\endgroup$
    – gandalf61
    Commented Feb 24 at 11:59
  • $\begingroup$ if you are able to further explain about the example where it fails (tyre and road surface ) why do they become dependent on contact area I have some speculations but nothing really plausible as an explanation? $\endgroup$
    – lodo
    Commented Feb 24 at 12:07
  • $\begingroup$ @lodo Rubber, especially when it is warm, adheres (sticks) to the road surface. When adhesion (stickiness) is involved, the Coulomb model no longer applies, and static friction depends on the are of contact between the surfaces. $\endgroup$
    – gandalf61
    Commented Feb 27 at 12:19
  • $\begingroup$ thanks for the explanation it is helping me grasp the concept $\endgroup$
    – lodo
    Commented Feb 27 at 12:23

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