It's simple, right? Let's do this. In order to keep everything the same except for the mass, I am going to put masses into one of these small boxes. There is also a variable angle inclined plane. This one in particular has a large angle measurement on the side and here you can see the friction box with a large amount of mass both inside and on top of it. Actually, there is also a similar plane that is made of metal instead of wood.
I tried this experiment both with a felt-bottomed box on wood and a teflon box on metal. For each mass, I slowly lifted the incline until the box slipped and then recorded the angle.
I repeated the experiment for the same mass 5 or 6 times so that I could get an average angle and a standard deviation in the angle measurement.
Here is a plot of friction force vs. The error bars are calculated using the crank three times method from the standard deviation in angle measurements. View Iframe URL. What's going on here? Let's look at the data for the teflon the blue data. I fit a linear function to the first 4 data points and you can see it is very linear. The slope of this line gives a coefficient of static friction with a value of 0. However, as I add more and more mass to the friction box, the normal force keeps increasing but the friction force doesn't increase as much.
The same thing happens for friction box with felt on the bottom. This shows that the "standard" friction model is just that - a model. Models were meant to be broken. Really, what is friction? You could say that when two surfaces come near each other call them surface A and surface B , the atoms in surface B get close enough to interact with surface A.
The more atoms that are interacting in the two surfaces, the greater the total frictional force. How do you get more atoms to interact from the two surfaces? Well, if you push the surfaces together you can get more atoms from A to be close enough to the atoms from B to interact. Yes, I am simplifying this a bit. However, the point is that contact area does indeed matter. I am talking about contact area, not surface area. Suppose you put a rubber ball on a glass plate. As you push down on the rubber ball, it will deform such that more of the ball will come in "contact" with the glass.
Here is a diagram of this. Greater contact area means greater frictional force. If the contact area is proportional to the normal force, then this looks just like Amontons' Law with the frictional force proportional to the normal force. Of course this model "breaks" when the contact area can no longer increase. As I add more and more mass onto the friction box, there is less and less available contact area to expand into. In a sense, the contact area becomes saturated.
I suppose that if I kept piling on the weight, the friction force would eventually level out and stop increasing. This really isn't a big deal. The Amontons' Law isn't a law at all ok - it depends on your definition of Law.
It's just a model. Let me give an example. Gravitational Model. Because, even though surface gripping would scale with contact area, so does other parameters that are in the friction formula.
You can both have mechanical interlocking - as velcro - but also adhesion of one material onto the other - like glue - which tries to prevent sideways sliding.
Friction is then the force needed to rip this adhesion free again. I find it useful to think of the surfaces as very rough with "stickey" peaks and valleys. Peaks can grip into valleys and when pressed together like that they don't want to slide. Sign up to join this community.
The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Asked 4 years, 9 months ago. Active 7 months ago. Viewed 9k times. Improve this question. Add a comment. Active Oldest Votes. Improve this answer. Paul Paul 1, 8 8 silver badges 18 18 bronze badges. But realistically frictional force is very complex and nonlinear to the point it cannot be accurately predicted except under very controlled conditions that force a more linear relationship.
Friction also depends on other parameters such as temperature and other intervening materials such as lubricants. There are regimes of friction: static and dynamic equally difficult to model and almost impossible to model in the transition.
Few models are fitting in the entire range, and this is one of them - nothing wrong in stating linearity, because we assume everyday cases as long as nothing else is mentioned in the question.
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