as the normal contact force increases, what happens to the friction force?

It'south perhaps the second week of your introductory physics course. Your instructor starts talking virtually friction and writes the following ii formulas on the lath.

Then there is probably some sort of lecture like this:

Friction is a contact strength when ii surfaces interact. The second equation is the kinetic frictional force that is used when two surfaces are sliding against each other. The frictional strength in this case depends on the ii types of materials interacting (described by the coefficient μ_g) and how difficult these two surfaces are pushed together (the normal forcefulness). The static friction example is like for when the two surfaces are stationary relative to each other. In static friction, the frictional strength is whatsoever value information technology needs to be to prevent sliding up to some maximum value.

Technically, this is chosen Amontons' Outset and Second Law of Friction. Meet, information technology's not merely Newton that has laws. Discover that both of these friction formulas ONLY depend on the coefficient of friction and the normal force. Information technology does not depend the expanse of contact, it doesn't depend on the sliding speed.

Side by side, there volition probably be some type of friction laboratory experiment. In this lab, students will measure coefficients of friction and show that the frictional force doesn't depend on surface area in contact. Also, the coefficient of friction doesn't depend on the mass of the object. Pretty standard stuff here.

Friction Is But a Model

How about another experiment? In this experiment, I am going to put an object on an moveable plane. I can and then increase the angle of inclination until this cake only starts to slide. At the moment it starts to slide, I can summate both the normal force (pushing the plane against the object) and the friction force (the maximum static friction force).

Here is a force diagram at the instant the block starts to slide.

Just at the instant this thing starts to slide, all of these forces still take to add upwardly to the nada vector (object is in equilibrium). That means that the component of the gravitational force perpendicular to the plane must exist equal to the magnitude of the normal force and the component parallel to the plane must be equal to the frictional force.

With just the mass and the sliding angle, I can get both the frictional force and the normal force. How can I calculate the coefficient of friction? What if I made a plot of friction vs. normal forcefulness for the aforementioned surface but with different masses? If the normal force and the frictional force are really proportional (like in the model above) then this data should exist linear with the slope of the line beingness the coefficient of friction.

It'southward simple, right? Ok. Permit's do this. In society to go along everything the same except for the mass, I am going to put masses into 1 of these minor boxes.

This box has a teflon bottom with an open up peak so you tin put masses inside (oh, it's from PASCO). At that place is as well a variable bending inclined plane. This one in particular has a large bending measurement on the side and hither you lot tin run across the friction box with a large corporeality of mass both inside and on top of it.

Actually, there is also a similar plane that is made of metal instead of forest. 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 aforementioned mass 5 or 6 times and then that I could get an boilerplate angle and a standard deviation in the bending measurement.

Here is a plot of friction force vs. normal force for both surfaces. The error bars are calculated (using the crank three times method) from the standard deviation in angle measurements.

What's going on here? Allow's look at the data for the teflon (the bluish data). I fit a linear function to the first four data points and yous can see it is very linear. The slope of this line gives a coefficient of static friction with a value of 0.235. However, as I add more and more mass to the friction box, the normal force keeps increasing but the friction force doesn't increase every bit 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.

A More Detailed Look at Friction

Really, what is friction? You could say that when 2 surfaces come nigh 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 2 surfaces, the greater the total frictional force. How practise you go more atoms to interact from the ii surfaces? Well, if you push button the surfaces together you tin can become more atoms from A to be close enough to the atoms from B to collaborate. Yes, I am simplifying this a bit. Notwithstanding, the point is that contact area does indeed matter.

I am talking about contact surface area, non surface area. Suppose you lot put a rubber brawl on a glass plate. Every bit you push down on the safety ball, it will deform such that more than of the ball will come up in "contact" with the drinking glass. Here is a diagram of this.

Greater contact area means greater frictional force. If the contact surface area is proportional to the normal force, then this looks merely like Amontons' Police force with the frictional force proportional to the normal force. Of course this model "breaks" when the contact area can no longer increase. Equally I add more than and more than mass onto the friction box, there is less and less available contact area to aggrandize into. In a sense, the contact surface area becomes saturated. I suppose that if I kept piling on the weight, the friction force would eventually level out and stop increasing.

It'southward Just a Model

This actually isn't a big deal. The Amontons' Law isn't a law at all (ok - it depends on your definition of Law). Information technology'southward just a model. A model is not THE TRUTH, it'southward but something that works some of the time. Let me give an case.

Gravitational Model. Nearly the surface of the Earth, we tin can summate the gravitational force on an object using the following model.

The one thousand vector is the local gravitational field. On Earth, it points "down" and has a magnitude around nine.viii N/kg. We often call this gravitational force the weight and it'southward a very useful model.

Even though this model is useful, nosotros still know it'south wrong. The to a higher place gravitational model says that information technology doesn't matter how high in a higher place the surface of the Earth you are, the weight is the same. Of course that'due south not true, only information technology's approximately true when close to the surface.

Here is a better gravitational model.

This says that the gravitational force decreases equally the ii interacting objects get further away from each other. If yous put in the mass of the Earth and the radius of the Globe yous get a weight that looks just like the mg version. So, at some point the two versions of gravity agree.

The aforementioned is true for friction. The introductory physics version of friction works for some stuff and a more complicated version of friction works for other cases. Of grade you could still use the complicated version of friction for simple cases - but why brand your life difficult?

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Source: https://www.wired.com/2014/09/friction-isnt-always-think/

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