# Homework Help: Why is the kinetic friction always smaller than the static friction?

1. Oct 29, 2006

### photobillyli

Why is the kinetic friction always smaller than the limiting static friction?

Thank you very much!

2. Oct 29, 2006

### kreil

It is based on the concept that it takes more force to accelerate a mass from rest than to keep it moving.

3. Oct 29, 2006

### photobillyli

Thanks!
Can you tell me more about that?

4. Oct 29, 2006

This link should help: http://hyperphysics.phy-astr.gsu.edu/hbase/frict2.html" [Broken].

Last edited by a moderator: May 2, 2017
5. Oct 29, 2006

### photobillyli

I have done an experiment to study the relationship between the static friction and kinetic friction of a wooden block.
I have found that the static one was larger than the kinetic one.
My text book also tells me that result.
However, that web tells me that there should be no any difference between static and kinetic friction.
Then, what should I answer to the question:
Why is the coefficient of kinetic friction smaller than the coefficient of static friction?
Should I write
1. In fact, the frictional force had no any relationship to the velocity of the body. Many people believe that the friction to be overcome to get something started(static friction) exceeds the force required to keep it moving(kinetic friction), but with dry metals it is very hard to show any difference.
The difference between static friction and kinetic friction of the wooden block was because of irregular surfaces, impurities, or other factors. (It is taken from that web)
or
2. It can be explained by the inertia.
When the body was at rest, it tended to remain at rest. The applied force had to overcome both the static friction and the inertia.
On the other hand, when the body started moving, it tended to remain moving at constant speed. The applied force did not needed to overcome the body’s inertia but just needed to overcome the friction.
Therefore, the force needed to keep a body moving was smaller than to start a body to move. (It is the explanation I thought)

Moreover, how the irregular surfaces, impurities, or other factors make the difference between static friction and kinetic friction of the wooden block?

Thank you very much!

Last edited by a moderator: May 2, 2017
6. Oct 29, 2006

### Astronuc

Staff Emeritus
Interaction between the surfaces is more established when the surfaces are at rest.

Not quite. In the hyperphysics link provided by radou, it inidicates the kinetic friction is "the frictional resistance is almost constant over a wide range of low speeds", which implies that at higher speeds, the relationship is not necessarily constant.

It is not that people "believe that the friction to be overcome to get something started(static friction) exceeds the force required to keep it moving(kinetic friction)," but it has been demonstrated experimentally.

If an applied force exceeds the kinetic friction force, then a sliding body will accelerate. Once a body starts to move, the applied force may be decreased to a level equal to the kinetic friction force, and the body would move at constant speed.

The surface properties do not change (more or less), but the interaction changes. On the other hand, the 'effective roughness' of either or both surfaces may change with the application of shear forces due to motion.

Last edited: Oct 29, 2006
7. Oct 29, 2006

### OlderDan

#2 is not valid. You are comparing the forces, not the motion. An object has inertia whether it is moving or at rest. It takes the same amount of force to cause the same change in velocity regardless of what the initial velocity is. #1 is is in the right direction.

I will attempt to answer your last question that I have changed to blue text.

The force of friction characterized by the coefficiient of friction is the sum of forces distributed over the entire surface area in contact. The force that we call the normal force is also a sum of forces over the contact area. That normal force that we say is perpendicular to the surface is made up of a huge number of forces at the contact points, pointing in many different directions. It is the sum over all of these forces that gives us the net normal force.

In the purest sense, contact means the molecules of one object are as close as they can get to the molecules of another object before the electric forces of repulsion keep them from getting any closer. If you could create two surfaces that were perfectly smooth what would that mean? For a crystal material that would mean the surface was a crystal plane with no imperfactions. The atoms would form a very regular pattern of positions. Two such surfaces in contact would be the most perfect surface contact you could imagine. In principle, if you had two crystals of pure NaCl whose surfaces were perfect primary planes of alternating Na+ and Cl- ions, if they ever came into contact they should fuse together into one crystal, just like two drops of liquid that come together will fuse into one drop. Surface roughness and impurities keep that sort of thing from happening.

Think about the interaction between a piece of sandpaper and a block of wood. Why do people use sandpaper? They use it to shave off the surface irregularities. When two irregular surfaces come together, the peaks of one surface fit into the valleys of the second surface and vice versa until the closest possible contact is achieved. If it is sandpaper on wood, and pressure is applied, and the sandpaper is forced sideways it literaly shaves wood off the peaks. If you do this agan and again, the wood gets smoother until the sandpaper starts only cutting furrows into the surface. If you want smoother wood, you have to use finer sandpaper. A similar thing happens when polishing the surface of a crystal. A finer polishing grit has to be used to get a smoother surface.

Why do automobile engines use oil? Two very smooth peices of metal are rubbing together, and as they do they will shave the peaks off one another. To keep this from happening, a layer of fluid is applied to fill up the valleys so that at most only the very peaks of the metals come into conatact. This signifcantly reduces the amount of metal that gets shaved off.

Moving two dry surfaces relative to one another does something similar to oil, but far less effectively. Suppose the peaks of one surface aligned with the valleys of another surface, and you applied enough force to start slipping. One of two things must happen. Either the peaks get shaved off (which takes a lot of force), or the average distance between the two objects increases. Even if there is a little shaving taking place, the distance between the objects is increasing. If the objects start separating, they cannot suddenly return to have the peaks and valleys line up. It takes time, just like it takes time for a ball thrown into the air to return to earth. If the surfaces are kept in motion, the distance between them will reach some average that is greater than the average when they are at rest. Greater separation means that only the peaks of the surfaces are coming into contact at points closer to the tips of the peaks. There will be a reduced attraction between the molecules of the two objects, and a reduced component of the microscopic normal forces parallel to the direction of motion. This results in a lower component of force parallel to the direction of motion, i.e., less friction.

Last edited: Oct 30, 2006
8. Oct 30, 2006

### photobillyli

Thanks for OlderDan's detailed explanation.
Let me to answer my question.
There are always irregularities between the surfaces. The peaks of one surface will fit into the valleys of the other surface. A larger applied force is needed to starts the body's motion.
On the other hand, when the body is moving on a surface, it will separate from the surface. The body is just jumping up and falling down although we can not see the jumping. There will be a very small(relatively) friction during the period that the body is separating from the surface. Although this period of time is short, it happens many times during the motion.
As a result, the kinetic friction will be smaller than the static friction.

I have got some questions, you said"Greater separation means that only the peaks of the surfaces are coming into contact at points closer to the tips of the peaks. There will be a reduced attraction between the molecules of the two objects."However, the law of friction states that friction has no relationship to the contact surface area. Then, how "only the peaks of the surfaces are coming into contact at points closer to the tips of the peaks" can reduce the friction??

Besides, how this effect disappear on dry metals?

Thank you!

9. Oct 30, 2006

### OlderDan

For a rough surface, the molecular attraction is probably a minor contributor to the total friction. It is more likely that the sideways force of friction is a reaction to trying to push the nestled surface peaks over one another. If the molecular forces become the dominant effect, then I suspect friction would behave rather differently from what we usually observe.

The observation that the frictional force is proportional to the macroscopic normal force leads naturally to the observation that the force is independent of the contact area. It is also a logical consequence of the microscopic view of the normal force. Imagine the peaks and valleys of the two horizontal surfaces arranged as best they can be when the surfaces are in contact. All the little normal forces tilted at various angles at the microscopic points of contact add together to give the net vertical normal force. Suppoe you double the weight of the top object. Then all of the microscopic normal forces are doubled, and the total frictional force is doubled. If the friction is the result of the angles of attack at the microscopic surfaces when you try to slide the object, then doubling the microscopic forces should double the sideways force needed to get or keep the object moving, so this result is not surprising. And of course the proportionality of the frictional force to the normal force for any given contact area is exactly what has been observed in nature.

Now suppose you could take half the object and move it from being in contact with the supporting surface and place it on top of the other half, so the weight stays the same. What happens to the remaining microscopic normal forces at the points that are still in contact? If there is no change in the configuration of the surfaces in contact, every one of those microscopic normal forces has to double, just as they did when you doubled the weight of the object. But now you have eliminated half of the microscopic normal forces, so the sum of the forces is cut in half by reducing the area, and doubled by increasing the weight supported by the remaining contact area. These two effects cancel one another, so the friction stays the same.

The dry metal experiments showing little if any difference between static and coefficient friction suggests (as the article states) that the observed differences betwen the two coefficients for most pairs of surfaces are in fact the result of surface roughness. This observation is compatible with the microscopic model as well. If the surfaces are incredibly smooth, then all those microscopic normal forces will be in the same direction, perpendicular to the macroscopic surface. When sliding begins there are no peaks to climb, no increase in separation of the surfaces, and no obvious reason why the force should be reduced.

I'm not trying to convince you that this microscopic model accounts for everything perfectly. I'm just pointing out that the observed nature of friction does not violate any simple view of the microscopic picture. as I said earlier, if it were possible to create perfectly smooth surfaces of a pure material, the molecular forces whould become the dominant source of attraction between the objects, and they would actually fuse together. What I said about NaCl earlier would also be true of two perfectly smooth metalic surfaces of the same metal. If you put them together they would fuse together. Then you are no longer talking about frictional forces. You are talking about shear forces in a bulk material, and that is a different ball game altogether.

10. Oct 30, 2006

### arildno

It is of importance to realize what the discontinuity between the standard expressions between maximal static friction and kinetic friction actually entails:

It simply means that there exists a MINIMUM NON-ZERO acceleration that the object will start with, i.e, it will start with a JOLT.

This can be seen that if the applied force is arbitrarily close, but greater than maximal friction, then the least acceleration you can get is (on a horizontal plane):
$$a_{min}=(\mu_{s,max}-\mu_{kin})g>0$$

11. Oct 30, 2006

### Andrew Mason

The simple answer to this question is: if the initial kinetic friction force (ie. applied force - maximum static friction is arbitrarily small) was higher than static friction, the object would not begin to move - so we would call it static friction. If the object begins to move, then necessarily the force of kinetic friction has to be less than the maximum static friction force.

AM

12. Oct 30, 2006

### OlderDan

I get your point about why kinetic friction cannot be greater than static friction, but I do not agree with your conclusion. If the coefficient of kinetic friction and the coefficient of static friction were identical, then if I placed an object on an adjustable incline I could find an angle where the object could be placed at rest and stay there (static) or give the object an initial speed down the plane and have it move with constant speed (kinetic). An infinitesimal increase in the pitch of the plane would result in an infinitesimal net acceleration. An infinitesimal decrease in the pitch would result in the object remaining stationary if placed, or coming to a stop if given an initial velocity.

What we emprically observe is that if an object is at rest and we gradually increase the pitch, it remains at rest until a critical angle is reached and the object suddenly has a finite acceleration. There is no gradual change between zero acceleration and the mimimum acceleration. So we must conclude that it is possible (and common) for the kinetic friction to be less than the maximum static friction, but that does not require the kinetic friction to be less than the static friction. The world would be just fine if they were the same. According to that article at hyperphysics, it has been shown that there are cases where the two are the same.

13. Oct 30, 2006

### Andrew Mason

There may be cases where they are about the same, but if they were exactly the same there would be no minimum speed. The object would begin to move at an arbitrarily small speed as soon as the maximum static friction force was reached. But if that was the case, we could not call it the maximum static friction - because it is moving (albeit at an extremely slow speed)!

Now, once it is moving it is certainly possible that the coefficient of kinetic friction could increase with speed so that the kinetic friction at a particular speed is greater than the maximum static friction force. But not at an arbitrarily small speed.

AM

Last edited: Oct 30, 2006
14. Oct 30, 2006

### OlderDan

It (the object on a plane) would not begin to move when the gravity component just reached the maximum static frictional force. It would be in equlibrium. It would only begin to move if given a nudge by an external agent, and then it would move with constant velocity, or it would begin to move with acceleration if the gravity component exceeded the maximum static friction. If the kinetic friction were even the slightest bit less then the maximum static friction, the nudge while at maximum static equilibrium would get the object moving and then it would necessarily be accelerating. There is no fundamental reason why this has to happen.

This is a separate issue. Kinetic friction could certainly be speed dependent.

15. Nov 1, 2006

### photobillyli

Thanks for yours explanation!

Thank you!!

16. Aug 29, 2008