what friction force will the box begin to slide
When the surfaces of ii solid objects rub together, they tend to stick, opposing the rubbing. In our Newtonian framework, we interpret such an influence on the motion of the ii objects as a forcefulness. In order to be able to utilize this force, we need to sympathise how this strength behaves and what affects how big it is.
The phenomenology of friction
Physics (Wiley, 2003) permission requested.
To become an idea of how friction behaves, let's consider a simple experiment. Let'south hook a strength probe up to a block sitting on a table and slowly increase how hard we pull. The data from the forcefulness probe tin so exist displayed in LoggerPro™ and we can get a first thought of how the force of friction behaves. At first, even though we are pulling, the block doesn't move. As we increase our pull, it somewhen breaks abroad and starts to slide. We then pull to keep information technology going at almost a abiding speed. The graph of the strength is shown below.
Physics (Wiley, 2003) permission requested.
This is rather strange beliefs, but we can begin to make sense of information technology if we consider a costless body diagram of the block. The block is existence pulled to the right by the tension strength of the string (which we assume is the same as the force being measured past the strength probe on the other finish of the cord — encounter the discussion of massless strings in Tension Forces). When information technology is not moving, the forces on information technology must be balanced, and so the strength we are measuring should be equal and opposite to the friction force exerted on the box by the table (past Newton 2). When it is moving at a abiding velocity, the aforementioned matter must be true, since the box is not accelerating. The free-trunk diagram volition look like this, with the friction and tension forces equal in magnitude:
The cake only accelerates for a very short flow of time — say from nigh 32 s to 33 due south on the graph. At this fourth dimension, the forcefulness shown on the force probe must be greater than the forcefulness of friction — to speed the object up.
This is a tricky and surprising result! The force of friction doesn't seem to have a stock-still value, but seems instead to adapt to a maximum value in response to a forcefulness trying to slide the one object over the other, and and so, once the sliding starts, to driblet down to a lower value! The fact that the friction strength is not just determined by the position of the object but by what is beingness done to information technology, is a dangerous bend. Nosotros identify these two different forces with dissimilar names.
- The maximum value the friction forcefulness can have when the objects are NOT sliding is called the strength of static friction .
- The value the friction forcefulness has when the two surfaces are sliding over each other is called the force of kinetic friction.
The mechanism of friction
Finding out the phenomenology of friction from observing how it behaves is one affair. But we would similar to make sense of what's happening. Why should it behave like that? In order to understand what's going on, let's attempt to figure out some mechanism that might exist responsible for this behavior.
In fact, the underlying machinery of friction is quite complex and inquiry on the topic is notwithstanding going on today. If we think about two surfaces trying to rub on each other, and imagine looking at the surfaces through a microscope, we might guess that there are 2 basic phenomena that are happening: molecular attractions and interlocking of rough edges.
Molecular attractions
We know from chemistry that atoms concenter each other when they are close enough (just not too shut) by Van der Waals forces. Some of our friction could come up from the atoms in the surfaces of the two objects attracting each other. That this does happen is shown by the phenomenon of Johansson (gauge) Blocks. These are metal blocks that are polished to be and so smoothen that when their surfaces are slid together they stick quite strongly. But the surfaces have to be polished polish to a fare-thee-well to make this happen and they have to exist made of the same material. This suggests that something else is happening in ordinary friction.
Interlocking of rough edges
Since we know that typically smoothing surfaces produces LESS friction rather than more, nosotros might imagine that each surface has trivial bumps that get tangled up with the bumps on the other surface. The key thought hither is a sideways (shear) spring. Our simple motion picture of an extension-compression spring can be extended easily to a spring that bends sideways as shown in the moving picture below. Imagine a thin metal cobweb that has one end imbedded in a block of woods. If I press sideways on the top of the fiber, it will bend as shown. The more than I press, the more than it volition bend; like a spring, but sideways.
Now suppose our ii surfaces that are experiencing friction take lots of little protuberances similar this that can bend. This is shown in the figure below.
Nosotros've assumed that these tin be two different substances, and then nosotros've colored one blood-red, the other bluish. On the left, nosotros show the objects just sitting on each other. There is no sideways force. On the right nosotros prove some force applied to slide the top object to the right and the bottom object to the left. The little rough edges from the two objects now meet each other and try to bend each other. As the little protuberances curve in response to the applied force, they begin to exert a force back, but like a leap. The effect volition exist that there volition be a tiny shift in the relative position of the two objects (these piffling fingers are microscopic), but the two objects will exert a force dorsum on each other that opposes the force that is trying to slide the surfaces over each other. This will provide the static friction forcefulness that opposes the object's move.
If the applied strength gets large enough, the little irregularities will slide over each other and the objects will begin to move. The force of the occasional interfacing of the fingers volition provide the kinetic friction force that resists the object's motion when it is actually moving (macroscopically).
This model gives a reasonable mechanism for the funny behavior of the friction force -- the fact that it starts at 0, so builds upwards to friction match an applied strength, and finally drops down to a constant value as the objects slide over each other.
The equations of friction
We tin can set up an experiment to measure how the friction force depends on diverse situations equally shown in the effigy at the right. Of form nosotros would use a forcefulness probe to pull the blue cake in order to measure the force between the red surface and the bluish surface. (What does the FBD for the blue block expect similar?) Hither'south what is establish:
- The maximum static friction strength (force that the surfaces tin can exert on each other before the block starts to move) is directly proportional to the Normal strength squeezing the 2 surfaces together.
- The proportionality abiding depends on the two surfaces.
- The maximum static friction force does NOT depend on the area of the surfaces in contact.
- The maximum static friction force is greater than the kinetic friction force (friction while sliding).
These results are summarized in the equations for friction below. The symbols "μ" are chosen the coefficients of friction .
$$F^{static friction}_{A \rightarrow B} \le \mu^S_{AB} N_{A \rightarrow B}$$
$$F^{kinetic friction}_{A \rightarrow B} = \mu^K_{AB} N_{A \rightarrow B}$$
$$ \mu^S_{AB} \ge \mu^K_{AB}$$
These equation are quite complex and code for a lot of conceptual information almost friction. See explicitly how this works in the follow-on, Reading the content in the friction equations.
Workout: Friction
Source: https://www.compadre.org/nexusph/course/Friction
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