How to calculate the friction between the cylinder and the rope

1. road down the mountain, is really a kind

2.

Sinai's world of wild hope: the attachment of the complete works of Bimeng's novels has been uploaded to the Internet disk, Click to download for free:
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the wild world of Sinai bumeng
Author: Mengzhai
Chapter 1: your first meeting with me
update time: 2012-7-9 16:19:33 words: 3128
What do you need, I don't know what needs me, but...
I don't like this feeling...
the bustling Jing Town, standing alone in the smoke of troubled times, even the most authoritative place, has to be controlled by the most powerful princes recently, which is why all the princes are eager to go to Luoyang
the idea of holding the emperor to order the princes has been conveyed in another continent more than 1000 years ago
"..."
today's weather is just the right wind. There is always a peaceful place in the noisy center. There is an open space outside the solemn shrine, which is inaccessible to ordinary people. Only a little girl is flying a kite quietly
if you capture the plain expression carefully, you can detect a trace of happiness
I don't know what the bondage is, but temporary relief can have such an expression
"..."
after all, the young arm still failed to grasp the strength, and the kite graally flew away
she was unwilling to pace slowly. The girl knew that such leisure time was not easy to earn, so she quickened her pace and ran to the destination< br/>“……”
after confirming the location of the kite, the girl was surprised and hesitant
a wisp of light blue long hair scattered, close to the transparent blue, languidly fell on the tree branch, so that the girl can't help but look at it
"..."
her little face was slightly red, but she did not forget to stare at the paper kite on the unknown person
it seems that she is sleeping deeply, and the girl doesn't know why she doesn't want to speak. Instead, she stands in the same place and seems to be using something
once, twice
the tree branches fell continuously on the sleeping person's face, but they didn't react much. The girl's forehead trembled slightly< br/>“……”……
I need to ask you something else

3. Chapter 2 Newton's law

I. main content

this chapter includes the concept and calculation method of force, the concept and calculation of gravity, elastic force and friction force, Newton's law of motion, the concept and law of object balance, weightlessness and overweight. The key content is the application of gravity, elastic force and friction force in Newton's second law, which requires students to be able to establish a correct "relationship between motion and force". Therefore, a deep understanding of Newton's first law is the basis of solving specific physical problems with Newton's second law in this chapter< The basic methods involved in this chapter are: the parallelogram rule of the decomposition and composition of forces, which is the general rule of the addition and subtraction of all vectors; When using Newton's second law to solve specific practical problems, it is often necessary to isolate an object from many other objects for force analysis. The isolation method is the basis of analyzing the force situation of objects, and the analysis of the force situation of objects is the basis of applying Newton's second law. Therefore, this method of isolating an isolated object from complex objects for research is very important in this chapter< In the process of knowledge application in this chapter, the mistakes that beginners often make are as follows: they can't correctly analyze the force on objects, and the reasons usually appear in the analysis and calculation of elastic force and friction force, especially the analysis of friction force (especially static friction force); For example, when using Newton's second law and kinematic formula to solve problems, it often shows the error of positive and negative sign when using vector formula to calculate. The essential reason is that the relationship between motion and force can not be correctly grasped, and the object will move in that direction if it is mistakenly thought that the object is subject to external force in any direction

example 1 A and B play tug of war hand in hand, and in the end, a wins and B loses, so which one of them is more affected

[wrong explanation] because a is better than B, the pull of a to B is greater than that of B to a. Just like tug of war, Party A's victory must be e to Party A's great pull on Party B

[causes of misinterpretation] the causes of the above misinterpretation are students' subjective imagination rather than analyzing problems according to physical laws. According to the laws of physics, we know that the motion state of an object is not determined by which force, but by the combined external force. The reason why a wins B is that a is affected by external forces. According to Newton's third law, the pulling force between a and B is the interaction force. The pulling force between a and B is the same

[analytical solution] the pulling force between a and B is the interaction force. According to Newton's third law, the force is equal in size and opposite in direction, acting on a and B

[comment and analysis] some feelings in life are not always correct. We can't use the experience and feelings in life as laws. We should use physical laws to solve problems

example 2 is shown in Figure 2-1. A block of wood is placed on a horizontal table, and it is subjected to three forces in the horizontal direction, F1, F2 and friction, and is in a static state. Where F1 = 10N, F2 = 2n. If the force F1 is removed, the combined external force on the block in the horizontal direction is ()

a.10n to the left, b.6n to the right, c.2n to the left, d.0

[misinterpretation] the block remains static under the action of three forces. When F1 is removed, the resultant force of the other two forces is equal to the removal force, but the direction is opposite. So a is correct

[cause of misinterpretation] the reason for the above misinterpretation is the result of the conclusion that "the object is in equilibrium under the action of several forces, if one force is removed at a certain time, the resultant force of other forces is equal to the force removed, and the direction is opposite to that of the force". In fact, there is a prerequisite for this law to be true, that is, one of the forces is removed, while the other forces remain unchanged. After F1 is removed from this question, the conclusion does not hold because the friction force changes

[analytical solution] because the wood block is in a static state, the friction force is static. According to Newton's law, f1-f2-f = 0, and the static friction force is 8N to the left. When F1 is removed, the horizontal direction of the block is forced by 2n to the left, and it tends to move to the left. Because F2 is less than the maximum static friction, the friction is still static friction. In this case - F2 + F ′ = 0 means that the resultant force is zero. So option D is correct

[comment and analysis] the problem of friction is mainly used to analyze the motion trend and relative motion of objects. The so-called motion trend is generally interpreted as the state that an object has not yet moved. Motionless is e to the existence of static friction, which hinders the relative motion and makes the relative motion between objects show a trend. The way to determine the direction of the motion trend is to assume that there is no static friction and judge which direction the object moves in, which is the direction of the motion trend. If the static friction is removed and there is no relative motion, there will be no relative motion trend and the static friction will not exist

example 3 as shown in Figure 2-2, an object m is placed on a long rough board placed horizontally. When it is used to lift one end slowly, how will the pressure and friction force on the board change

[wrong solution] the object on the board is taken as the research object. Objects are subject to gravity, friction and supporting force. Because the object is still, according to Newton's second law, there is a wrong solution 1: according to formula 2 θ F increases< Wrong solution 2: there is another wrong solution, that is, according to formula 2 θ When n increases, f decreases= μ N indicates that f decreases

[reason for misinterpretation] both misinterpretation 1 and misinterpretation 2 failed to fully understand the whole process of slowly lifting the board. Only one side is grasped, and the analysis of physical situation is lacking. If we can start from the static wood block relative to the board, we can find out that if we raise it again, it will slide relatively, which will avoid the wrong solution. If you think of F= μ If n is the criterion of sliding friction, we should consider what happened before sliding, so as to avoid Missolving the second problem

[analytical solution] take the object as the research object, as shown in Figure 2-3. The object is subject to gravity, friction and supporting force. In the process of slowly lifting, the object first stands still and then slides. At rest, according to the solution in wrong solution 1, we can see that θ The static friction increases with the increase of temperature. When an object slides on an inclined plane, it can be solved in the same way as in the second solution= μ N. By analyzing the change of N, we know the change of f-slip. θ The sliding friction decreases with the increase of friction. In the whole process of slowly lifting, the equation relationship in Y direction remains unchanged. According to the misinterpretation of Chinese formula (2), we know that the pressure has been decreasing. Therefore, in the process of lifting the board, the change of friction first increases and then decreases. The pressure keeps decreasing

[comment and analysis] there are some changing processes in physical problems, which are not monotonic. It can be regarded as a kind of problem in the balance problem. This kind of problem should focus on the relationship between variables and invariants. We can start from the force analysis, find the relationship by using the balance equation, or solve the problem with the vector triangle rule by using the diagram. When the object is not sliding, it is in equilibrium and the acceleration is zero. The three forces acting on it form a closed triangle. As shown in Figure 2-4. Similar problems are shown in Fig. 2-5. When a ball is hung on a smooth wall with a rope, how will the tension of the rope and the pressure of the ball on the wall change when the rope becomes shorter. It is not difficult to see from the corresponding vector triangle figure 2-6 that when the rope becomes shorter, θ As the angle increases, n increases and t increases. Figure 2-7 hang a weight g on the AC rope, tie a rope Bo at the middle o point of the AC rope, pull the rope Bo with the horizontal force F, keep the Ao direction unchanged, and make the Bo rope move up slowly along the direction indicated by the dotted line. During this process, what is the change of force F and tension on AO rope? Using the vector triangle (as shown in Figure 2-8), we can see that t becomes smaller and f becomes smaller first and then larger. This kind of problem is characterized by the balance of three common forces. Usually, the size and direction of one force remain unchanged, the direction of the other force remains unchanged, the size changes, and the size and direction of the third force change. Sometimes the size and direction of one force remain unchanged, the size and direction of the other force remain unchanged, and the size and direction of the third force change

example 4, as shown in Figure 2-9, the object is still on the inclined plane. Now the horizontal external force F is used to push the object. In the process of graal increase of external force F from zero, the object always remains static. How does the friction force on the object change

[wrong solution] wrong solution 1: take the object on the inclined plane as the research object, and the force on the object is shown in Figure 2-10. The object is subject to gravity mg, thrust F, supporting force N, and static friction F. since the thrust f is horizontally to the right, the object tends to move upward, and the direction of friction f is downward along the inclined plane. According to Newton's second law, the equation

F + mgsin is formulated θ= Fcos θ ①

N-Fsin θ- mgcos θ= (2)

it can be seen from formula (1) that f increases and f also increases. So the friction increases in the process of change< Some students think that if the direction of friction is upward along the inclined plane, f will increase and friction will decrease

[reason for misinterpretation] the reason for the above misinterpretation is that the static friction is not clearly understood, so the change of friction in the process of external force change cannot be analyzed< The key of this problem is to determine the direction of friction. Due to the change of the external force, the movement trend of the object on the inclined plane changes, as shown in Figure 2-10 θ＜ mgsin θ The object tends to move downward, and the direction of friction is upward along the slope. F increases and f decreases. It's the same as misinterpretation two. As shown in Figure 2-11, when the external force is large (fcos) θ＞ mgsin θ The object tends to move upward, the direction of friction is downward along the inclined plane, the external force increases, and the friction increases. When fcos θ= mgsin θ The friction is zero. Therefore, in the process of increasing the external force from zero, the change of friction first decreases and then increases

[analysis] if the object on the inclined plane slides down along the inclined plane, the mass is m, and the friction coefficient between the object and the inclined plane is m μ， We can consider two problems to consolidate the previous analysis method

(1) when f is what value, the object will remain stationary

(2) when f is what value, the object starts to move along the inclined plane with acceleration a from rest

inspired by the previous question, we can think that the value of F should be a range

firstly, the object is taken as the research object. When f is small, as shown in Figure 2-10, the object is subjected to gravity mg, supporting force N, oblique upward friction F and F. When the body is just at rest, it should be the boundary value of F, and the friction force is the maximum static friction force, which can be approximately regarded as the static friction force of F= μ According to Newton's second law, the equation

is formulated. When f starts to increase from this value, the direction of static friction is still inclined upward, but the size decreases. When f increases to fcos, the direction of static friction is still inclined upward θ= mgsin θ F = mg · TG θ When f increases again, the direction of friction is changed to oblique downward, and the equation

can still be listed according to the stress analysis figure 2-11. With the increase of F, the static friction increases, and the maximum value of F corresponds to the maximum static friction of oblique downward

to make the object stationary, the value of F should be

as for the second question, the reader should be reminded that it is not proposed to move upward or downward with acceleration a in the question, and two solutions should be considered. The solution is not detailed here, and the answer is given for reference

example 5 is shown in Figure 2-12

4. First, static friction or sliding friction
sliding friction: F= μ F (F is positive pressure)
if it is static friction, it is usually solved by force balance
if you need to ask, I can give you an example.

5. Tension, a physics term. When a body is under tension, the mutual traction force existing in its interior and perpendicular to the contact surface of two adjacent parts
the force exerted by the stretched string, rope and other flexible objects on other stretched objects, or the force between the internal parts of the stretched flexible objects. For example, a rope AB can be regarded as AC and CB, where C is any cross section of the rope AB, and the interaction force between AC and CB is tension. The tension per unit area on the cross section of the rope is called tensile stress.

7. In daily life and labor proction, people have long found that when a rope is wound on a cylinder (such as a stake, a tree trunk, a telegraph pole), it can often proce a lot of static friction when there is a relative movement trend, so people often tie very strong livestock (cattle, horses) to the stake, and they are difficult to break free from its shackles; If there is a large ship berthing at the wharf, people always wind the rope around the tie pile for several times, and then nail the free end of the rope to the ground, or pull the rope head by one person to tie the large ship

the friction in static friction is called static friction. When the tangential force increases graally but the two objects remain relatively static, the static friction increases with the increase of the tangential force, but the increase of the static friction can only reach a certain maximum. When the tangential force is larger than the maximum value, the two objects will move from relative static to relative sliding. This maximum value of static friction is called "maximum static friction"

this limit friction is expressed in Fmax. The maximum static friction is directly proportional to the positive pressure n between the contact surfaces of two objects, that is, F= μ N denotes the maximum static friction force by F, and n denotes the positive pressure, where the proportional constant μ It's called static friction coefficient. It's a value with no unit. μ It is related to the material of contact surface, smooth roughness, dry and wet conditions, but not to the size of contact surface. 1. The magnitude of sliding friction is related to the material and surface smoothness of the objects in contact with each other; It is related to the positive pressure between objects; Note the explanation of positive pressure. 2. The sliding friction force can be calculated by the formula F= μ N. Dynamic friction coefficient μ In fact, when the surface of two objects is very rough, the dynamic friction coefficient will be very large e to the staggered engagement on the contact surface; For a very smooth surface, especially a very clean surface, because molecular force plays a major role, the dynamic friction coefficient is greater. The smoother the surface is, the greater the dynamic friction coefficient is. However, in mechanics, it is often said that "the surface of an object is smooth". This is a formulation that ignores the friction force between objects. In fact, it is an idealized model, which has nothing to do with the above description The dynamic friction coefficient u is a physical quantity without unit, which can directly affect the motion state and force condition of the object. 4. The magnitude of static friction increases with the increase of external force and is equal to the magnitude of external force. But the static friction can not be increased infinitely, but there is a maximum value. When the external force exceeds the maximum value, the object will start to slide. The maximum static friction is called the maximum static friction Fmax. 5. The direction of static friction is always tangent to the contact surface, and opposite to the direction of the relative motion trend of the object.

8. First of all, you need to consider the original state of the object, static or moving, where the moving trend is, and then analyze the force. We should analyze specific problems.

9. The balance of force! N = 2F, left. In this way, the external force on the cylinder can be zero
How can it be f / R? The dimension (or the unit of physical quantity) is wrong
the pressure distribution on the cylindrical surface is relatively complex, but the sum of all the small pressures n on the parts of the cylinder in contact with the rope can be easily obtained from the analysis that the external force is 0< It suddenly occurred to me that what you want is not the elastic force, but the linear density N on the semicircle of the elastic force along the circumference of the cylinder
the tension of the rope is equal everywhere, and the cylinder should be assumed to be smooth, so that n everywhere points out of the column along the radial direction, and the size of N everywhere is the same
take the vertical upward ray passing through the axis as the polar axis and the counterclockwise direction as the positive direction of the angle< br /> θ The elastic force on a small cylinder near the corner is n * r * D θ， Its horizontal component is n * r * D θ* sin θ， The sum of them is n
(the lower limit and upper limit of the following integral are 0 and 0 respectively π N=∫n*R*d θ* sin θ= nR∫sin θ d θ= nR∫d(-cos θ)= nR[(-cos π)-(- Cos0)] = 2nr, n = 2F, so n = f / R.