What's the friction between the object above and the object a
Publish: 2021-05-24 13:49:31
1. You can't withdraw money, can you? help
2. Kudos is honor; fame and prestige; Praise for his work
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
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. There can also be friction between two relatively static objects - static friction
friction generally has two situations: dynamic friction and static friction
If equal motion occurs between two objects, then the force hindering their relative motion is called dynamic friction
If two objects remain static, but there is a relative motion trend, There will also be friction, which is called static friction
for example: "push a table on the ground, but do not push it". In this event, the table and the ground are relatively static, but there will be static friction between them!
friction generally has two situations: dynamic friction and static friction
If equal motion occurs between two objects, then the force hindering their relative motion is called dynamic friction
If two objects remain static, but there is a relative motion trend, There will also be friction, which is called static friction
for example: "push a table on the ground, but do not push it". In this event, the table and the ground are relatively static, but there will be static friction between them!
5. Limit it
6. First of all, it depends on the way it moves, whether it accelerates, decelerates or moves at a constant speed. If it accelerates, it has nothing to do with others. Use F= μ FN to find the maximum static friction force, or use f = Ma to find the sum of external forces, and then use orthogonal decomposition (see topic conditions). If the velocity is uniform, then the force in the same direction after orthogonal is equal, or use f = Ma to find the sum of external forces= μ If the method of decelerating is basically the same as that of accelerating, there are some differences in the addition and subtraction after decomposition Note: maximum static friction ≈ sliding friction]
7. At present, China does not allow other digital currencies, and there is no security of digital currency.
8. Introction: Xi'an Municipal Center for Disease Control and prevention, based on the unified requirements of the Ministry of health on the implementation of the reform of health supervision system, was established by the Xi'an municipal government and the editorial board of the city on the basis of Xi'an municipal health and epidemic prevention station, Xi'an Endemic Disease Control Institute, Xi'an tuberculosis control center and Xi'an STD monitoring center, and was formally established in September 30, 2002. It was officially put into operation on November 4, 2002. The CDC is located at 599 Xiying Road, the site of the former municipal epidemic prevention station, covering an area of 11360 square meters, with a construction area of 10000 square meters, of which the laboratory area is about 5000 square meters. The office building of the center (located at 599 Xiying Road, opposite to the Party School of Xi'an municipal Party committee) and the office building of preventive medicine outpatient department (located at 2 Baimiao Road, Xi'an)
registered capital: RMB 106.0842 million
registered capital: RMB 106.0842 million
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