How to calculate the decomposition of force

1. 1. The parallelogram rule is actually a visualized graphic representation, which is more intuitive. The parallelogram rule only plays the role of illustration, and can not be directly used to solve the problem,
2. The real method is: the parallelogram rule must combine sine theorem and cosine theorem to solve the problem
3. There are two solutions: (1) it can be calculated according to cosine theorem and sine theorem without coordinate system 2) Using coordinate system is to decompose all vectors into x component, Y component and Z component, then use algebraic method to add and subtract, and then use Pythagorean theorem to calculate
the answer needs to give the angle of vector, through arctangent calculation!

2. Because the force is a vector, the composition and decomposition of the force are carried out according to the principle of vector operation, that is, the parallelogram principle. The inverse operation of the composition and decomposition of forces is in accordance with, and the parallelogram rule: if you use two parallelograms on adjacent sides of the common point force F1 and F2 segments, then F1 f?? The magnitude and direction angle of the force F are represented by the size of the clamp Note: those who require force and contribute force are called?? For known joint efforts, forcing components is called force decomposition. The parallelogram rule of the composition and decomposition of the power of law [1]. That is to say, the problem of forced composition is composed of two adjacent parallelograms and diagonals on both sides. Diagonals are provided and decomposed by the force of two adjacent edges of the problem. 3. When the two forces are opposite, the smallest force is opposite and the largest Note: the force decomposition of parallelogram rule is based on the actual effect of force or orthogonal decomposition). Force and the combination of forces: the effect of a force can proce a force with the same result as the original force, which is called the resultant force of several forces. The resultant force seeks the combination of several forces??. 2 We can use the adjacent side parallelogram to seek the common stress point. The size and direction of the resultant force of the two forces of the two corner segments can be represented by the diagonal of the parallelogram. The magnitude of the two forces F1, F2, F of the common point, and the angle?? degree θ 0≤ θ ≤ π The correlation is large, θ， And force the smaller; θ When the forces F1 and F2 in the same direction are in the range of the lowest resultant force of the reverse force, F1-F2 | ≤ f ≤ (F1 + F2) work together. Within the range of the positive force, they force their maximum force in the same direction, that is, the lowest value of their algebraic sum? It can be divided into the following two cases: ① if the maximum force of n is greater than the algebraic sum of other forces, they force the minimum to be the maximum force and other forces, algebra and differential (at this point, all forces in a straight line, and the direction of the maximum force and other forces are opposite)

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tan^2(α)
1=sec^2(α)
cot^2(α)
1=csc^2(α)
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β)/2]cos[(α-β)/2]
cos α-cosβ=-2sin[(α
β)/2]sin[(α-β)/2]

4. The decomposition of a force is the inverse operation of the composition of a force, which also follows the parallelogram rule: if a known force is regarded as the diagonal of a parallelogram, then the two adjacent sides of the parallelogram which are at the same point with the known force represent the two components of the known force. However, if there are no other restrictions, for the same diagonal, you can make countless different parallelograms. For this reason, when decomposing a force, the following two ways can be used: 1) decomposing according to the actual effect of the force -- first, determine the direction of the component force according to the actual effect of the force, and then calculate the size of the component force according to the parallelogram rule. ② According to the "orthogonal decomposition method", the rectangular coordinate system is selected reasonably, and then the known force is projected onto the coordinate axis to obtain its two components. As for the second decomposition method, here we focus on several typical problems of decomposing the force according to the actual effect: decomposing the oblique upward pulling force on the object placed on the horizontal plane, placing the object on the spring platform scale, paying attention to the indication of the spring platform scale, then applying a horizontal pulling force, and slowly deflecting the direction of the pulling force from the horizontal direction, the indication of the platform scale graally decreases, It shows that the pulling force not only has the effect of pulling the object forward horizontally, but also has the effect of lifting the object upward vertically. Therefore, the oblique upward pulling force can be decomposed along the horizontal forward and vertical upward directions. As shown in the decomposition of gravity on the inclined plane, when a layer of sponge is laid on the inclined plane and a cylindrical weight is placed, it can be observed that when the weight rolls down, it can also make the sponge deform and have pressure effect, which explains why the gravity is decomposed into two components F1 and F2. The research object of orthogonal decomposition method is subject to many forces. There are many ways to analyze it. I think orthogonal decomposition method is a good method. Although it is cumbersome to use it for simple problems, it is better to use orthogonal decomposition method for beginners (commonly used in high school). Can deal with a large number of mechanical problems, after more skilled, natural other methods will also be. The orthogonal decomposition method is used to calculate the resultant force when the object is subjected to multiple forces. Each force can be decomposed in two mutually perpendicular directions, and then the resultant force can be calculated in these two directions. The orthogonal decomposition method is the basic method to deal with the problems of multiple forces. It is worth noting that when choosing the direction, the force on the axis should be as much as possible; As far as possible, the decomposed force is known. The steps are as follows: 1) select the right angle coordinate system correctly, generally select the action point of the common point force as the origin, the horizontal direction or the acceleration direction of the object movement as the X axis, so as to make as many forces as possible on the coordinate axis. ② Orthogonal decomposition of the forces, that is, each force is projected on the coordinate axis, and the resultant force of each force projection on the coordinate axis is obtained. FX = f1x + f2x +... + fnx FY = F1y + f2y +... + fny ③ the size of the resultant force of the common point force is f = √ FX2 + √ FY2 (the square of FX under the root sign plus the square of FY under the root sign), the direction of the resultant force and the angle between the X axis and the direction of the resultant force are tan = FY / FX (that is, the value of Tan is calculated, and then the degree of K is obtained by comparing with the known value of Tan), The dynamic friction coefficient is 0.5. Find the magnitude of F and the solution of acceleration: F1 = sin37 * F, F2 = cos37 * F= μ N = 0.5 * (g-sin37 * f) f = f2-f = m * a, a = (cos37 * F - (0.5 * (g-sin37 * f)) / (g / g) note; Gravity decomposition sliding force on inclined plane = mg · sin angle positive pressure = mg · cos angle

5. Check out the mechanics section of physics book

6.

The resolution of a force transforms a force into two or more equivalent components. The basis of decomposition is the parallelogram rule of force (see the axiom of statics). In general, this problem can have innumerable solutions. Only when sufficient conditions are attached, can the definite solution be obtained

The decomposition of a force is the inverse operation of the composition of forces, which also follows the parallelogram rule (triangle rule, rarely used): if a known force is regarded as the diagonal of a parallelogram, then the two adjacent sides of the parallelogram which are at the same point with the known force represent the two components of the known force. However, if there are no other restrictions, for the same diagonal, you can make countless different parallelograms

For this reason, when decomposing a force, the following two ways can be used:

① decomposing according to the actual effect of the force -- first determine the direction of the component force according to the actual effect of the force, and then calculate the size of the component force according to the parallelogram rule

(2) according to the "orthogonal decomposition method", the rectangular coordinate system is selected reasonably, and then the known force is projected onto the coordinate axis to obtain its two components

for the second decomposition method, we will focus on several typical problems of decomposing the force according to the actual effect: decomposing the oblique upward tension on the object placed on the horizontal plane, placing the object on the spring platform scale, paying attention to the indication of the spring platform scale, then applying a horizontal tension, and slowly deflecting the direction of the tension upward from the horizontal direction, The indication of the platform scale graally decreases, which indicates that the pulling force not only has the effect of pulling the object horizontally forward, but also has the effect of lifting the object vertically upward. Therefore, the oblique upward pulling force can be decomposed along the horizontal forward and vertical upward directions. As shown in the decomposition of gravity on the inclined plane, when a layer of sponge is laid on the inclined plane and a cylindrical weight is placed, it can be observed that when the weight rolls down, it can also make the sponge deform and have pressure effect, which explains why the gravity is decomposed into two components F1 and F2

7. The decomposition of force is the inverse budget of the synthesis of force, which is to find two components of a known force. When the known force is decomposed, the direction of the two components is determined according to the effect of the force. On the basis of the previous section of the synthesis of force, students will master the operation law quickly, but the difficulty is how to decompose the force according to the effect of the force, Two cases are listed in the textbook for analysis, one is the decomposition of the object on the horizontal plane under oblique tension, the other is the decomposition of the gravity received by the object on the inclined plane, which has a typical example function. Teachers should pay attention to the detailed analysis from the following aspects when explaining:
1. The description of the characteristics of the resultant force, such as several key descriptive sentences in example 1: horizontal plane, oblique upward, vertical direction The pull force is at an angle with the horizontal direction. There is no need to discuss the gravity, the elastic force and the friction force of the ground to the object for the time being, so as not to distract the students.

2. The component effect of the resultant force can let the students start from the daily phenomenon (as shown in the figure below), First, the wooden pole is pressed against the wall. The teacher can let the students use the pencil and rubber band instead of the wall to experience the two sub effects of pencil gravity.

3. The calculation and writing of component force are standard. During the calculation, the teacher can tell the students some knowledge about sine and cosine in advance.

2 Suggestions on the teaching method of orthogonal decomposition of force:

orthogonal decomposition of force is a relatively simple method to solve resultant force, which actually decomposes forces into two mutually perpendicular directions by using the principle of decomposition of force, Then it becomes the problem of the composition of forces on the same straight line, which makes the calculation simple. Since students are not exposed to the concept of mapping in junior high school, when teachers explain this part, they should first start with the right angle decomposition, especially when analyzing the force balance of static objects on the inclined plane, and roughly introce the concept of orthogonal decomposition

8. The decomposition of force is the inverse budget of the synthesis of force, which is to find two components of a known force. When the known force is decomposed, the direction of the two components is determined according to the effect of the force. On the basis of the previous section of the synthesis of force, students will master the operation law quickly, but the difficulty is how to decompose the force according to the effect of the force, Two cases are listed in the textbook for analysis. One is the decomposition of the oblique pull on the horizontal plane, and the other is the decomposition of the gravity received by the object on the inclined plane, which is a typical example. The teacher should pay attention to the detailed analysis from the following aspects when explaining: 1. The description of the characteristics of the resultant force, such as several key descriptive sentences in example 1: horizontal plane, oblique upward, pull, It is not necessary to discuss the gravity and the elastic force and friction force of the ground to the object for the time being, so as not to distract the students. 2. The component effect of the resultant force can let the students start from the daily phenomenon (as shown in the figure below). Because of the gravity of the object, there are two force effects, one is that the rubber band is stretched, the other is that the wooden pole is pressed against the wall, Teachers can let students use pencil and rubber band instead of wall to experience the two effects of pencil gravity. 3. The writing standard of component force calculation. In the calculation, we can tell students some knowledge about sine and cosine in advance. 2. Teaching method of orthogonal decomposition of force: orthogonal decomposition of force is a relatively simple method to solve resultant force, In fact, it uses the principle of force decomposition to decompose the forces into two mutually perpendicular directions, and then it becomes the problem of the composition of forces on the same straight line. It makes the calculation simple. Since students are not exposed to the concept of mapping in junior high school, teachers should start with the right angle decomposition when explaining this part, Especially in the analysis of force balance of static body on inclined plane, the concept of orthogonal decomposition is introced