How does the decomposition of force calculate the component forc
Publish: 2021-05-02 08:22:31
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. 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. 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
3. Originally, the resultant force can be divided arbitrarily, but according to our actual situation, what kind of effect the resultant force proces depends on its effect. For example, an object that is still on an inclined plane, its gravity will proce two effects, one is to press the inclined plane, the other is to make the object have a downward trend, so it is divided according to these two directions
4. (1)
graphical method:
①
parallelogram rule: as shown in Fig. 1-8. When drawing, the action points of resultant force and component force should be the same, the ray representing force should be solid line, and the rest lines should be dashed line.
F2 = 2n
F = 5.3n
1n
F = 5.3n
F2 = 2n
F1 = 4N
Fig. 1-8
F1 = 4N
Fig. 1-9
②
triangle rule: calculate two known forces F1, F1, F1 = 4N
F1 = 4N
F1 = 4N
F1 = 4N
F1 = 4N
F1 = 4N
F1 = 4N < The resultant force of F2 can be illustrated at the end of F1, and then a directed line segment can be made from the beginning of F1 to the end of F2. The directed line segment represents the magnitude and direction of the resultant force of F1 and F2. This is the triangle rule. The resultant force can be obtained by using the triangle rule, as shown in Figure 1-9.
(2)
calculation method:
① composition of forces on the same line: when several forces are on the same line, the, Finding their resultant force can be simplified as an algebraic operation. First, the positive direction is defined, and the force in the same direction is positive. On the contrary, it is negative. When the component forces are on the same straight line and in the same direction, they are directly added, that is, f-sum =
F1 + F2; When the component forces are on the same straight line and in opposite directions, the larger force is directly used to subtract the smaller force, and the direction of the resultant force is the same as that of the great force, that is, fhe = F1-F2.
② when the component forces are perpendicular to each other, the resultant force can be obtained by Pythagorean theorem, that is, F2 =
F12 + F22, tan θ= F2 / F1.
③ composition of forces in special cases: if the two components are forces of equal size, the parallelogram drawn is a diamond. If the angle between the two components is a special angle, the two diagonals of the diamond can be used to divide each other equally, which can be summarized as a solution right triangle.
(3)
the size range of resultant force
the resultant force of two known forces varies with the angle between the two forces θ When you change θ From 0o to 180o, f = F1-F2 & lt; F & lt<
F1-F2.
7.
decomposition of force
1.
decomposition of force is the inverse operation of the composition of force.
it also follows the parallelogram rule, that is, taking the known force as the diagonal of the parallelogram, and the two adjacent sides of the parallelogram are the two components of the known force.
2.
decomposition of force
attention should be paid to the actual situation when decomposing the force, A given force can be decomposed into countless components. A force can be decomposed uniquely in the following cases: ① when the directions of two forces are known; ② when the magnitude and direction of a component are known. There are two common decomposition methods:
(1)
according to the actual effect of the force: determine the direction of two forces according to the actual effect of the force, (2)
(2)
orthogonal decomposition method: decompose a known force in the plane rectangular coordinate system along the mutually perpendicular X and Y axes. This decomposition method is called orthogonal decomposition method. It is applicable to decompose a known force in two mutually perpendicular directions. As shown in Figure 1-10, decompose f along the X and Y axes into FX = fcos θ、 Fy=Fsin θ.
3.
equivalence of resultant force and component force
when discussing resultant force and component force, great attention should be paid to their equivalence. The essence of force synthesis is to replace the effect of several forces with the effect of one (resultant force) on the premise of ensuring the same effect; The decomposition of forces is to replace the action of a force (resultant force) with the action of several forces (components) on the premise of ensuring the same effect.
just because the relationship between resultant force and component force is equivalent substitution, they cannot exist at the same time, For example, in Figure 1-11, an object on a smooth inclined plane can't add another resultant force f-joint considering its gravity g and the supporting force n of the inclined plane. If f-joint is included, the effect of F and N can't be included.
n
f-joint
G
figure 1-11
graphical method:
①
parallelogram rule: as shown in Fig. 1-8. When drawing, the action points of resultant force and component force should be the same, the ray representing force should be solid line, and the rest lines should be dashed line.
F2 = 2n
F = 5.3n
1n
F = 5.3n
F2 = 2n
F1 = 4N
Fig. 1-8
F1 = 4N
Fig. 1-9
②
triangle rule: calculate two known forces F1, F1, F1 = 4N
F1 = 4N
F1 = 4N
F1 = 4N
F1 = 4N
F1 = 4N
F1 = 4N < The resultant force of F2 can be illustrated at the end of F1, and then a directed line segment can be made from the beginning of F1 to the end of F2. The directed line segment represents the magnitude and direction of the resultant force of F1 and F2. This is the triangle rule. The resultant force can be obtained by using the triangle rule, as shown in Figure 1-9.
(2)
calculation method:
① composition of forces on the same line: when several forces are on the same line, the, Finding their resultant force can be simplified as an algebraic operation. First, the positive direction is defined, and the force in the same direction is positive. On the contrary, it is negative. When the component forces are on the same straight line and in the same direction, they are directly added, that is, f-sum =
F1 + F2; When the component forces are on the same straight line and in opposite directions, the larger force is directly used to subtract the smaller force, and the direction of the resultant force is the same as that of the great force, that is, fhe = F1-F2.
② when the component forces are perpendicular to each other, the resultant force can be obtained by Pythagorean theorem, that is, F2 =
F12 + F22, tan θ= F2 / F1.
③ composition of forces in special cases: if the two components are forces of equal size, the parallelogram drawn is a diamond. If the angle between the two components is a special angle, the two diagonals of the diamond can be used to divide each other equally, which can be summarized as a solution right triangle.
(3)
the size range of resultant force
the resultant force of two known forces varies with the angle between the two forces θ When you change θ From 0o to 180o, f = F1-F2 & lt; F & lt<
F1-F2.
7.
decomposition of force
1.
decomposition of force is the inverse operation of the composition of force.
it also follows the parallelogram rule, that is, taking the known force as the diagonal of the parallelogram, and the two adjacent sides of the parallelogram are the two components of the known force.
2.
decomposition of force
attention should be paid to the actual situation when decomposing the force, A given force can be decomposed into countless components. A force can be decomposed uniquely in the following cases: ① when the directions of two forces are known; ② when the magnitude and direction of a component are known. There are two common decomposition methods:
(1)
according to the actual effect of the force: determine the direction of two forces according to the actual effect of the force, (2)
(2)
orthogonal decomposition method: decompose a known force in the plane rectangular coordinate system along the mutually perpendicular X and Y axes. This decomposition method is called orthogonal decomposition method. It is applicable to decompose a known force in two mutually perpendicular directions. As shown in Figure 1-10, decompose f along the X and Y axes into FX = fcos θ、 Fy=Fsin θ.
3.
equivalence of resultant force and component force
when discussing resultant force and component force, great attention should be paid to their equivalence. The essence of force synthesis is to replace the effect of several forces with the effect of one (resultant force) on the premise of ensuring the same effect; The decomposition of forces is to replace the action of a force (resultant force) with the action of several forces (components) on the premise of ensuring the same effect.
just because the relationship between resultant force and component force is equivalent substitution, they cannot exist at the same time, For example, in Figure 1-11, an object on a smooth inclined plane can't add another resultant force f-joint considering its gravity g and the supporting force n of the inclined plane. If f-joint is included, the effect of F and N can't be included.
n
f-joint
G
figure 1-11
5. Vertical decomposition force
6. Originally, the resultant force can be divided arbitrarily, but according to our actual situation, what kind of effect the resultant force proces depends on its effect. For example, if an object is stationary on an inclined plane, its gravity will proce two effects, one is to press the inclined plane, the other is to make the object have a downward trend, so it is divided according to these two directions.
7. The smaller the angle between the force and the resultant force is, the larger the component force is
8. Sine theorem and cosine theorem
Hot content