"End of Chapter Review Lesson" Force and Balance PPT

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"End of Chapter Review Lesson" Force and Balance PPT

Part One: Consolidation Layer Knowledge Integration

[Core Quick Fill]

1. Synthesis and decomposition of force

(1) Obey the rules: _________ rules or _________ rules.

(2) The range of the resultant force of two common point forces: _________≤F≤____________.

2. balance of common point forces

(1) Equilibrium state: The object remains in a _________ or _________ state.

(2) The equilibrium condition of common point force: _________.

End-of-chapter review lesson PPT, part 2 content: Strengthening the ability of the promotion layer

Application of synthesis and decomposition thinking methods of force

Analyze the size of the unknown force based on the known force. The analysis steps are as follows:

1. Determine the research object.

2. Conduct stress analysis on the research object.

3. When the object receives no more than three forces, the force synthesis and decomposition method is generally used:

(1) Determine the forces to be synthesized and decomposed.

(2) Determine the resultant force or component force according to the parallelogram rule.

(3) Calculate the resultant force or component force based on mathematical knowledge.

4. When an object experiences more than three forces, the orthogonal decomposition method is generally used:

(1) Establish a rectangular coordinate system so that as much force as possible falls on the coordinate axis.

(2) Decompose each force orthogonally onto the coordinate axis.

(3) Make equations along the coordinate axis according to the equilibrium conditions.

[Example 1] (Multiple choice) As shown in the figure, the mass of the heavy object is m, and the A and B ends of the light strings AO and BO are fixed. When in equilibrium, AO is horizontal, and the angle between BO and the horizontal direction is θ. The magnitude of the pulling force F1 of AO and the pulling force F2 of BO is ()

A. F1＝mgcos θB. F1＝mgcotθ

C. F2=mgsin θ D. F2＝mgsinθ

[One word to clear customs]

The synthesis and decomposition of force follow the parallelogram rule  or the triangle rule ____. When calculating, you must first make a schematic diagram of the synthesis or decomposition of force according to the parallelogram rule of force according to the requirements, and then solve the triangle based on mathematical knowledge. Mainly to solve right triangles.

Application of Holistic Method and Isolation Method in Balance

In practical problems, we often encounter several connected objects moving under the action of external forces, and we need to solve the external forces they receive or the interaction forces between them. This type of problem is called a connected body problem. Compared with solving mechanical problems of a single object, connected body problems are much more complex. The problem of connected bodies with the same acceleration is relatively simple. At present, we are limited to discussing this type of problem. There are two common solutions to connected body problems, namely the overall method and the isolation method.

1. Holistic method: A method that takes a system composed of several objects as the research object to solve. In many problems, it is more convenient to use the holistic method, but the holistic method cannot solve the internal forces of the system.

2. Isolation method: Divide the system into several parts and isolate them, use each part as the research object to conduct force analysis, list the equations separately, and then solve them jointly.

3. Selection principle: Usually when analyzing the effect of external forces on the system, the overall method is used; when analyzing the interaction between objects in the system, the isolation method is used. Sometimes when answering the same question, it is necessary to select research objects multiple times, and the holistic method and the isolation method need to be used alternately.

2. A cylindrical object A with a semicircular cross-section is placed on a rough horizontal ground parallel to the wall. A smooth sphere B is placed between A and the vertical wall. The entire device is in a stationary state. Now add a vertical downward force F to B. The line of action of F passes through the center of the sphere. Let the force of the wall on B be F1, the force of A on B be F2, and the force of the ground on A be F3. If F increases slowly and the entire device remains stationary, the cross-section is as shown in the figure, during this process ()

A. F1 remains unchanged and F3 slowly increases

B． F1 increases slowly and F3 remains unchanged

C. F2 increases slowly, F3 increases slowly

D． F2 increases slowly and F3 remains unchanged

Dynamic Analysis Problems in Equilibrium

This type of problem has a certain degree of comprehensiveness and flexibility in solving. Commonly used methods to analyze and deal with the dynamic balance of objects include: vector graphics method, function method, whole and isolation method, similar triangle method, etc. Generally speaking, for static and dynamic problems, the "vector diagramming method" is preferred, which decomposes a certain force according to its effect and constructs a schematic diagram to intuitively and vividly reflect the dependence and restriction relationships between the forces, making it simple and rapid purpose of judgment.

[One word to clear customs]

1 The analytical method is to conduct stress analysis on any state of the research object, establish a balance equation, find the general functional formula of the dependent variable and the independent variable, and then determine the change of the dependent variable based on the change of the independent variable.

2. A common method to solve dynamic balance problems is the "vector diagramming method". The basic procedure of using vector diagramming method to analyze dynamic balance problems is: conduct force analysis on several states of the research object during the dynamic change process → based on the change of a certain parameter Generally at a certain angle, draw the force balance diagram of the object in several states in the same figure The parallelogram or the triangle of the force→The length and direction of the side of the dynamic parallelogram or triangle of force change , determine the changes in the magnitude and direction of a certain force.

Critical and extreme value problems in equilibrium

1. Critical problem: When a certain physical quantity changes, it will cause changes in other physical quantities, causing the equilibrium state of the object to "just happen" or "just not happen". The most effective way to deal with this type of problem is the hypothetical reasoning method, that is, first make assumptions, then formulate equilibrium equations based on equilibrium conditions and relevant knowledge, and finally solve them.

2. Extreme value problem: It refers to the problem of the maximum and minimum values ​​of the force during the change in the equilibrium problem.

3. The following two methods are commonly used to solve this type of problem:

(1) Analytical method: Make equations based on the equilibrium conditions of the object. When solving the equations, use mathematical knowledge to find the extreme value or find the extreme value based on physical critical conditions.

(2) Graphical method: Make a force analysis diagram of the object based on the equilibrium condition of the object, draw a parallelogram or vector triangle for dynamic analysis, and determine the maximum or minimum value.

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Update Time: 2024-09-27

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