"Optimization Summary of this Chapter" Force and Balance PPT

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"Optimization Summary of this Chapter" Force and Balance PPT

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"Optimization Summary of this Chapter" Force and Balance PPT

Integration and improvement

Common equilibrium models of objects

1. "Light rope" model: The light rope can only stretch and deform, so it can only produce pulling force. The direction is always pointing in the direction of rope contraction, and the internal tension of the rope is equal everywhere.

2. "Pulley" model: The pulley model usually refers to the combination of a pulley and a light rope. The friction between the pulley and the light rope is ignored. At this time, the pulling force of the rope on both sides of the pulley is equal.

3. "Node" model: "Nodes" are often connected to heavy objects. The forces acting on the nodes are not necessarily equal, but the resultant force of all forces must be zero.

4. "Slip ring" model: The slip ring can exert tensile force and also bear pressure. The direction of the force is along the radial direction of the slip ring.

5. "Light spring" model: A light spring can not only undergo tensile deformation, but also compressive deformation, so a light spring can generate both tension and pressure, and the elastic force inside the spring is equal everywhere. The direction of the elastic force is always along the axis of the spring. Within the elastic limit, the magnitude of the elastic force is F=kx.

6. "Light rod" model: The light rod can not only undergo tensile deformation, but also compressive deformation, so the light rod can not only exert tension but also withstand pressure, and the elastic force is equal everywhere in the rod. Light rods can also undergo bending deformation, so the elastic force of the rod is not necessarily along the direction of the rod.

(1) "Dead rod" type

A "dead rod" means that the light rod cannot rotate, and the elastic force it generates is not necessarily along the direction of the rod. Its magnitude and direction must be solved according to equilibrium conditions.

(2) "Living rod" type

A "living rod" is a light rod that can rotate around a smooth axis. The elastic force it generates must be along the direction of the rod (otherwise the rod will rotate). The size of the elastic force is solved according to the equilibrium condition.

Mathematical methods commonly used in solving equilibrium problems

Convert rhombus to right triangle method

If the two components of the force are equal in magnitude, then the parallelogram made with the two components as adjacent sides is a rhombus, and the two diagonals of the rhombus are perpendicular to each other. The rhombus can be divided into four identical right-angled triangles, so the rhombus is transformed into right triangle

Orthogonal decomposition method

The equilibrium condition (F=0) of an object under the action of a common point force is a vector equation. To find the resultant force, you need to apply the parallelogram rule, which is quite troublesome. Usually transformed into Fx=0, Fy=0 using orthogonal decomposition method

similar triangle method

If the force triangle is similar to the geometric triangle during the operation of the force using the parallelogram rule (or the triangle rule), the solution can be solved based on properties such as the proportion of the corresponding sides of similar triangles.

Selection and application of holistic method and isolation method

The overall method and the isolation method are two commonly used methods for force analysis of objects. The comparison of these two methods is as follows:

1. Steps to solve problems using isolation method

In order to study the force and motion of an object in the system (connected body), the isolation method is generally adopted. The basic steps are:

(1) Clarify the research object, process or status;

(2) Isolate a certain research object or a certain movement process from the entire process;

(3) Draw a force analysis diagram or motion diagram of an object in a certain state;

(4) Select appropriate physical laws to solve equations.

2. Steps to solve problems using the holistic approach

The whole and the part are relative. The part becomes the whole in a larger scope, and the whole becomes a part in a smaller scope. The key lies in how to define the scope of the whole and the part when dealing with specific problems.

When it only involves studying the system without involving the forces and motions of certain objects within the system, the overall method can generally be used. Its basic steps are:

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