The nature of spring and the problem of spring connection body

As a typical elastic force model, springs have the following properties: springs can withstand both pressure and tension; because springs usually do not consider mass,

The elastic force is equal; the elastic force of the spring factory is related to the deformation, and the change of the deformation takes time, so the elastic force cannot be changed suddenly.

Spring connector refers to a group of objects connected by a spiral spring. There are many spring connector problems that can be solved directly by the nature and characteristics of the spring model

, the following is an example.

Example 1. A mass point with a mass of m is connected to three identical spiral light springs. When at rest, the angle between adjacent springs is 120°, as shown in Figure 1. Known bullets

The force of spring a and b on the mass point is F, then the force of spring C on the mass point may be: []

A.F B.F+mg

C.F-mg D.mg+F

Analysis: Spring a, b may be in the extended state or in the compressed state, and the direction of the elastic force is different in different states. The same spring C has two possibilities

state.

When a and b are in the extended state, the combined force of their elastic forces is upward, and the magnitude is F. If C is in the extended state, the elastic force Fc is downward, and

Fc+mg=F,

Fc=F-mg.

If C is in a compressed state, the elastic force Fc is upward, and the

Fc+F=mg,

Have

Fc=mg-F.

When mg=2F,

Fc=F.

When a and b are in a compressed state, the combined force of their elastic forces is downward, and the magnitude is F, and C must be in a compressed state, and the elastic force Fc is upward, Fc=mg+F. So A, B, C

, D is possible.

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Example 2. As shown in Figure 2, objects B and C are respectively connected to the two ends of the light spring, and placed on the horizontal bottom plate of the hanging basket A. The masses of A, B, and C are known

and so on, all are m, then at the moment when the light rope of the hanging basket is burnt, what is the acceleration of each object?

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Analysis: This problem is applied to the nature of the elasticity of the spring factory that cannot be changed suddenly. Before the rope is burned, C is subjected to a gravity mg and the elastic force f of the spring, and the two are balanced

. At the moment the rope burns, f cannot be changed suddenly, and the size is still mg, so ac=0

A and B can be considered as a whole for analysis.Before the rope is broken, they are subjected to 2mg of gravity, the downward elastic force of the spring f=mg, and the upward pulling force of the rope T=3mg,

is in a state of equilibrium. The moment the rope breaks, the tension T disappears, and the elastic force of the spring cannot change suddenly, so the resultant force they receive is downward and the magnitude is

F+2mg=3mg