Can the spring force change suddenly?

Can the spring force change suddenly?

In the mechanics problems of middle school physics, the elastic force of light bar, light rope and light spring often appears. Many authors of teaching books and physics teaching magazines often summarize it as follows: the elastic force of light bar and light rope can be mutated, but the elastic force of light spring can only be mutated gradually, not mutated, Is it true that the elastic force of light spring can not mutate? The author thinks that this view is too superficial and one-sided. The elastic force of light rod and light rope can mutate, but the elastic force of light spring can only gradually change. Many books and periodicals have explained this: because the idealized light rod and light rope can not be extended, that is, the length of rod and rope will not change no matter how much tension the rod and rope are subjected to, Therefore, the elastic force of light rod and light rope can be mutated. When the light spring is under tension or pressure, its deformation is large, and it takes a period of time for the deformation to occur and recover. Therefore, the elastic force of light spring can not be mutated, but can only be gradually changed. In fact, when the light rod and light rope produce elastic force, the rod and light rope must be deformed, but the deformation is small, This is the fundamental reason why the elastic force of rod and rope can change suddenly. In fact, the spring in middle school physics usually refers to the light spring. The mass of the spring itself is negligible, and its inertia is not taken into account. These are the same as the light rod and rope, except that there is obvious or not obvious deformation when the elastic force is generated, The essence is the same. Therefore, when the external conditions change, the deformation of the spring can also have a sudden change, so that the spring force will have a sudden change. Let's take a look at several related college entrance examination questions. Figure 1. (2 pages in total) [continue to read this article]

When x tends to 1, the limit of x ^ 2-1 / (x ^ 2-x) is proved to be 2 by limit definition

When x is near 1, let | f (x) - 2 | ε
That is | (x ^ 2-1) / (x ^ 2-x) - 2 | < ε
The results are as follows
|1/x-1|＜ε
That is: - ε < 1 / X-1 < ε
1-ε＜1/x＜1+ε
So the range of X is:
1/(1+ε)＜x＜1/(1-ε)
|ε/(1+ε)|＜|x-1|＜|ε/(1-ε)|
Then δ (ε) = min {| ε / (1 + ε) |, | ε / (1 - ε) |}
So that for any E
There are δ = min {| ε / (1 + ε) |, | ε / (1 - ε) |}
When | X-1 | δ
There is | f (x) - 2 | ε
Get proof

Find: LIM (x - > - 1) ln (2 + x) / (1 + 2x) ^ 1 / 3 + 1

If the denominator of LIM (x - > - 1) [ln (2 + x)] / [(1 + 2x) ^ 1 / 3 + 1] is derived at the same time = LIM (x - > - 1) [(x + 2) ^ (- 1)] * [(3 / 2) * (1 + 2x) ^ (2 / 3)] = (3 / 2) LIM (x - > - 1) [(1 + 2x) ^ (2 / 3)] / (x + 2) x - > - 1, the numerator (1 + 2x) ^ (2 / 3) → 1, the denominator → 1 = 3 / 2