forked from bai/curriculum-project-hub
sjfhsjfh
c73a2c903f
Real-content fixture for the end-to-end pipeline. TH-141 (39 parts: 22 segment, 15 lemma, 2 example) migrated from the prototype's typst `#let parts` manifest to ADR-0008: declarative manifest.toml (project+info+ordered parts+targets) + per-element element.toml (kind + scalars; examples carry `source`). Content .typ files copied byte-identical (no math corruption); per-element main.typ + meta.toml dropped (wiring is now generated). Part order matches source exactly; 5 lemmas have no proof.typ (optional); no cross-file imports / paralearn refs / figs. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
4 lines
724 B
Typst
4 lines
724 B
Typst
考虑一根原长 $L_0$、劲度系数 $k$ 的弹性绳，把它拉伸至长度 $L$。宏观上张力为 $F = k(L - L_0)$，随长度线性增大。从微观上看，弹性绳内部的所有分子被一同拉远，分子间距由 $d_0$ 增至 $d_0 (L \/ L_0)$，键能上升，张力即为这些键被拉长所提供的回复力之和。
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二维弹性膜的情形与此完全平行。设原面积 $A_0$、二维劲度系数 $k_("2D")$，把面积拉至 $A$，则单位长度上的张力沿两个主方向各贡献一份，随应变 $(A - A_0) \/ A_0$ 线性增大。无论一维还是二维，弹性体被拉伸时承担应力的始终是同一批分子——拉伸前后分子数不变，变的是它们之间的距离。
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