🪢 弹性势能计算器（E = ½kx²，可反求 k 或 x，弹力）Elastic Potential Energy Calculator (E = ½kx², Solve for k or x, Spring Force)

使用说明与常见问题How-to & FAQ

「弹性势能计算器（E = ½kx²，可反求 k 或 x，弹力）」是什么？What is the Elastic Potential Energy Calculator (E = ½kx², Solve for k or x, Spring Force) tool?

胡克弹簧的弹性势能 E = ½kx²：由劲度系数和形变量求能量，或由能量反求劲度系数或形变量；同时给出弹力 F = kx。形变量可用 m、cm 或 mm。本地处理。Elastic potential energy of a Hookean spring, E = ½kx²: get the energy from the spring constant and displacement, or solve for the spring constant or displacement from the energy. Also gives the spring force F = kx. Displacement in m, cm or mm. Processed locally.

如何使用「弹性势能计算器（E = ½kx²，可反求 k 或 x，弹力）」？How do I use the Elastic Potential Energy Calculator (E = ½kx², Solve for k or x, Spring Force) tool?

在「弹性势能计算器（E = ½kx²，可反求 k 或 x，弹力）」中，填写「求」、「劲度系数 k（N/m）」、「形变量 x」、「形变量单位」、「势能 E（J）」等参数，结果会随输入实时计算并显示在下方。In the Elastic Potential Energy Calculator (E = ½kx², Solve for k or x, Spring Force): Fill in "Solve for", "Spring constant k (N/m)", "Displacement x", "Displacement unit", "Energy E (J)"; results are recalculated instantly as you type.

弹性势能公式是什么？What is the elastic potential energy formula?

E = ½kx²，k 是劲度系数（N/m），x 是偏离原长的形变量（m）。k = 200 N/m 的弹簧拉伸 10 cm：½ × 200 × 0.1² = 1 J。E = ½kx², where k is the spring constant (N/m) and x the displacement from rest (m). A 200 N/m spring stretched 10 cm stores ½ × 200 × 0.1² = 1 J.

能举个计算实例吗？Can you show a worked example?

例如在「弹性势能计算器（E = ½kx²，可反求 k 或 x，弹力）」中填 求 = 势能 E，劲度系数 k（N/m） = 200，形变量 x = 10，形变量单位 = cm，结果区显示：势能 E：1 J；劲度系数 k：200 N/m；形变量 x：0.1 m（10 cm）；弹力 F = kx：20 N；ℹ 只在弹性限度内成立（胡克定律）；拉伸和压缩用形变量的绝对值For example, entering Solve for = Energy E, Spring constant k (N/m) = 200, Displacement x = 10, Displacement unit = cm in the Elastic Potential Energy Calculator (E = ½kx², Solve for k or x, Spring Force) gives: Energy E: 1 J; Spring constant k: 200 N/m; Displacement x: 0.1 m (10 cm); Spring force F = kx: 20 N; ℹ valid only within the elastic limit (Hooke's law); use the size of the stretch or compression

哪些输入会被检查？Which inputs are validated?

「弹性势能计算器（E = ½kx²，可反求 k 或 x，弹力）」会检查这些输入——「劲度系数 k（N/m）」：须大于 0且不大于 1,000,000,000,000；「形变量 x」：须不小于 0且不大于 1,000,000,000；「势能 E（J）」：须大于 0且不大于 1,000,000,000,000,000；绝对值超过 10¹⁵ 的数也会被拒绝。不符合时结果区显示具体提示，不会给出数字。The Elastic Potential Energy Calculator (E = ½kx², Solve for k or x, Spring Force) checks its inputs — "Spring constant k (N/m)": must be more than 0 and at most 1,000,000,000,000; "Displacement x": must be at least 0 and at most 1,000,000,000; "Energy E (J)": must be more than 0 and at most 1,000,000,000,000,000; numbers above 10¹⁵ in absolute value are rejected too. When a value fails, the result area names the problem instead of showing a number.

有哪些选项可以调整？What options can I adjust?

「弹性势能计算器（E = ½kx²，可反求 k 或 x，弹力）」的设置：「求」可选 势能 E、劲度系数 k、形变量 x（默认 势能 E）；「劲度系数 k（N/m）」默认 200；「形变量 x」默认 10；「形变量单位」可选 m、cm、mm（默认 cm）；「势能 E（J）」默认 1。每次生成结果都按当前设置处理。Settings in the Elastic Potential Energy Calculator (E = ½kx², Solve for k or x, Spring Force) — "Solve for": Energy E, Spring constant k, Displacement x (default Energy E); "Spring constant k (N/m)" default 200; "Displacement x" default 10; "Displacement unit": m, cm, mm (default cm); "Energy E (J)" default 1. The result always uses the current settings.

计算结果可以用于作业或工程吗？Can I use the results for homework or engineering?

「弹性势能计算器（E = ½kx²，可反求 k 或 x，弹力）」使用教科书标准公式（公式写在说明和常见问题中），适合学习和估算核对；涉及安全的工程设计请以规范和实测为准。The Elastic Potential Energy Calculator (E = ½kx², Solve for k or x, Spring Force) uses standard textbook formulas (given in the description and FAQ), which is good for learning and checking estimates; for safety-critical engineering follow codes and measured values.

「弹性势能计算器（E = ½kx²，可反求 k 或 x，弹力）」免费吗？需要注册吗？Is the Elastic Potential Energy Calculator (E = ½kx², Solve for k or x, Spring Force) free? Do I need an account?

「弹性势能计算器（E = ½kx²，可反求 k 或 x，弹力）」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Elastic Potential Energy Calculator (E = ½kx², Solve for k or x, Spring Force) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.