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⛰️ 斜面受力（含摩擦）Inclined Plane Calculator
质量 m 的物体在倾角 θ 的斜面上：沿斜面分力 mg sinθ，法向力 mg cosθ，摩擦力 μ mg cosθ，净加速度 a = g(sinθ - μ cosθ)。本地处理。For mass m on a slope of angle θ: parallel force mg sinθ, normal force mg cosθ, friction μ mg cosθ and acceleration a = g(sinθ - μ cosθ). Processed locally.
使用说明与常见问题How-to & FAQ
「斜面受力（含摩擦）」是什么？What is the Inclined Plane Calculator tool?
质量 m 的物体在倾角 θ 的斜面上：沿斜面分力 mg sinθ，法向力 mg cosθ，摩擦力 μ mg cosθ，净加速度 a = g(sinθ - μ cosθ)。本地处理。For mass m on a slope of angle θ: parallel force mg sinθ, normal force mg cosθ, friction μ mg cosθ and acceleration a = g(sinθ - μ cosθ). Processed locally.
如何使用「斜面受力（含摩擦）」？How do I use the Inclined Plane Calculator tool?
在「斜面受力（含摩擦）」中，填写「质量 kg」、「倾角 °」、「摩擦系数 μ」等参数，结果会随输入实时计算并显示在下方。In the Inclined Plane Calculator: Fill in "Mass kg", "Angle °", "Friction coefficient μ"; results are recalculated instantly as you type.
临界角？Angle of repose?
物体刚开始下滑时 tanθ = μ（静摩擦系数）。Sliding starts when tanθ = μ (static).
能举个计算实例吗？Can you show a worked example?
例如在「斜面受力（含摩擦）」中填 质量 kg = 10，倾角 ° = 30，摩擦系数 μ = 0.2，结果区显示：沿斜面分力：49.033 N；法向力：84.928 N；最大摩擦力：16.986 N；加速度：3.2048 m/s²For example, entering Mass kg = 10, Angle ° = 30, Friction coefficient μ = 0.2 in the Inclined Plane Calculator gives: Parallel force: 49.033 N; Normal force: 84.928 N; Friction force: 16.986 N; Acceleration: 3.2048 m/s²
哪些输入会被检查？Which inputs are validated?
「斜面受力（含摩擦）」会检查这些输入——「质量 kg」：必须填写，须大于 0；「倾角 °」、「摩擦系数 μ」：必须填写；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 Inclined Plane Calculator checks its inputs — "Mass kg": required, must be greater than 0; "Angle °", "Friction coefficient μ": required; 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?
「斜面受力（含摩擦）」的设置：「质量 kg」默认 10；「倾角 °」默认 30；「摩擦系数 μ」默认 0.2。每次生成结果都按当前设置处理。Settings in the Inclined Plane Calculator — "Mass kg" default 10; "Angle °" default 30; "Friction coefficient μ" default 0.2. 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?
「斜面受力（含摩擦）」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 Inclined Plane Calculator 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.
「斜面受力（含摩擦）」免费吗？需要注册吗？Is the Inclined Plane Calculator free? Do I need an account?
「斜面受力（含摩擦）」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 Inclined Plane Calculator is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.