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💥 冲量与动量计算器Impulse and Momentum Calculator
按冲量定理 J = F·Δt = Δp = m(v₂ − v₁) 计算冲量：可由力和作用时间求冲量及速度变化，也可由质量和前后速度求冲量、动量和平均作用力。Calculate impulse with the impulse–momentum theorem J = F·Δt = Δp = m(v₂ − v₁) — from a force and its duration (with the velocity change), or from mass and the velocities before and after (with momentum and the average force).
使用说明与常见问题How-to & FAQ
「冲量与动量计算器」是什么？What is the Impulse and Momentum Calculator tool?
按冲量定理 J = F·Δt = Δp = m(v₂ − v₁) 计算冲量：可由力和作用时间求冲量及速度变化，也可由质量和前后速度求冲量、动量和平均作用力。Calculate impulse with the impulse–momentum theorem J = F·Δt = Δp = m(v₂ − v₁) — from a force and its duration (with the velocity change), or from mass and the velocities before and after (with momentum and the average force).
如何使用「冲量与动量计算器」？How do I use the Impulse and Momentum Calculator tool?
在「冲量与动量计算器」中，填写「已知条件」、「平均力 F（N）」、「作用时间 Δt（s）」、「质量 m（kg）」、「初速度 v₁（m/s）」等参数，结果会随输入实时计算并显示在下方。In the Impulse and Momentum Calculator: Fill in "Known values", "Average force F (N)", "Contact time Δt (s)", "Mass m (kg)", "Initial velocity v₁ (m/s)"; results are recalculated instantly as you type.
冲量和动量是什么关系？How are impulse and momentum related?
冲量定理：物体受到的冲量等于它的动量变化，J = F·Δt = Δp = m·v₂ − m·v₁。冲量和动量的单位相同，N·s = kg·m/s。By the impulse–momentum theorem, the impulse on an object equals its change in momentum: J = F·Δt = Δp = m·v₂ − m·v₁. Impulse and momentum share units: N·s = kg·m/s.
为什么末速度是负数？Why is the final velocity negative?
速度带方向。默认例子里 2 kg 的球以 3 m/s 撞墙后以 5 m/s 反弹，反向记为 −5 m/s，所以冲量 = 2 × (−5 − 3) = −16 N·s，方向与原运动方向相反；若接触 0.2 s，平均作用力为 −80 N。Velocity has direction. In the default example a 2 kg ball hits a wall at 3 m/s and rebounds at 5 m/s, written −5 m/s, so the impulse is 2 × (−5 − 3) = −16 N·s, opposite to the original motion; over 0.2 s of contact the average force is −80 N.
为什么延长作用时间能减小冲击力？Why does a longer contact time reduce the force?
动量变化一定时，F = Δp ÷ Δt，作用时间越长平均力越小，这就是气囊、护垫和接球时手往回收的原理。For a fixed change in momentum, F = Δp ÷ Δt, so a longer contact time means a smaller average force — the idea behind airbags, padding and 'giving' with your hands when catching.
计算结果可以用于作业或工程吗？Can I use the results for homework or engineering?
「冲量与动量计算器」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 Impulse and Momentum 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.
「冲量与动量计算器」免费吗？需要注册吗？Is the Impulse and Momentum Calculator free? Do I need an account?
「冲量与动量计算器」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 Impulse and Momentum 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.