高中/物理/力学

$$\sum_{i=1}^n m_iv_i=\sum_{i=1}^n m_iv'_i\\ \sum F\triangle t=\sum_{i=1}^n m_i\triangle v_i\Rightarrow F=\frac{\text{d}(mv)}{\text{d}t}$$ $$\sum F\triangle x=\frac12mv^2-\frac12mv_0^2$$ $$v_1=\frac{m_1-m_2}{m_1+m_2}v_0\\v_2=\frac{2m_1}{m_1+m_2}v_0$$ $$x_{重心}=\frac{\sum G_ix_i}{\sum G_i}\\x_{质心}=\frac{\sum m_ix_i}{\sum m_i}$$ $$\begin{align} \text{E}_p&=\int_0^{\Delta x} kx\text{d}x \\&=\left.\frac12kx^2\right|_0^{\Delta x} \\&=\frac12k{\Delta x}^2 \end{align}$$ $$F = G\frac{m_1m_2}{r^2}\\ \begin{cases} r \to 距离 \\ R \to 半径 \\ h = r - R \hfill \\ \end{cases}$$