솔루션피아

$$ \put \begin{cases} m_A=m_1=m\\ m_B=m_2=2m\\ M=m_A+m_B=3m \end{cases} $$ $$ \begin{cases} h&=2.50\ut{m}\\ m_B&=2.00m_A=2m\\ \mu&=0.600\\ \end{cases} $$ $$ \put \begin{cases} 0:\text{Start}\\ 1:\text{A Landing Before A B Crash}\\ 2:\text{After A B Crash}\\ 3:\text{Stop} \end{cases} $$ $$ \put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \TE : \text{T..

$$ \begin{cases} m_A&=2400\ut{kg}\\ m_B&=1600\ut{kg}\\ v_A&=80\ut{km/h}\\ v_B&=40\ut{km/h}\\ \end{cases} $$ $$r_\com=\frac{\Sigma rm}{M},$$ $$ \begin{aligned} v_\com&=\dyt{r_\com}\\ &=\dt\(\frac{\Sigma rm}{M}\)\\ &=\(\frac{1}{M}\)\sum \(\dyt{r}m\)\\ &=\(\frac{1}{M}\)\sum \(vm\)\\ &=\frac{\Sigma mv}{M}\\ &=\frac{m_Av_A+m_Bv_B}{M}\\ &=64\ut{km/h} \end{aligned} $$

$$ \begin{cases} m_A&=m_B=m=500\ut{g}\\ x_A&=0\\ x_B&=50\ut{mm}\\ \end{cases} $$ $$r_\com=\frac{\Sigma rm}{M},$$ $$ \begin{aligned} x_\com&=\frac{\Sigma xm}{M}\\ &=\frac{x_Am_A+x_Bm_B}{2m}\\ &=\frac{m_B}{2m}x_B\\ \end{aligned} $$ $$\ab{a}$$ $$ \begin{aligned} x_\com&=\frac{m_B}{2m}x_B\\ &=\frac{m}{2m}x_B\\ &=\frac{x_B}{2}\\ &=25\ut{mm} \end{aligned} $$ $$\ab{b}$$ $$ \begin{cases} m_A&=m-\Delta m..

(풀이자 주 : 배기물의 배출방향에 대한 정보가 없습니다. 따라서 풀이자 임의로 뒤로 배출했다고 가정했습니다. 만일 앞으로 배출한 것이라면 답은 달라집니다.) $$ \begin{cases} M&=m_A+m_B=6090\ut{kg}\\ v_i&=140\ut{m/s}\\ m_B&=80.0\ut{kg}\\ v_{B\larr A}&=-253\ut{m/s}\\ \end{cases} $$ $$v_{B\larr A}=v_{Bf}-v_{Af},$$ $$v_{Bf}=v_{B\larr A}+v_{Af}$$ $$\Delta \Sigma \vec P=0,$$ $$ \begin{aligned} Mv_i&=m_Av_{Af}+m_Bv_{Bf}\\ &=m_Av_{Af}+m_B(v_{B\larr A}+v_{Af})\\ \end{ali..

$$ \put \begin{cases} M : \text{Moon}\\ E : \text{Earth}\\ \end{cases} $$ $$ \begin{cases} r_{E}&=0\\ r_{M}&=3.82\times10^8\ut{m}\\ m_E&=5.98\times10^{24}\ut{kg}\\ m_M&=7.36\times10^{22}\ut{kg}\\ R_E&=6.37\times10^6\ut{m}\\ \end{cases} $$ $$\ab{a}$$ $$r_\com=\frac{\Sigma rm}{M},$$ $$ \begin{aligned} r_\com&=\frac{r_Em_E+r_Mm_M}{m_E+m_M}\\ &=\frac{m_M}{m_E+m_M}r_M\\ &=\frac{1528}{329}\times10^6\u..

$$ \put\begin{cases} 0:\text{Start}\\ 1:\text{After Crash}\\ 2:\text{Landing Ground} \end{cases} $$ $$ \put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \end{cases} $$ $$ \begin{cases} m_A&=3.2\ut{kg}\\ m_B&=2.0\ut{kg}\\ h&=0.30\ut{m}\\ v_{0}&=3.0\ut{m/s} \end{cases} $$ $$\put M = m_A+m_B=5.2\ut{kg}$$ $$\Delta \Sigma \vec P=0,$$ $$m_Av_{A0}=Mv_1,$$ $$..

$$ \put \begin{cases} a:m_a\\ b:m_b \end{cases} $$ $$ \begin{cases} v_{ai}&=0.75\ut{m/s}\\ m_a&=0.25\ut{kg}\\ m_b&=0.50\ut{kg}\\ L_a&=5.0\ut{cm}=5\times10^{-2}\ut{m}\\ L_b&=6.0\ut{cm}=6\times10^{-2}\ut{m}\\ x_{ai}&=-1.50\ut{m}\\ x_{bi}&=0\ut{m}\\ \end{cases} $$ $$\put M=m_a+m_b=0.75\ut{kg}$$ $$\vec r_{\com} = \frac{\Sigma m\vec r}{M},$$ $$ \begin{aligned} x_\com&=\frac{\Sigma mx}{M}\\ &=\frac{m_..

$$ \begin{cases} m_1&=16.7\times10^{-27}\ut{kg}\\ m_2&=8.35\times10^{-27}\ut{kg}\\ m_3&=11.7\times10^{-27}\ut{kg}\\ \vec v_1&=+6.00\times10^6\i\ut{m/s}\\ \vec v_2&=-8.00\times10^6\j\ut{m/s}\\ \end{cases} $$ $$\ab{a}$$ $$\Delta \Sigma \vec P=0,$$ $$ \vec P_i=\Sigma \vec P_f $$ $$ 0=m_1\vec v_1+m_2\vec v_2+m_3\vec v_3 $$ $$ \begin{aligned} \vec v_3&=\frac{-m_1\vec v_1-m_2\vec v_2}{m_3}\\ &=-\frac{..

$$ \put\begin{cases} A:\text{3d x 3d Box}\\ B:\text{2d x 2d Box}\\ C:\text{A-B Box} \end{cases} $$ $$ \begin{cases} 6d&=6.0\ut{m}\\ \end{cases} $$ $$\ab{a}$$ $$ \begin{cases} x_{\com A} &=0\\ x_{\com B}&=2d\\ \end{cases} $$ $$\vec r_{\com} = \frac{\Sigma m\vec r}{M}= \frac{\Sigma V\vec r}{V_s},$$ $$ \begin{aligned} x_{\com A}&= \frac{\Sigma V\vec r}{V_A}\\ &=\frac{V_Bx_{\com B}+V_Cx_{\com C}}{V_..

$$ \begin{cases} p_0&=8.0\ut{kg\cdot m/s}\\ p_1&=4.0\ut{kg\cdot m/s}\\ \end{cases} $$ $$ \begin{aligned} \vec p_0&=8\cos\theta\i+8\sin\theta\j\\ \vec p_1&=8\cos\theta\i=4\i \end{aligned} $$ $$ \begin{aligned} \theta&=\cos^{-1}\frac{4}{8}\\ &=\frac{\pi}{3}\ut{rad}\\ &\approx 1.0471975511965976\ut{rad}\\ &\approx 1.0\ut{rad}\\ \end{aligned} $$