솔루션피아

$$ \begin{cases} m_A&=46.0\ut{kg}\\L&=5.00\ut{m}\\m_B&=250\ut{kg}\\d&=0.540\ut{m}\\\end{cases} $$$$ \begin{cases} x_1&=d\\x_2&=L-d\\x_A&=L\\x_B&={L\over2}\\\end{cases} $$$$ \begin{cases} \Sigma F_{y}&=0\\\Sigma \tau&=0\\\end{cases} $$$$ \begin{cases} 0&=N_1+N_2-m_Ag-m_Bg\\0&=x_1N_1+x_2N_2-x_Am_Ag-x_Bm_Bg\\\end{cases} $$$$\ab{a,b}$$$$ \begin{cases} N_1&=\cfrac{ m_A (x_A-x_2)+m_B (x_B-x_2)}{x_1-..

$$ \begin{cases} m&=95\ut{kg}\\L&=15\ut{m}\\2R&=9.6\ut{mm}\\\Delta L &= 1.3\ut{cm}\\\end{cases} $$$${F\over A}=E{\Delta L\over L},$$$$ \begin{aligned}E&={F\over A}\cdot{L\over\Delta L}\\&={mgL\over \pi R^2\Delta L}\\&=\frac{185546875000 g}{39 \pi }\\&\approx 1.4851141642012506\times10^{10}\ut{N/m^2}\\&\approx 1.5\times10^{10}\ut{N/m^2}\\&\approx 15\ut{GN/m^2}\\\end{aligned} $$

$$ \begin{cases} m&=300\ut{kg}\\A&=2.0\times10^{-6}\ut{m^2}\\L_1=L_3&=2.0000\ut{m}\\L_2&=L_1+d\\d&=6.00\ut{mm}\\g&=9.80665\ut{m/s^2}\\E_{\text{steel}}&=200\times10^9\ut{N/m^2}\end{cases} $$$${F\over A}=E{\Delta L\over L},$$$$ \begin{cases} F_1&=AE\cfrac{\Delta L_1}{L_1}\\F_2&=AE\cfrac{\Delta L_2}{L_2}\\\end{cases} $$$$ \begin{cases} F_1&=AE\cfrac{\Delta L_1}{L_1}\\F_2&=AE\cfrac{\Delta L_1-d}{L_1..

$$ \begin{cases} L&=2.50\ut{m}\\mg&=500\ut{N}\\d&=1.50\ut{m}\\\end{cases} $$$$ x=\sqrt{L^2-d^2},$$$$\ab{a}$$$$ \begin{aligned}\Sigma \tau&=0\\&=-\frac{x}{2}mg+LP\\\end{aligned} $$$$ \begin{aligned}P&=\frac{mgx}{2L}\\&=\frac{mg}{2L}\sqrt{L^2-d^2}\\&=200\ut{N}\\\end{aligned} $$$$\ab{b}$$$$\put x=\sqrt{L^2-d^2}$$$$\sin\theta=\frac{d}{L},$$$$ \begin{aligned}\vec P &=-P\sin\theta\i+P\cos\theta\j\\&=-..

$$ \begin{cases} T&=535\ut{N}\\\end{cases} $$$$ \put\begin{cases} T&=\overline{AB}\\F_v&=\overline{AD},\overline{BC}\\F_d&=\overline{AC},\overline{BD}\\F_h&=\overline{CD}\\\end{cases} $$$$ \put \begin{cases} \text{Tensile Force} : +\\\text{Compressive Force} :-\end{cases} $$$$ \begin{cases} \Sigma \vec F_B&=0\\\Sigma \vec F_C&=0\\\end{cases} $$$$ \begin{cases} \Sigma F_{Bx}&=0\\\Sigma F_{By}&=0\..

$$ \begin{cases} L&=6.2\ut{m}\\mg&=400\ut{N}\\\mu&=0.39\\\end{cases} $$$$ \begin{cases} \Sigma F_{x}&=0\\\Sigma F_{y}&=0\\\Sigma \tau&=0\\\end{cases} $$$$ \put\begin{cases} F=\text{Force Wall}\\N=\text{Force Floor}\\h=\text{Wall Distance}\\x=\text{Floor Distance}\\\end{cases} $$$$ h=\sqrt{L^2-x^2} $$$$ \begin{cases} 0&=F-\mu N\\0&=N-mg\\0&=-\frac{x}{2}mg+xN-h\mu N\\\end{cases} $$$$ \begin{aligne..

$$ \begin{cases} L_A&=2.40\ut{m}\\m_A&=54.0\ut{kg}\\m_B&=68.0\ut{kg}\\d&=1.60\ut{m}\\g&=9.80665\ut{m/s^2}\\\end{cases} $$$$ \begin{cases} \Sigma \vec F_A&=0\\\Sigma \vec F_B&=0\\\end{cases} $$$$ \begin{cases} \Sigma F_{Ax}&=0\\\Sigma F_{Bx}&=0\\\Sigma F_{Ay}&=0\\\Sigma F_{By}&=0\\\Sigma \tau_A&=0\\\Sigma \tau_B&=0\\\end{cases} $$$$\put \vec F=\text{Force }A \lrarr B$$$$ \begin{cases} 0&=N_{Ax}+F..

$$ \begin{cases} L&=12.0\ut{m}\\ \theta&=50.0\degree\\ T&=400\ut{N}\\ \end{cases} $$ $$ \begin{cases} \Sigma F_{x}&=0\\ \Sigma F_{y}&=0\\ \Sigma \tau&=0\\ \end{cases} $$ $$ \begin{cases} 0&=-T+N_x\\ 0&=-mg+N_y\\ 0&=TL\cos\theta-mg{L\over2}\sin\theta\\ \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} m\vec g&={2T\over\tan\theta}\j\\ &=800\tan40\degree\j\ut{N}\\ &\approx 671.279704941824\j\ut{N}\\ &\a..

$$ \begin{cases} 2x&=3.44\ut{m}\\y&=25.0\ut{cm}\\mg&=3160\ut{N}\end{cases} $$$$ \begin{aligned}\tan\theta&={y\over x},\\\end{aligned} $$$$\Sigma F_y=0,$$$$ \begin{aligned}0&=2T_y-mg\\T_y&={mg\over2}\end{aligned} $$$$ \begin{aligned}T&={T_y\over \sin\theta}\\&=m g\cdot\frac{ x }{2 y}\sqrt{\frac{y^2}{x^2}+1}\\&=\frac{316 }{5}\sqrt{30209}\ut{N}\\&\approx 1.098462544468404\times 10^4\ut{N}\\&\approx..

$$ \begin{cases} H&=59.1\ut{m}\\2R&=7.44\ut{m}\\\Delta x_{\text{top}0} &= 4.01\ut{m}\\\end{cases} $$$$\ab{a}$$$$\Delta x_\com = R,$$$$ \begin{aligned}\Delta x_{\text{top}}&=2\Delta x_\com\\&=2R\\\end{aligned} $$$$ \begin{aligned}\Ans&=2R-\Delta x_{\text{top}0}\\&=3.43\ut{m}\end{aligned} $$$$\ab{b}$$$$ \begin{aligned}\theta&=\sin^{-1}{2R\over H}\\&=\sin^{-1}{124\over 985}\\&\approx 0.126223229105..