솔루션피아

$$ \begin{cases} m_1&=40.0\ut{kg}=4m\\m_2&=10.0\ut{kg}=m\\L&=0.800\ut{m}\\g&=9.80665\ut{m/s^2}\end{cases} $$$$ \begin{cases} \Sigma F_{y}&=0\\\Sigma \tau&=0\\\end{cases} $$$$ \begin{cases} 0&=N_A+N_B-m_1g-m_2g\\0&=-r_1m_1g-r_2m_2g+r_BN_B\\\end{cases} $$$$ \begin{cases} N_A&=\cfrac{r_B-r_1}{r_B}m_1g+\cfrac{r_B-r_2}{r_B}m_2g\\N_B&=\cfrac{r_1}{r_B}m_1g+\cfrac{r_2}{r_B}m_2g\\\end{cases} $$$$ \begin{..

$$ \begin{cases} L&=6.10\ut{m}\\mg&=510\ut{N}\\h&=4.00\ut{m}\\\theta_0&=70\degree\\\end{cases} $$$$ \begin{cases} r_f&=h\\r_{\text{floor}}\tan\theta&=h\\\br{r_{mg}+\frac{L}{2}\cos\theta}\tan\theta&=h\end{cases} $$$$ \begin{cases} N_{\text{edge }x}&=N_{\text{edge}}\sin\theta\\N_{\text{edge }y}&=N_{\text{edge}}\cos\theta\\\end{cases} $$$$ \begin{aligned}f&=\mu N_{\text{floor}},\end{aligned} $$$$ \..

$$ \begin{cases} 2R&=2.4\ut{cm}\\m&=670\ut{kg}\\E_{\text{steel}}&=200\times10^9\ut{N/m^2}\\g&= 9.80665\ut{m/s^2}\end{cases} $$$$ {F\over A}= E{\Delta L\over L}, $$$$ \begin{aligned}\Delta L&={ FL \over A E} \\&={ mgL \over \pi R^2 E} \\&={ 67g \over 2880000\pi } L\\\end{aligned} $$$$\ab{a}$$$$ \begin{aligned}\Delta L&={ 67g \over 2880000\pi } L\\&=\frac{13140911}{4800000000 \pi }\ut{m}\\&\approx..

$$ \begin{cases} \theta&=36.9\degree\\\phi&=53.1\degree\\L&=4.35\ut{m}\\\end{cases} $$$$L=x+y,$$$$ \begin{cases} \Sigma F_{x}&=0\\\Sigma F_{y}&=0\\\Sigma \tau&=0\\\end{cases} $$$$ \begin{cases} 0&=-T_1\sin\theta+T_2\sin\phi\\0&=T_1\cos\theta+T_2\cos\phi-mg\\0&=-xT_1\cos\theta+yT_2\cos\phi\\\end{cases} $$$$ \begin{aligned}x&={\cos\phi\sin\theta\over\sin\br{\theta+\phi}}L\\&=L \sin ^236.9\degree\\..

$$ \begin{cases} mg&=60\ut{N}\\L&=3.2\ut{m}\\F&=50\ut{N}\\\theta&=25\degree\\h&=2.0\ut{m}\\\end{cases} $$$$ \begin{cases} \Sigma F_{x}&=0\\\Sigma F_{y}&=0\\\Sigma \tau&=0\\\end{cases} $$$$ \begin{cases} 0&=F+N_x-T\cos\theta\\0&=N_y-mg-T\sin\theta\\0&=hT\cos\theta-LF\\\end{cases} $$$$ \begin{cases} T&={F L\over h\cos\theta}\\N_x&={F(L-h)\over h}\\N_y&={FL\over h}\tan\theta+mg\\\end{cases} $$$$\ab..

$$ \begin{cases} 2R&=4.8\ut{cm}\\L&=5.3\ut{cm}\\m&=1500\ut{kg}\\G&=3.0\times10^{10}\ut{N/m^2}\\g&=9.80665\ut{m/s^2}\\\end{cases} $$$$\ab{a}$$$$ \begin{aligned}F&=mg\\&=14709.975\ut{N}\\&\approx 1.5\times10^4\ut{N}\\&\approx 15\ut{kN}\\\end{aligned} $$$$\ab{b}$$$${F\over A}=G{\Delta x\over L},$$$$ \begin{aligned}\Delta x&={FL\over AG}\\&={Lmg\over \pi R^2 G}\\&=\frac{53 g}{11520000 \pi }\ut{m}\\&..

$$ \begin{cases} \theta_1&=51.0\degree\\\theta_2&=66.0\degree\\m&=704\ut{kg}\\g&=9.80665\ut{m/s^2}\end{cases} $$$$\ab{a}$$$$ \begin{aligned}T_A&=mg\\&=6.9038816\times10^3\ut{N}\\&\approx 6.90\times10^3\ut{N}\\&\approx 6.90\ut{kN}\\\end{aligned} $$$$\ab{b,c}$$$$ \begin{cases} \theta&=\theta_1+\theta_2-90\degree&=27.0\degree\\\phi&=90\degree-\theta_2&=24.0\degree\\\end{cases} $$$$ \begin{aligned}0..

$$ \begin{cases} r_A&=7.0\ut{cm}\\r_B&=4.0\ut{cm}\\R&=4.0\ut{cm}\\F&=220\ut{N}\\\end{cases} $$$$ \begin{cases} 0&=F-N_A+N_B\\0&=RF-r_AN_A-r_BN_B\end{cases} $$$$ \begin{cases} N_A&=\cfrac{R+r_B}{2r_B}F\\N_B&=\cfrac{R-r_B}{2r_B}F\\\end{cases} $$$$\ab{a,b}$$$$ \begin{cases} N_A&=220\ut{N}\\N_B&=0\\\end{cases} $$

$$ \put \begin{cases} A : \text{Top Ball}\\B : \text{Bottom Ball}\\L : \text{Left Wall}\\R : \text{Right Wall}\\G : \text{Ground}\\\end{cases} $$$$ \begin{cases} \Sigma F_{Ax}&=0\\\Sigma F_{Ay}&=0\\\Sigma F_{Bx}&=0\\\Sigma F_{By}&=0\\\end{cases} $$$$ \begin{cases} 0&=N_{ABx}-N_R\\0&=N_{ABy}-mg\\0&=N_L-N_{ABx}\\0&=N_G-N_{ABy}-mg\\\end{cases} $$$$\theta=45\degree\Rarr N_{ABx}=N_{ABy}$$$$\ab{a,b,c,..

$$ \begin{cases} L&=2.00\ut{m}\\m&=78.0\ut{kg}\\d_h&=3.00\ut{m}\\d_v&=4.00\ut{m}\\g&=9.80665\ut{m/s^2}\end{cases} $$$$x_1=d_h-{L\over2},$$$$\theta=\tan^{-1}{d_h\over d_v}$$$$ \begin{cases} \Sigma F_{x}&=0\\\Sigma F_{y}&=0\\\Sigma \tau&=0\\\end{cases} $$$$ \begin{cases} 0&=N_x-T\sin\theta\\0&=N_y+T\cos\theta-mg\\0&=-x_1 mg+Td_h\cos\theta\\\end{cases} $$$$\ab{a}$$$$ \begin{aligned}T&= {x_1 mg\over..