솔루션피아

$$\begin{cases} m_A&=430\ut{kg}\\m_B&=45.0\ut{kg}\\\phi&=30.0\degree\\\theta&=45.0\degree\\\end{cases}$$$$\begin{cases} T_x&=T\cos\phi\\T_y&=T\sin\phi\\\end{cases}$$$$\begin{cases} \Sigma F_{x}&=0\\\Sigma F_{y}&=0\\\Sigma \tau&=0\\\end{cases}$$$$\begin{cases} 0&=N_x-T_x\\0&=N_y-T_y-m_Ag\\0&=T_xL\sin\theta-\br{T_y+m_Ag}L\cos\theta-m_Bg\br{L\over2}\cos\theta\\\end{cases}$$$$\ab{a}$$$$ \beg..

$$\begin{cases} m_A&=10\ut{kg}\\m_B&=5.0\ut{kg}\\\theta&=30\degree\end{cases}$$$$0=\vec F_A+\vec F_B+\vec T,$$$$\begin{aligned}\tan\theta&={F_A\over F_B}\\&={\mu m_Ag\over m_Bg}\\\end{aligned}$$$$\begin{aligned}\mu&={m_B\over m_A}\tan\theta\\&={1\over2\sqrt3}\\&\approx 0.2886751345948129\\&\approx 0.29\\\end{aligned}$$

$$\begin{cases} M&=m_b+m_p=89.00\ut{kg}\\T_a&=500\ut{N}\\T_b&=700\ut{N}\\g&=9.80665\ut{m/s^2}\end{cases}$$$$\put {x\over L}=k,$$$$\Sigma \tau=0,$$$$\begin{aligned}0&=-{L\over2}m_bg-\br{x\over L}Lm_pg+LT_y \\&={m_bg}+2km_pg-2T\sin\theta \\\end{aligned}$$$$\begin{cases} 0&={m_bg}+2\br{0}m_pg-2\br{500}\sin\theta \\0&={m_bg}+2\br{1}m_pg-2\br{700}\sin\theta \\89&=m_b+m_p\end{cases}$$$$\ab{a,b,..

$$\begin{cases} \vec F_1&=8.40\i-5.70\j\ut{N}\\\vec F_2&=16.0\i+4.10\j\ut{N}\\\end{cases}$$$$\ab{a,b}$$$$\begin{aligned}\vec F_3&=-\br{\vec F_1+\vec F_2}\\&=-24.4\i+1.6\j\ut{N}\\\end{aligned}$$$$\begin{cases} F_{3x}&=-24.4\ut{N}\\F_{3y}&=1.6\ut{N}\\\end{cases}$$$$\ab{c}$$$$ \begin{aligned}\theta&=\tan^{-1}{1.6\over-24.4}\\&\approx 3.0761126286663285\ut{rad}\\&\approx 3.08\ut{rad}\\\end{ali..

$$\begin{cases} m_1&=85.0\ut{kg}\\m_2&=30.0\ut{kg}\\L_2&=2.00\ut{m}\\m_3&=20.0\ut{kg}\\d&=0.500\ut{m}\\L_1&=L_2+2d\\\end{cases}$$$$\begin{cases} \Sigma F_{1y}&=0\\\Sigma \tau_1&=0\\\Sigma F_{2y}&=0\\\Sigma \tau_2&=0\\\end{cases}$$$$ \begin{cases} 0&=T_{1L}+T_{1R}-T_{2L}-T_{2R}-m_1g\\0&=-dT_{2L}-{L_1\over2}m_1g-\br{L_1-d}T_{2R}+L_1T_{1R} \\0&=T_{2L}+T_{2R}-m_2g-m_3g\\0&=-dm_3g-{L_2\over2}m_2g..

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