솔루션피아

$$ \begin{cases} a&=2.5\ut{m}\\b&=3.0\ut{m}\\c&=1.0\ut{m}\\F_1&=20\ut{N}\\F_2&=10\ut{N}\\F_3&=8.0\ut{N}\\\end{cases} $$$$ \begin{cases} \Sigma F_{x}&=0\\\Sigma F_{y}&=0\\\Sigma \tau&=0\\\end{cases} $$$$ \begin{cases} 0&=F_h-F_3\\0&=F_v-F_1-F_2\\0&=dF_v-bF_2-aF_3\\\end{cases} $$$$\ab{a}$$$$ \begin{aligned}F_h&=F_3=8.0\ut{N}\\\end{aligned} $$$$\ab{b}$$$$ \begin{aligned}F_v&=F_1+F_2\\&=30\ut{N}\\\e..

$$ \begin{cases} F_h&=13.4\ut{N}\\F_v&=162.4\ut{N}\\\end{cases} $$$$ \begin{aligned} \Sigma \tau&=-{d\over3}F_t\sin45\degree+d F_v \sin10\degree+dF_h\sin80\degree\\ &=0\end{aligned} $$$$ \begin{aligned}F_t&=3\sqrt2\br{F_h\cos10\degree+F_v\sin10\degree}\\&={3\sqrt2\over5}\br{67\cos10\degree+812\sin10\degree}\\&\approx 175.63212110909666\ut{N}\\&\approx 176\ut{N}\\\end{aligned} $$

$$ \begin{cases} h&=3.00\ut{cm}\\r&=6.00\ut{cm}\\m&=0.415\ut{kg}\\g&=9.80665\ut{m/s^2}\\\end{cases} $$$$ \begin{cases} x&=\sqrt{r^2-y^2}\\y&=r-h\\\end{cases} $$$$ \begin{aligned}\Sigma \tau&=-yF+xmg=0\\F&={x\over y} mg\\&=\frac{ \sqrt{h (2r-h)}}{r-h}mg\\&={83\sqrt3\over200}g\\&=\frac{16279039 \sqrt{3}}{4000000}\ut{N}\\&\approx 7.049030661598812\ut{N}\\&\approx 7.05\ut{N}\\\end{aligned} $$

$$ \begin{cases} \theta_1&=40\degree\\\end{cases} $$$$ \begin{cases} \Sigma F_{x}&=0\\\Sigma F_{y}&=0\\\end{cases} $$$$ \begin{cases} 0&=-T_1\cos\theta_1+T_2\cos\theta_2\\0&=T_1\sin\theta_1+T_2\sin\theta_2-mg\\\end{cases} $$$$ T_2={mg\cos\theta_1\over\sin\br{\theta_1+\theta_2}}$$$$\ab{a}$$$$ \begin{aligned}\min (T_2),\\ {\sin\br{\theta_1+\theta_2}}&=1\\\theta_1+\theta_2&=90\degree\\\theta_2&=50\..

$$ \begin{cases} y&=2.1\ut{m}\\x&=0.91\ut{m}\\h&=0.25\ut{m}\\m&=27\ut{kg}\\g&=9.80665\ut{m/s^2}\end{cases} $$$$ \begin{cases} p&=y-h\\q&=h\\\end{cases} $$$$$$$$ \begin{cases} A&=(0,0)\\B&=(x,0)\\C&=(x,y)\\D&=(0,y)\\P&=(0,p)\\Q&=(0,q)\\\end{cases} $$$$ \begin{cases} N_{Py}&={mg\over2}\\N_{Qy}&={mg\over2}\\\end{cases} $$$$ \begin{cases} \Sigma F_{x}&=0\\\Sigma \tau&=0\\\end{cases} $$$$ \begin{case..

$$ \begin{cases} S_{\text{wood}}&=50\times10^6\ut{N/m^2}\\\rho_{\text{wood}}&=525\ut{kg/m^3}\\A_{\text{wood}}&=d^2\\M&=430\ut{kg}\\a&=1.9\ut{m}\\b&=2.5\ut{m}\\g&=9.80665\ut{m/s^2}\end{cases} $$$$ \begin{cases} \Sigma F_{x}&=0\\\Sigma F_{y}&=0\\\Sigma \tau&=0\\\end{cases} $$$$ \begin{cases} 0&=N_x-T_x\\0&=N_y-Mg-mg\\0&=aT_x-bMg-{b\over2}mg\\\end{cases} $$$$ \begin{cases} N_x&={b\over2a}\br{m+2M}g..

$$ \put \begin{cases} A : \text{Rod}\\B : \text{Box}\\\end{cases} $$$$ \begin{cases} L&=1.82\ut{m}\\W_{A}&=200\ut{N}\\W_{B}&=300\ut{N}\\\theta&=30.0\degree\\T_{\max}&=412\ut{N}\\\end{cases} $$$$ \begin{cases} \Sigma F_{x}&=0\\\Sigma F_{y}&=0\\\Sigma \tau&=0\\\end{cases} $$$$ \begin{cases} 0&=N_x-T\cos\theta\\0&=N_y-W_A-W_B+T\sin\theta\\0&=-xW_B-{L\over2}W_A+TL\sin\theta\\\end{cases} $$$$\ab{a}$$..

$$\ab{a}$$$$\com(1)={L\over2}\le L-a_1,$$$$ \begin{aligned}a_1\le{L\over2}\taag1\end{aligned} $$$$\therefore \max(a_1)={L\over2}$$$$\ab{b}$$$$\com(12)={L+a_1\over2}\le L-a_2,$$$$ \begin{aligned}a_2\le{L-a_1\over2}\taag2\end{aligned} $$$$\therefore \max(a_2)={L\over2}\\(a_1=0)$$$$\ab{c}$$$$\com(123)={L+a_1+a_2\over2}\le L-a_3,$$$$ \begin{aligned}a_3\le{L-a_1-a_2\over2}\taag3\end{aligned} $$$$\the..

$$ \begin{cases} E_\text{Iron}&=200\times10^9\ut{N/m^2}\\m&=210\ut{kg}\\R&=1.20\ut{mm}\\p&=2.00\ut{mm}\\L_{A}&=2.50\ut{m}\\L_{B}&=L_{A}+p\\\Delta L_B&=\Delta L_A-p\\\end{cases} $$$${F\over A}=E\cdot{\Delta L\over L},$$$$ \begin{cases} 0&=\Sigma F=T_A+T_B-mg\\T_A&=E (\pi R^2)\cdot{\Delta L_A\over L_A}\\T_B&=E (\pi R^2)\cdot{\Delta L_B\over L_B}\\\end{cases} $$$$ \begin{aligned}\Delta L_A&=\frac{{..

$$ \begin{cases} m_A&=11.0\ut{kg}\\\theta&=30.0\degree\\m_B&=7.00\ut{kg}\\g&=9.80665\ut{m/s^2}\end{cases} $$$$T_A=m_Ag\sin\theta,$$$$ \begin{aligned}\vec T_A&=-m_Ag\sin\theta\cos\theta\i-m_Bg\sin^2\theta\j\\&=-{11\sqrt3g\over4}\i-{11g\over4}\j\taag1\\\end{aligned} $$$$T_B=m_Bg,$$$$ \begin{aligned}\vec T_B&=-m_Bg\j\\&=-7g\j\taag2\\\end{aligned} $$$$ \begin{aligned}\vec T_S&=-\br{\vec T_A+\vec T_B..