12-30 할리데이 11판 솔루션 일반물리학 {m1=40.0[kg]=4mm2=10.0[kg]=mL=0.800[m]g=9.80665[m/s2] \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} ⎩⎨⎧m1m2Lg=40.0[kg]=4m=10.0[kg]=m=0.800[m]=9.80665[m/s2]{ΣFy=0Στ=0 \begin{cases} \Sigma F_{y}&=0\\\Sigma \tau&=0\\\end{cases} {ΣFyΣτ=0=0{0=NA+NB−m1g−m2g0=−r1m1g−r2m2g+rBNB \begin{cases} 0&=N_A+N_B-m_1g-m_2g\\0&=-r_1m_1g-r_2m_2g+r_BN_B\\\end{cases} {00=NA+NB−m1g−m2g=−r1m1g−r2m2g+rBNB{NA=rB−r1rBm1g+rB−r2rBm2gNB=r1rBm1g+r2rBm2g \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} ⎩⎨⎧NANB=rBrB−r1m1g+rBrB−r2m2g=rBr1m1g+rBr2m2g$$ \begin{.. 11판/12. 평형과 탄성 2024.10.09
12-29 할리데이 11판 솔루션 일반물리학 {L=6.10[m]mg=510[N]h=4.00[m]θ0=70° \begin{cases} L&=6.10\ut{m}\\mg&=510\ut{N}\\h&=4.00\ut{m}\\\theta_0&=70\degree\\\end{cases} ⎩⎨⎧Lmghθ0=6.10[m]=510[N]=4.00[m]=70°{rf=hrfloortanθ=h(rmg+L2cosθ)tanθ=h \begin{cases} r_f&=h\\r_{\text{floor}}\tan\theta&=h\\\br{r_{mg}+\frac{L}{2}\cos\theta}\tan\theta&=h\end{cases} ⎩⎨⎧rfrfloortanθ(rmg+2Lcosθ)tanθ=h=h=h{Nedge x=NedgesinθNedge y=Nedgecosθ \begin{cases} N_{\text{edge }x}&=N_{\text{edge}}\sin\theta\\N_{\text{edge }y}&=N_{\text{edge}}\cos\theta\\\end{cases} {Nedge xNedge y=Nedgesinθ=Nedgecosθf=μNfloor, \begin{aligned}f&=\mu N_{\text{floor}},\end{aligned} f=μNfloor,$$ \.. 11판/12. 평형과 탄성 2024.10.09
12-28 할리데이 11판 솔루션 일반물리학 {2R=2.4[cm]m=670[kg]Esteel=200×109[N/m2]g=9.80665[m/s2] \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} ⎩⎨⎧2RmEsteelg=2.4[cm]=670[kg]=200×109[N/m2]=9.80665[m/s2]FA=EΔLL, {F\over A}= E{\Delta L\over L}, AF=ELΔL,ΔL=FLAE=mgLπR2E=67g2880000πL \begin{aligned}\Delta L&={ FL \over A E} \\&={ mgL \over \pi R^2 E} \\&={ 67g \over 2880000\pi } L\\\end{aligned} ΔL=AEFL=πR2EmgL=2880000π67gL(a)\ab{a}(a)$$ \begin{aligned}\Delta L&={ 67g \over 2880000\pi } L\\&=\frac{13140911}{4800000000 \pi }\ut{m}\\&\approx.. 11판/12. 평형과 탄성 2024.10.08
12-27 할리데이 11판 솔루션 일반물리학 {θ=36.9°ϕ=53.1°L=4.35[m] \begin{cases} \theta&=36.9\degree\\\phi&=53.1\degree\\L&=4.35\ut{m}\\\end{cases} ⎩⎨⎧θϕL=36.9°=53.1°=4.35[m]L=x+y,L=x+y,L=x+y,{ΣFx=0ΣFy=0Στ=0 \begin{cases} \Sigma F_{x}&=0\\\Sigma F_{y}&=0\\\Sigma \tau&=0\\\end{cases} ⎩⎨⎧ΣFxΣFyΣτ=0=0=0{0=−T1sinθ+T2sinϕ0=T1cosθ+T2cosϕ−mg0=−xT1cosθ+yT2cosϕ \begin{cases} 0&=-T_1\sin\theta+T_2\sin\phi\\0&=T_1\cos\theta+T_2\cos\phi-mg\\0&=-xT_1\cos\theta+yT_2\cos\phi\\\end{cases} ⎩⎨⎧000=−T1sinθ+T2sinϕ=T1cosθ+T2cosϕ−mg=−xT1cosθ+yT2cosϕ$$ \begin{aligned}x&={\cos\phi\sin\theta\over\sin\br{\theta+\phi}}L\\&=L \sin ^236.9\degree\\.. 11판/12. 평형과 탄성 2024.10.07
12-26 할리데이 11판 솔루션 일반물리학 {mg=60[N]L=3.2[m]F=50[N]θ=25°h=2.0[m] \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} ⎩⎨⎧mgLFθh=60[N]=3.2[m]=50[N]=25°=2.0[m]{ΣFx=0ΣFy=0Στ=0 \begin{cases} \Sigma F_{x}&=0\\\Sigma F_{y}&=0\\\Sigma \tau&=0\\\end{cases} ⎩⎨⎧ΣFxΣFyΣτ=0=0=0{0=F+Nx−Tcosθ0=Ny−mg−Tsinθ0=hTcosθ−LF \begin{cases} 0&=F+N_x-T\cos\theta\\0&=N_y-mg-T\sin\theta\\0&=hT\cos\theta-LF\\\end{cases} ⎩⎨⎧000=F+Nx−Tcosθ=Ny−mg−Tsinθ=hTcosθ−LF{T=FLhcosθNx=F(L−h)hNy=FLhtanθ+mg \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} ⎩⎨⎧TNxNy=hcosθFL=hF(L−h)=hFLtanθ+mg$$\ab.. 11판/12. 평형과 탄성 2024.10.07
12-25 할리데이 11판 솔루션 일반물리학 {2R=4.8[cm]L=5.3[cm]m=1500[kg]G=3.0×1010[N/m2]g=9.80665[m/s2] \begin{cases} 2R&=4.8\ut{cm}\\L&=5.3\ut{cm}\\m&=1500\ut{kg}\\G&=3.0\times10^{10}\ut{N/m^2}\\g&=9.80665\ut{m/s^2}\\\end{cases} ⎩⎨⎧2RLmGg=4.8[cm]=5.3[cm]=1500[kg]=3.0×1010[N/m2]=9.80665[m/s2](a)\ab{a}(a)F=mg=14709.975[N]≈1.5×104[N]≈15[kN] \begin{aligned}F&=mg\\&=14709.975\ut{N}\\&\approx 1.5\times10^4\ut{N}\\&\approx 15\ut{kN}\\\end{aligned} F=mg=14709.975[N]≈1.5×104[N]≈15[kN](b)\ab{b}(b)FA=GΔxL,{F\over A}=G{\Delta x\over L},AF=GLΔx,$$ \begin{aligned}\Delta x&={FL\over AG}\\&={Lmg\over \pi R^2 G}\\&=\frac{53 g}{11520000 \pi }\ut{m}\\&.. 11판/12. 평형과 탄성 2024.10.07
12-24 할리데이 11판 솔루션 일반물리학 {θ1=51.0°θ2=66.0°m=704[kg]g=9.80665[m/s2] \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} ⎩⎨⎧θ1θ2mg=51.0°=66.0°=704[kg]=9.80665[m/s2](a)\ab{a}(a)TA=mg=6.9038816×103[N]≈6.90×103[N]≈6.90[kN] \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} TA=mg=6.9038816×103[N]≈6.90×103[N]≈6.90[kN](b,c)\ab{b,c}(b,c){θ=θ1+θ2−90°=27.0°ϕ=90°−θ2=24.0° \begin{cases} \theta&=\theta_1+\theta_2-90\degree&=27.0\degree\\\phi&=90\degree-\theta_2&=24.0\degree\\\end{cases} {θϕ=θ1+θ2−90°=90°−θ2=27.0°=24.0°$$ \begin{aligned}0.. 11판/12. 평형과 탄성 2024.10.07
12-23 할리데이 11판 솔루션 일반물리학 {rA=7.0[cm]rB=4.0[cm]R=4.0[cm]F=220[N] \begin{cases} r_A&=7.0\ut{cm}\\r_B&=4.0\ut{cm}\\R&=4.0\ut{cm}\\F&=220\ut{N}\\\end{cases} ⎩⎨⎧rArBRF=7.0[cm]=4.0[cm]=4.0[cm]=220[N]{0=F−NA+NB0=RF−rANA−rBNB \begin{cases} 0&=F-N_A+N_B\\0&=RF-r_AN_A-r_BN_B\end{cases} {00=F−NA+NB=RF−rANA−rBNB{NA=R+rB2rBFNB=R−rB2rBF \begin{cases} N_A&=\cfrac{R+r_B}{2r_B}F\\N_B&=\cfrac{R-r_B}{2r_B}F\\\end{cases} ⎩⎨⎧NANB=2rBR+rBF=2rBR−rBF(a,b)\ab{a,b}(a,b){NA=220[N]NB=0 \begin{cases} N_A&=220\ut{N}\\N_B&=0\\\end{cases} {NANB=220[N]=0 11판/12. 평형과 탄성 2024.10.04
12-22 할리데이 11판 솔루션 일반물리학 put {A:Top BallB:Bottom BallL:Left WallR:Right WallG:Ground \put \begin{cases} A : \text{Top Ball}\\B : \text{Bottom Ball}\\L : \text{Left Wall}\\R : \text{Right Wall}\\G : \text{Ground}\\\end{cases} put ⎩⎨⎧A:Top BallB:Bottom BallL:Left WallR:Right WallG:Ground{ΣFAx=0ΣFAy=0ΣFBx=0ΣFBy=0 \begin{cases} \Sigma F_{Ax}&=0\\\Sigma F_{Ay}&=0\\\Sigma F_{Bx}&=0\\\Sigma F_{By}&=0\\\end{cases} ⎩⎨⎧ΣFAxΣFAyΣFBxΣFBy=0=0=0=0{0=NABx−NR0=NABy−mg0=NL−NABx0=NG−NABy−mg \begin{cases} 0&=N_{ABx}-N_R\\0&=N_{ABy}-mg\\0&=N_L-N_{ABx}\\0&=N_G-N_{ABy}-mg\\\end{cases} ⎩⎨⎧0000=NABx−NR=NABy−mg=NL−NABx=NG−NABy−mgθ=45°⇒NABx=NABy\theta=45\degree\Rarr N_{ABx}=N_{ABy}θ=45°⇒NABx=NABy$$\ab{a,b,c,.. 11판/12. 평형과 탄성 2024.06.30
12-21 할리데이 11판 솔루션 일반물리학 {L=2.00[m]m=78.0[kg]dh=3.00[m]dv=4.00[m]g=9.80665[m/s2] \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} ⎩⎨⎧Lmdhdvg=2.00[m]=78.0[kg]=3.00[m]=4.00[m]=9.80665[m/s2]x1=dh−L2,x_1=d_h-{L\over2},x1=dh−2L,θ=tan−1dhdv\theta=\tan^{-1}{d_h\over d_v}θ=tan−1dvdh{ΣFx=0ΣFy=0Στ=0 \begin{cases} \Sigma F_{x}&=0\\\Sigma F_{y}&=0\\\Sigma \tau&=0\\\end{cases} ⎩⎨⎧ΣFxΣFyΣτ=0=0=0{0=Nx−Tsinθ0=Ny+Tcosθ−mg0=−x1mg+Tdhcosθ \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} ⎩⎨⎧000=Nx−Tsinθ=Ny+Tcosθ−mg=−x1mg+Tdhcosθ(a)\ab{a}(a)$$ \begin{aligned}T&= {x_1 mg\over.. 11판/12. 평형과 탄성 2024.06.30