11판/1. 측정

1-11 할리데이 11판 솔루션 일반물리학

짱세디럭스 2022. 9. 30. 04:39

{1[acre]=4047[m2]1[ft]=12[in]1[in]=2.54[cm]S=17[km2]h=2.0[in] \begin{cases} 1\ut{acre} &= 4047\ut{m^2}\\ 1\ut{ft} &= 12\ut{in}\\ 1\ut{in} &= 2.54\ut{cm}\\ S &= 17\ut{km^2}\\ h &= 2.0\ut{in}\\ \end{cases} (a)\ab{a} V=Sh=(17[km2])(2.0[in])={17[km2](1000[m]1[km])21[acre]4047[m2]}(2.0[in]1[ft]12[in])=17100022.0404712[acreft]=850000012141[acreft]700.1070752[acreft]7.0×102[acreft] \begin{aligned} V &= S \cdot h \\ &= (17\ut{km^2}) \cdot (2.0\ut{in})\\ &=\bra{17\ut{km^2} \cdot \(\cfrac{1000\ut{m}}{1\ut{km}}\)^2 \cdot \cfrac{1\ut{acre}}{4047\ut{m^2}}}\cdot\(2.0\ut{in}\cdot\cfrac{1\ut{ft}}{12\ut{in}}\)\\ &=\cfrac{17\cdot1000^2\cdot2.0}{4047\cdot12}\ut{acre-ft}\\ &=\cfrac{8500000}{12141}\ut{acre-ft}\\ &\approx700.1070752\ut{acre-ft}\\ &\approx7.0\times10^2\ut{acre-ft} \end{aligned} (b)\ab{b} ρ=1.0×103[kg/m3]\rho=1.0\times10^3\ut{kg/m^3} V=Sh=(17[km2])(2.0[in])={17[km2](1000[m]1[km])2}(2.0[in]2.54[cm]1[in]1[m]100[cm])=17100022.02.54100[m3]=863600[m3] \begin{aligned} V &= S \cdot h \\ &= (17\ut{km^2}) \cdot (2.0\ut{in})\\ &=\bra{17\ut{km^2} \cdot \(\cfrac{1000\ut{m}}{1\ut{km}}\)^2 }\cdot\(2.0\ut{in}\cdot\cfrac{2.54\ut{cm}}{1\ut{in}}\cdot\cfrac{1\ut{m}}{100\ut{cm}}\)\\ &=\cfrac{17\cdot1000^2\cdot2.0\cdot2.54}{100}\ut{m^3}\\ &=863600\ut{m^3} \end{aligned} m=ρV=1.0×103[kg/m3]863600[m3]=863600000[kg]8.6×108[kg]8.6×105[ton]0.86[megaton] \begin{aligned} m&=\rho \cdot V\\ &=1.0\times10^3\ut{kg/m^3}\cdot863600\ut{m^3}\\ &=863600000\ut{kg}\\ &\approx 8.6\times10^8\ut{kg}\\ &\approx 8.6\times10^5\ut{ton}\\ &\approx 0.86\ut{megaton}\\ \end{aligned}

풀이자주 : 톤이나 메가톤 단위는 SI비표준이므로 필수적인 표현은 아니나 풀이자가 좋아해서 넣었음.