5-31 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} m&=6.3\ut{kg}\\ \vec F_1&=-11\i\ut{N}\\ \vec F_2&=-25\j\ut{N}\\ \vec F_3&=6.0\i\ut{N}\\ F_4&=14\ut{N},\theta_4&=30\degree\\ \vec F_5&=5.0\j\ut{N}\\ \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} \vec a&=\frac{1}{m}\Sigma \vec F\\ &=\frac{1}{6.3}\bra{\(7\sqrt3-5\)\i-13\j}\ut{m/s^2}\\ &=\frac{10\(7 \sqrt{3}-5\)}{63} \i-\frac{130}{63}\j\ut{m/s^2}\\ &\approx 1.1\i-2.1\j\ut{m/s^2}\\ \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} a&=\sqrt{\bra{\frac{10\(7 \sqrt{3}-5\)}{63}}^2+\(\frac{130}{63}\)^2}\ut{m/s^2}\\ &=\frac{10}{63} \sqrt{341-70 \sqrt{3}}\ut{m/s^2}\\ &\approx 2.353045144704056\ut{m/s^2}\\ &\approx 2.4\ut{m/s^2}\\ \end{aligned} $$ $$\ab{c}$$ $$ \begin{aligned} \theta&=\tan ^{-1}\frac{13}{5-7 \sqrt{3}}\\ &\approx -1.069468881780697\ut{rad}\\ &\approx -1.07\ut{rad}\\ \end{aligned} $$