5-35 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} m&=4.00\ut{kg}\\ \vec F_1 &= 18.0\i\ut{N}\\ a&=14.0\ut{m/s^2},\theta_a=20.0\degree\\ \end{cases} $$ $$\ab{a}$$ $$\Sigma \vec F = m\vec a,$$ $$\vec F_1 +\vec F_2= m \vec a$$ $$ \begin{aligned} \vec F_2&= m \vec a-\vec F_1\\ &=4\br{-14\sin20\degree\i-14\cos20\degree}-18\i\ut{N}\\ &={\br{-56\sin20\degree-18}\i-56\cos20\degree\j}\ut{N}\\ &\approx -37.15312802623745\i-52.62278676401087\j\ut{N} \\ &\approx -37.2\i-52.6\j\ut{N} \\ \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} F_2 &=\sqrt{\br{-56\sin20\degree-18}^2+\(-56\cos20\degree\)^2}\\ &=2 \sqrt{504 \sin 20 \degree+865}\ut{N}\\ &\approx 64.41671063431095\ut{N}\\ &\approx 64.4\ut{N}\\ \end{aligned} $$ $$\ab{c}$$ $$ \begin{aligned} \theta&=\tan^{-1}\frac{-56\cos20\degree}{-56\sin20\degree-18}\\ &\approx -2.18555606539747\ut{rad}\\ &\approx -2.19\ut{rad}\\ \end{aligned} $$