5-11 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} F_1 &= 23\ut{N}\\ F_2 &= 38\ut{N}\\ \theta &= 80\degree\\ a&= 15\ut{m/s^2} \end{cases} $$ $$ \begin{aligned} &\text{Law of cosines,}\\ c^2&=a^2+b^2-2ab\cos\theta,\\ {F_S}^2 &= {F_1}^2+{F_2}^2-2 F_1 F_2 \cos(\pi-\theta) \\ &={F_1}^2+{F_2}^2+2F_1F_2\cos\theta\\ \end{aligned} $$ $$ \begin{aligned} F_S&=\sqrt{{F_1}^2+{F_2}^2+2F_1F_2\cos\theta}\\ &=\sqrt{{23}^2+{38}^2+2\cdot23\cdot38 \cos80 \degree }\\ &=\sqrt{1748 \sin10\degree+1973} \end{aligned} $$ $$ \begin{aligned} m&=\frac{F_S}{a}\\ &=\frac{\sqrt{1748 \sin10\degree+1973}}{15}\ut{kg}\\ &\approx 3.180871309396422\ut{kg}\\ &\approx 3.2\ut{kg}\\ \end{aligned} $$