8-73 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} m&=12.0\ut{kg}\\ x_1&=10.0\ut{cm}=0.1\ut{m}\\ \Delta x&=30.0\ut{cm}=0.3\ut{m}\\ g&=9.80665\ut{m/s^2}\\ \end{cases} $$ $$x_2=x_1+\Delta x=0.4\ut{m}$$ $$ \put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \LE : \text{Elastic Potential Energy}\\ \end{cases} $$ $$\ab{a}$$ $$F=kx,$$ $$ \begin{aligned} k&=\frac{F}{x}\\ &=\frac{mg}{x_1}\\ &=120g\\ &=1176.798\ut{N/m}\\ &\approx 1.18\times10^3\ut{N/m}\\ &\approx 1.18\ut{kN/m}\\ \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} \LE_i&=\frac{1}{2}kx^2\\ &=\frac{1}{2}\(\frac{mg}{x_1}\){x_2}^2\\ &=\frac{48g}{5}\\ &=94.14384\ut{J}\\ &\approx 94.1\ut{J}\\ \end{aligned} $$ $$\ab{c}$$ $$\Sigma \Delta E=0,$$ $$\Delta \KE+\Delta \GE+\Delta \LE=0$$ $$ \begin{aligned} \Delta \GE&=-\Delta \LE-\Delta \KE\\ &=-\Delta \LE\\ &=\LE_i-\LE_f\\ &=\LE_i\\ &=94.14384\ut{J}\\ &\approx 94.1\ut{J}\\ \end{aligned} $$ $$\ab{d}$$ $$\GE=mgh,$$ $$ \begin{aligned} h&=\frac{\GE}{mg}\\ &=\frac{\frac{1}{2}\(\frac{mg}{x_1}\){x_2}^2}{mg}\\ &=\frac{{x_2}^2}{2x_1}\\ &=\frac{4}{5}\ut{m}\\ &=0.8\ut{m}\\ &=0.80\ut{m}\\ &=80\ut{cm}\\ \end{aligned} $$