11판/9. 질량중심과 선운동량

9-59 할리데이 11판 솔루션 일반물리학

짱세디럭스 2024. 4. 30. 21:20
{m2=1.0[kg]v2i=0k=490[N/m]m1=2.0[kg]M=m1+m2=3[kg]v1i=4.0[m/s] \begin{cases} m_2&=1.0\ut{kg}\\ v_{2i}&=0\\ k&=490\ut{N/m}\\ m_1&=2.0\ut{kg}\\ M&=m_1+m_2=3\ut{kg}\\ v_{1i}&=4.0\ut{m/s}\\ \end{cases} ΔΣp=0,\Delta \Sigma \vec p=0, m1v1i=Mvf,vf=m1Mv1i \begin{aligned} m_1v_{1i}&=Mv_f,\\ v_f&=\frac{m_1}{M}v_{1i} \end{aligned} ΣΔE=0,\Sigma \Delta E=0, 12Mvf2=12kx2\frac{1}{2}M{v_f}^2=\frac{1}{2}kx^2 x=vfMk=m1v1iMk=47215[m]0.2086562123829204[m]0.21[m]21[cm] \begin{aligned} x&=v_f\sqrt\frac{M}{k}\\ &=\frac{m_1v_{1i}}{\sqrt{Mk}}\\ &=\frac{4}{7}\sqrt{\frac{2}{15}}\ut{m}\\ &\approx 0.2086562123829204\ut{m}\\ &\approx 0.21\ut{m}\\ &\approx 21\ut{cm}\\ \end{aligned}