Problem 6.75

สมมติให้หลังการระเบิด วัตถุทั้งสามชิ้นมีอัตราเร็ว v

จาก \(\Delta K = \Sigma K_{f}- \Sigma K_{i}\)

\(\Delta K =\frac{|\vec{p}_{1}|^{2} + |\vec{p}_{2}|^{2} + |\vec{p}_{3}|^{2}}{2m}-\frac{(3m)^{2}u^{2}}{2(3m)}\)

\(\Delta K =\frac{|\vec{p}_{1}|^{2} + |\vec{p}_{2}|^{2} + |\vec{p}_{3}|^{2}}{2m}-\frac{3mu^{2}}{2}\cdots \cdots (1)\)

จาก \(|\Sigma \vec{p}_{f}|^{2} = |\vec{p}_{1}|^{2} + |\vec{p}_{2}|^{2} + |\vec{p}_{3}|^{2}\)

\(|\Sigma \vec{p}_{i}|^{2} = |\vec{p}_{1}|^{2} + |\vec{p}_{2}|^{2} + |\vec{p}_{3}|^{2}\)

\((3mu)^{2} = |\vec{p}_{1}|^{2} + |\vec{p}_{2}|^{2} + |\vec{p}_{3}|^{2}\cdots \cdots (2)\)

\((2)\) แทนใน \((1)\) จะได้ \(ΔK = \frac{(3mu)^{2}}{2m}-\frac{3mu^{2}}{2}\)

\(\Delta K =\frac{(3mu)^{2}}{2m}-\frac{3mu^{2}}{2}\)

\(\Delta K = 3mu^{2} \;\blacksquare\)