David Gronlund edited Analysis and Interpretation.tex  over 9 years ago

Commit id: 036a3a3b47a4a64d87f68b70e5da5c8d4274c4b4

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\vec p\sub{total,i} &= \vec p\sub{1i} + \vec p\sub{2i}\\  &= \vec r\sub{1i} / \Delta t * m\sub{1} + \vec r\sub{2i} / \Delta t * m\sub{2}\\  &= \langle2.4,1.5\rangle \sci{-2} \units m * 0.146 \units kg / 0.456 \units s + \langle-1.5,1.8\rangle \sci{-2} \units m * 0.057 \units kg / 0.456 \units s\\  &= \langle7.68,4.80\rangle \sci{-3} \langle0.030,0.019\rangle  \units kgm/s + \langle-4.80,5.76\rangle \sci{-3} \langle-0.048,0.058\rangle  \units kgm/s\\ &= \langle2.88,10.56\rangle \sci{-3} \langle-0.018,0.077\rangle \units kgm/s  \end{align}  and again for the final momentum  \begin{align}  \vec p\sub{total,f} &= \vec p\sub{1f} + \vec p\sub{2f}\\  &= \vec r\sub{1f} / \Delta t * m\sub{1} + \vec r\sub{2f} / \Delta t * m\sub{2}\\  &= \langle-2.5,1.6\rangle \sci{-2} \units m * 0.146 \units kg / 0.456 \units s + \langle0.4,1.6\rangle \sci{-2} \units m * 0.057 \units kg / 0.456 \units s\\  &= \langle-0.03,0.02\rangle \units kgm/s + \langle0.013,0.051\rangle \units kgm/s\\  &= \langle-0.017,0.071\rangle  \units kgm/s \end{align}