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Skill 9 of 14
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Energy conservation vs momentum conservation

Roll a cart off a hillside towards a bridge. Energy conservation can easily tell that the energy stored to begin with, in moment $\unicode{x2460}$, turns into kinetic energy in moment $\unicode{x2461}$. From this, we can easily figure out the speed $v_2$ that the cart will reach:

$$\begin{align}\unicode{x2460}&\rightarrow \unicode{x2461}\\
E_1+\cancel W_{1\rightarrow 2}+\cancel Q_{1\rightarrow 2}&=E_2\\
\underbrace{U_{g,1}}_{E_1}&=\underbrace{K_2}_{E_2}\\
mgh_1&=\frac 12mv_2^2\end{align}$$

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