content(warnings): Add W6-W7, X2-X3, N4 — energy misconceptions + cross-refs

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2026-05-04 23:36:54 -05:00
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@@ -17,6 +17,8 @@ Thus the work done by the conservative force is
W_c=-\Delta U.
\]}
\wc{Potential energy belongs to a system}{Gravitational $U=mgh$ requires both the object \emph{and} the Earth. Spring $U=\tfrac12 kx^2$ requires both the block \emph{and} the spring. An isolated single object cannot have potential energy --- it is stored in the \emph{interaction}.}
\thm{Equivalent conservative-force relations}{Let $\vec{F}_c$ denote a conservative force and let $d\vec{r}$ denote an infinitesimal displacement. Then the following relations hold:
\[
\oint \vec{F}_c\cdot d\vec{r}=0,
@@ -146,3 +148,5 @@ W_s=+2.25\,\mathrm{J},
\qquad
v_f=3.0\,\mathrm{m/s}.
\]
The same spring restoring force $-kx$ governs the simple harmonic motion studied in Unit 7 (Sections 7.1--7.4).