content(warnings): Add W3-W5, N2-N3 — drag, work, and rolling warnings + notes
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@@ -10,6 +10,10 @@ The negative sign means that the drag force always points opposite the velocity.
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If an object falls vertically through the fluid and eventually moves with constant velocity, that steady velocity is called the \emph{terminal velocity}. At terminal velocity, the net force is zero, so the acceleration is zero.}
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\wc{Terminal velocity is not zero speed}{Terminal velocity is a \emph{nonzero constant speed}: the object is still moving, but its acceleration is zero because drag balances the driving force. The object approaches $v_T$ asymptotically as $t\to\infty$; it never stops.}
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\wc{Drag force is not kinetic friction}{Drag $F_D=bv$ or $F_D=\tfrac12 C\rho A v^2$ is velocity-dependent and acts in fluids. Kinetic friction $f_k=\mu_k N$ is approximately velocity-independent and acts at solid-solid contacts. They are physically distinct interactions.}
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\thm{Vertical-fall ODE and terminal-speed result}{Choose the vertical axis positive downward. Let $v(t)$ denote the downward velocity of an object of mass $m$ at time $t$, let $g$ denote the gravitational field strength, and let $b>0$ denote the linear-drag coefficient. Then the vertical equation of motion is
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\[
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m\frac{dv}{dt}=mg-bv.
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