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zWi!@CMXk(_-to;gXU}YL>pkHFZeJa#@@?Q3xS{?qdx+J9c3;mrQ&>5CGzeV_Di z^Zrk`_v!sjS=-XOYx}KR_E=d;f3Q1RFZs*<#iCC?rwi}o&IxidH#D>`H#RgeH*z#J zHZe9gaB^{Tb2V_WFf?{-mJ;UUOHV0RGv6Pg{SS7j#lsKD8bpCu`Mo1g7pmV zi>LYTd%h>Xuj7Qg${wu=y>p(v3b0Xf6tMQ%+ozl|$Cjt-zs^1&ynFkTX)O27`Tq@awK-67t?p!Aq}Tp$Ute4d+9ety zTE?>P#N^bEXNorD?K~MV?{w9ISw9}w>c6n?ob(}dAM3x8sB+UI{PnNAAE=m>JQtWQ zA*8T%N#B*pY?nM{c}!^Wm|=3*^VruAmUHjg!?@?{HeDNLv0iem*^Y^}Ys+?6a&L~3 zE$Hrz3fwW(d#%Ks@9b+Wd^FZy*v6&&4s;aBM8y5i5?hUN~ diff --git a/physics/final.tex b/physics/final.tex index fabacef..1db6640 100644 --- a/physics/final.tex +++ b/physics/final.tex @@ -68,18 +68,18 @@ $\Sigma F, a$ towards centre, $v$ tangential - $F_{centrip} = {{mv^2} \over r} = {{4 \pi^2 rm} \over T^2}$ + $\Sigma F = F_{centrip} = {{mv^2} \over r} = {{4 \pi^2 rm} \over T^2}=T \sin \theta = mg \tan \theta$ \includegraphics[height=4cm]{graphics/circ-forces.png} % ----------------------- \subsection*{Vertical circular motion} - $T =$ tension, e.g. circular pendulum + % $T =$ tension, e.g. circular pendulum - $T+mg = {{mv^2}\over r}$ at highest point + $T+mg = {{mv^2}\over r}, v = \sqrt{rg}$ (top) - $T-mg = {{mv^2} \over r}$ at lowest point + $T-mg = {{mv^2} \over r}, v = \sqrt{2rg}$ (bottom) $E_K_{\text{bottom}}=E_K_{\text{top}}+mgh$ @@ -115,7 +115,7 @@ \item{Force-time: $A=\Delta \rho$} \item{Force-disp: $A=W$} \item{Force-ext: $m=k,\quad A=E_{spr}$} - \item{Force-dist: $A=\Delta \operatorname{gpe}$} + \item{$F_g$-dist: $A=\Delta \operatorname{gpe}$} \item{Field-dist: $A=\Delta \operatorname{gpe} / \operatorname{kg}$} \end{itemize} @@ -340,7 +340,7 @@ \includegraphics[height=4cm]{graphics/dc-motor-2.png} \includegraphics[height=3cm]{graphics/ac-motor.png} \\ - Force on current-carying wire, not copper \\ + Force on I-carying wire, not Cu \\ $F=0$ for front & back of coil (parallel) \\ Any angle $> 0$ will produce force \\ % \end{wrapfigure} @@ -428,9 +428,10 @@ % \(\Delta x\) = fringe spacing \\ \(l\) = distance from source to observer\\ \(d\) = separation between each wave source (e.g. slit) \(=S_1-S_2\) - \item diffraction $\propto {\lambda \over d}$ + \item diffraction $\propto {\lambda \over d} \propto$ fringe spacing + \item $d(|\overrightarrow{S_1W}|-|\overrightarrow{S_2W}|)=d \Delta x = \lambda l$ \item significant diffraction when ${\lambda \over \Delta x} \ge 1$ - \item diffraction creates distortion (electron $>$ optical microscopes) + \item diffraction creates distortion (electron $\gt$ optical microscopes) \end{itemize} @@ -553,7 +554,9 @@ $f \cdot V$ & ${h \over q}$ & $f_0$ & $-\phi \over q$ & \subsection*{Uncertainty principle} - measuring location of an e- requires hitting it with a photon, but this causes $\rho$ to be transferred to electron, moving it. + $\Delta x \approx {\text{slit width} \over 2$} + + measurement: $\rho$ transferred to e-\\ slit: possibility of diff. before slit \subsection*{Wave-particle duality} -- 2.52.0