From: Andrew Lorimer Date: Sun, 22 Jul 2018 05:52:01 +0000 (+1000) Subject: rendered physics stuff X-Git-Tag: yr11~85 X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/f239b400194361fa6603c4e34aa3b3ddaeeedeab?ds=sidebyside rendered physics stuff --- diff --git a/physics/midyear.fdb_latexmk b/physics/midyear.fdb_latexmk index 8d8598f..48a4005 100644 --- a/physics/midyear.fdb_latexmk +++ b/physics/midyear.fdb_latexmk @@ -1,5 +1,5 @@ # Fdb version 3 -["pdflatex"] 1531987725 "midyear.tex" "midyear.pdf" "midyear" 1531987726 +["pdflatex"] 1532049248 "midyear.tex" "midyear.pdf" "midyear" 1532049249 "/mnt/andrew/graphics/ac-generator.png" 1529320281 28991 f74a831edcaed66632e709a6b2e2ebfd "" "/mnt/andrew/graphics/ac-motor.png" 1529313736 18626 d0f4943be26fdce44a4ce45ccb01633c "" "/mnt/andrew/graphics/banked-track.png" 1531025364 51228 cc5d8f3f8efb06a64aca4afabfd63eed "" @@ -70,9 +70,9 @@ "/usr/share/texmf-dist/web2c/texmf.cnf" 1525040116 33301 a3134070eacafb10b1f371612ce2650d "" "/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map" 1530607795 2586890 ddabbb88c498d59d5daa7919afb0a27f "" "/var/lib/texmf/web2c/pdftex/pdflatex.fmt" 1530607774 7906415 c2bc2a1e85cbebe301ae391211242f7e "" - "midyear.aux" 1531987726 223 c9c8cc73e6c5d1c4bae220d8eb29b53c "" - "midyear.tex" 1531987725 9117 4a1990d0b0ea8d63b7cd19f496ac4706 "" + "midyear.aux" 1532049249 223 c9c8cc73e6c5d1c4bae220d8eb29b53c "" + "midyear.tex" 1532049248 9329 b74d77b1da90c209352ffa9ba1392fc8 "" (generated) - "midyear.log" - "midyear.pdf" "midyear.aux" + "midyear.pdf" + "midyear.log" diff --git a/physics/midyear.fls b/physics/midyear.fls index fd1ed4e..a75a253 100644 --- a/physics/midyear.fls +++ b/physics/midyear.fls @@ -76,8 +76,6 @@ INPUT /usr/share/texmf-dist/fonts/map/fontname/texfonts.map INPUT /usr/share/texmf-dist/fonts/tfm/public/cm/cmr17.tfm INPUT /usr/share/texmf-dist/fonts/tfm/public/cm/cmr12.tfm INPUT /usr/share/texmf-dist/fonts/tfm/public/cm/cmbx12.tfm -INPUT /usr/share/texmf-dist/fonts/tfm/public/cm/cmr12.tfm -INPUT /usr/share/texmf-dist/fonts/tfm/public/cm/cmbx12.tfm INPUT /usr/share/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm INPUT /usr/share/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm INPUT /usr/share/texmf-dist/tex/latex/amsfonts/umsa.fd @@ -90,6 +88,8 @@ INPUT /usr/share/texmf-dist/tex/latex/amsfonts/umsb.fd INPUT /usr/share/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm10.tfm INPUT /usr/share/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm7.tfm INPUT /usr/share/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm5.tfm +INPUT /usr/share/texmf-dist/fonts/tfm/public/cm/cmr12.tfm +INPUT /usr/share/texmf-dist/fonts/tfm/public/cm/cmbx12.tfm INPUT /mnt/andrew/graphics/banked-track.png INPUT /mnt/andrew/graphics/banked-track.png OUTPUT midyear.pdf diff --git a/physics/midyear.log b/physics/midyear.log index 60f4e25..26cfccd 100644 --- a/physics/midyear.log +++ b/physics/midyear.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.14159265-2.6-1.40.19 (TeX Live 2018/Arch Linux) (preloaded format=pdflatex 2018.7.3) 19 JUL 2018 18:08 +This is pdfTeX, Version 3.14159265-2.6-1.40.19 (TeX Live 2018/Arch Linux) (preloaded format=pdflatex 2018.7.3) 20 JUL 2018 11:14 entering extended mode restricted \write18 enabled. file:line:error style messages enabled. @@ -239,24 +239,24 @@ Package grfext Info: Graphics extension search list: (/usr/share/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg File: epstopdf-sys.cfg 2010/07/13 v1.3 Configuration of (r)epstopdf for TeX Live )) -LaTeX Font Info: Try loading font information for U+msa on input line 28. +LaTeX Font Info: Try loading font information for U+msa on input line 27. (/usr/share/texmf-dist/tex/latex/amsfonts/umsa.fd File: umsa.fd 2013/01/14 v3.01 AMS symbols A ) -LaTeX Font Info: Try loading font information for U+msb on input line 28. +LaTeX Font Info: Try loading font information for U+msb on input line 27. (/usr/share/texmf-dist/tex/latex/amsfonts/umsb.fd File: umsb.fd 2013/01/14 v3.01 AMS symbols B ) File: /mnt/andrew/graphics/banked-track.png Graphic file (type png) -Package pdftex.def Info: /mnt/andrew/graphics/banked-track.png used on input line 33. +Package pdftex.def Info: /mnt/andrew/graphics/banked-track.png used on input line 35. (pdftex.def) Requested size: 151.73839pt x 113.81102pt. Package amsmath Warning: Foreign command \over; (amsmath) \frac or \genfrac should be used instead -(amsmath) on input line 35. +(amsmath) on input line 37. File: /mnt/andrew/graphics/circ-forces.png Graphic file (type png) @@ -272,10 +272,10 @@ LaTeX Font Info: Font shape `OMS/cmr/m/n' in size <10> not available File: /mnt/andrew/graphics/projectile-motion.png Graphic file (type png) -Package pdftex.def Info: /mnt/andrew/graphics/projectile-motion.png used on input line 94. +Package pdftex.def Info: /mnt/andrew/graphics/projectile-motion.png used on input line 96. (pdftex.def) Requested size: 164.9011pt x 91.04872pt. -Overfull \hbox (0.85123pt too wide) in paragraph at lines 94--95 +Overfull \hbox (0.85123pt too wide) in paragraph at lines 96--97 [][] [] @@ -285,50 +285,60 @@ Overfull \hbox (0.85123pt too wide) in paragraph at lines 94--95 File: /mnt/andrew/graphics/field-lines.png Graphic file (type png) -Package pdftex.def Info: /mnt/andrew/graphics/field-lines.png used on input line 267. +Package pdftex.def Info: /mnt/andrew/graphics/field-lines.png used on input line 222. (pdftex.def) Requested size: 172.75461pt x 56.9055pt. -Overfull \hbox (8.70474pt too wide) in paragraph at lines 267--268 +Overfull \hbox (8.70474pt too wide) in paragraph at lines 222--223 [][] [] +./midyear.tex:301: Missing $ inserted. + + $ +l.301 P_ + {\operatorname{loss}} = \Delta V I = I^2 R = {{\Delta V^2} \ov... +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +./midyear.tex:304: Missing $ inserted. + + $ +l.304 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + File: /mnt/andrew/graphics/ac-generator.png Graphic file (type png) -Package pdftex.def Info: /mnt/andrew/graphics/ac-generator.png used on input line 310. +Package pdftex.def Info: /mnt/andrew/graphics/ac-generator.png used on input line 312. (pdftex.def) Requested size: 149.97623pt x 113.81102pt. 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(pdftex.def) Requested size: 114.0009pt x 85.35826pt. -Underfull \hbox (badness 10000) in paragraph at lines 316--320 +Underfull \hbox (badness 10000) in paragraph at lines 318--322 [] [] - -Overfull \vbox (7.05737pt too high) has occurred while \output is active [] - - -Overfull \vbox (6.46721pt too high) has occurred while \output is active [] - - [2 ] (./midyear.aux) ) +[2 ] (./midyear.aux) ) Here is how much of TeX's memory you used: 2872 strings out of 492649 39467 string characters out of 6135779 - 145807 words of memory out of 5000000 + 136807 words of memory out of 5000000 6704 multiletter control sequences out of 15000+600000 7156 words of font info for 28 fonts, out of 8000000 for 9000 1141 hyphenation exceptions out of 8191 41i,10n,27p,274b,289s stack positions out of 5000i,500n,10000p,200000b,80000s -Output written on midyear.pdf (2 pages, 331247 bytes). +Output written on midyear.pdf (2 pages, 331326 bytes). PDF statistics: 69 PDF objects out of 1000 (max. 8388607) 43 compressed objects within 1 object stream diff --git a/physics/midyear.pdf b/physics/midyear.pdf index e86882b..fe8f6a4 100644 Binary files a/physics/midyear.pdf and b/physics/midyear.pdf differ diff --git a/physics/midyear.synctex.gz b/physics/midyear.synctex.gz index 353f42d..d23c75c 100644 Binary files a/physics/midyear.synctex.gz and b/physics/midyear.synctex.gz differ diff --git a/physics/midyear.tex b/physics/midyear.tex index 865a0ab..d522686 100644 --- a/physics/midyear.tex +++ b/physics/midyear.tex @@ -18,12 +18,14 @@ \begin{multicols}{3} % +++++++++++++++++++++++ - + {\huge Physics}\hfill Andrew Lorimer\hspace{2em} % +++++++++++++++++++++++ \section{Motion} + $\operatorname{m/s} \times 3.6 = \operatorname{km/h}$ + \subsection*{Inclined planes} $F = m g \sin\theta - F_{frict} = m a$ @@ -32,11 +34,11 @@ \includegraphics[height=4cm]{/mnt/andrew/graphics/banked-track.png} - $\theta = \tan^{-1} {{v^2} \over rg}$ (also for objects on string) + $$\theta = \tan^{-1} {{v^2} \over rg}$$ $\Sigma F$ always acts towards centre, but not necessarily horizontally - $\Sigma F = {{mv^2} \over r} = mg \tan \theta$ + $\Sigma F = F_{\operatorname{norm}} + F_{\operatorname{g}}={{mv^2} \over r} = mg \tan \theta$ Design speed $v = \sqrt{gr\tan\theta}$ @@ -52,9 +54,7 @@ $\Sigma E = {1 \over 2} mv^2 + mgh$ (energy transfer) % ----------------------- - \subsection*{Horizontal motion} - - $\operatorname{m/s} \times 3.6 = \operatorname{km/h}$ + \subsection*{Horizontal circular motion} $v = {{2 \pi r} \over T}$ @@ -62,7 +62,7 @@ $a_{centrip} = {v^2 \over r} = {{4 \pi^2 r} \over T^2}$ - $\Sigma F$ towards centre, $v$ tangential + $\Sigma F, a$ towards centre, $v$ tangential $F_{centrip} = {{mv^2} \over r} = {{4 \pi^2 rm} \over T^2}$ @@ -87,7 +87,9 @@ \begin{align*} v=\sqrt{v^2_x + v^2_y} \tag{vectors} \\ h={{u^2\sin \theta ^2}\over 2g} \tag{max height}\\ - y=ut \sin \theta-{1 \over 2}gt^2 \tag{time of flight} \\ + x=ut\cos\theta \tag{$\Delta x$ at $t$} \\ + y=ut \sin \theta-{1 \over 2}gt^2 \tag{height at $t$} \\ + t={{2u\sin\theta}\over g} \tag{time of flight}\\ d={v^2 \over g}\sin \theta \tag{horiz. range} \\ \end{align*} @@ -135,7 +137,7 @@ $\operatorname{impulse} = \Delta \rho, \quad F \Delta t = m \Delta v$ - Momentum is conserved. + $\Sigma mv_0=\Sigma mv_1$ (conservation) $\Sigma E_{K \operatorname{before}} = \Sigma E_{K \operatorname{after}}$ if elastic @@ -190,20 +192,11 @@ $$v={\rho \over {m\sqrt{1+{p^2 \over {m^2 c^2}}}}}$$ -% ----------------------- - \subsection*{Fusion and fission} - - $1 \operatorname{eV} = 1.6 \times 10^{-19} \operatorname{J}$ - - e- accelerated with $x$ V is given $x$ eV - % ----------------------- \subsection*{High-altitude muons} \begin{itemize} {\item $t$ dilation - more muons reach Earth than expected} - {\item normal half-life is $2.2 \operatorname{\mu s}$ in stationary frame} - {\item at $v \approx c$, muons observed from Earth have halflife $> 2.2 \operatorname{\mu s}$} - {\item slower time - more time to travel, so muons reach surface} + {\item normal half-life $2.2 \operatorname{\mu s}$ in stationary frame, $> 2.2 \operatorname{\mu s}$ observed from Earth} \end{itemize} % +++++++++++++++++++++++ @@ -222,27 +215,27 @@ \item monopoles: lines towards centre \item dipoles: field lines $+ \rightarrow -$ or $\operatorname{N} \rightarrow \operatorname{S}$ (or perpendicular to wire) \item closer field lines means larger force - \item dot means out of page, cross means into page + \item dot: out of page, cross: into page \item +ve corresponds to N pole \end{itemize} + \includegraphics[height=2cm]{/mnt/andrew/graphics/field-lines.png} + % ----------------------- \subsection*{Gravity} \[F_g=G{{m_1m_2}\over r^2}\tag{grav. force}\] - - \[g={F_g \over m}=G{M_{\operatorname{planet}} \over r^2}\tag{grav. acc.}\] - + \[g={F_g \over m_2}=G{m_{1} \over r^2}\tag{field of $m_1$}\] \[E_g = mg \Delta h\tag{gpe}\] - \[W = \Delta E_g = Fx\tag{work}\] - \[w=m(g-a) \tag{app. weight}\] + % \columnbreak + % ----------------------- \subsection*{Satellites} - \[v=\sqrt{GM \over r} = \sqrt{gr} = {{2 \pi r} \over T}\] + \[v=\sqrt{Gm_{\operatorname{planet}} \over r} = \sqrt{gr} = {{2 \pi r} \over T}\] \[T={\sqrt{4 \pi^2 r^2} \over {GM}}\tag{period}\] @@ -257,54 +250,63 @@ \item emf $\mathcal{E}$ measured in volts \end{itemize} - \[{E_1 \over E_2}={r_1 \over r_2}^2\] + % \[{E_1 \over E_2}={r_1 \over r_2}^2\] - \[F=qvB\tag{force on moving charged particles}\] + \[F=qvB\tag{$F$ on moving $q$}\] + \[F=IlB\tag{$F$ of $B$ on $I$}\] + \[r={mv \over qB} \tag{radius of $q$ in $B$}\] if $B {\not \perp} A, \Phi \rightarrow 0$ \hspace{1em}, \hspace{1em} if $B \parallel A, \Phi = 0$ - - \includegraphics[height=2cm]{/mnt/andrew/graphics/field-lines.png} - % ----------------------- \subsection*{Electric fields} - \begin{align*} - F=qE \tag{$E$ = strength} \\ - W=q_{\operatorname{point}}\Delta V \tag{in field or points} \\ - F=k{{q_1q_2}\over r^2}\tag{force between $q_{1,2}$} \\ - E=k{Q \over r^2} \tag{$r=||EQ||$} \\ - F=BInl \tag{force on a coil} \\ - \Phi = B_{\perp}A\tag{magnetic flux} \\ - \mathcal{E} = -N{{\Delta \Phi}\over{\Delta t}} \tag{induced emf} \\ - {V_p \over V_s}={N_p \over N_s}={I_s \over I_p} \tag{xfmr coil ratios} \\ - \end{align*} + \[F=qE \tag{$E$ = strength} \] + \[F=k{{q_1q_2}\over r^2}\tag{force between $q_{1,2}$} \] + \[E=k{q \over r^2} \tag{field on point charge} \] + \[E={V \over d} \tag{field between plates}\] + \[F=BInl \tag{force on a coil} \] + \[\Phi = B_{\perp}A\tag{magnetic flux} \] + \[\mathcal{E} = -N{{\Delta \Phi}\over{\Delta t}} \tag{induced emf} \] + \[{V_p \over V_s}={N_p \over N_s}={I_s \over I_p} \tag{xfmr coil ratios} \] - \textbf{Lenz's law:} ``$-n$'' in Faraday - emf opposes $\Delta \Phi$ + \textbf{Lenz's law:} $I_{\operatorname{emf}}$ opposes $\Delta \Phi$ \textbf{Eddy currents:} counter movement within a field - \textbf{Right hand grip:} thumb points to north or $I$ + \textbf{Right hand grip:} thumb points to $I$ (single wire) or N (solenoid / coil) - \textbf{Right hand slap:} field, current, force are $\perp$ + \textbf{Right hand slap:} $B \perp I \perp F$ - \textbf{Flux-time graphs:} gradient $\times n = \operatorname{emf}$ + \textbf{Flux-time graphs:} $m \times n = \operatorname{emf}$ \textbf{Transformers:} core strengthens \& focuses $\Phi$ +% ----------------------- + \subsection*{Particle acceleration} + + $1 \operatorname{eV} = 1.6 \times 10^{-19} \operatorname{J}$ + + e- accelerated with $x$ V is given $x$ eV + + \[W={1\over2}mv^2=qV \tag{field or points}\] + \[v=\sqrt{{2qV} \over {m}}\tag{velocity of particle}\] + + % ----------------------- \subsection*{Power transmission} - \begin{align*} - V_{\operatorname{rms}}={V_{\operatorname{p\rightarrow p}}\over \sqrt{2}} \\ + % \begin{align*} + $$V_{\operatorname{rms}}={V_{\operatorname{p\rightarrow p}}\over \sqrt{2}}$$ P_{\operatorname{loss}} = \Delta V I = I^2 R = {{\Delta V^2} \over R} \\ - \end{align*} + V_{\operatorname{loss}}=IR + % \end{align*} Use high-$V$ side for correct $|V_{drop}|$ \begin{itemize} - {\item Parallel - voltage is constant} - {\item Series - voltage is shared within branch} + {\item Parallel - $V$ is constant} + {\item Series - $V$ shared within branch} \end{itemize} \includegraphics[height=4cm]{/mnt/andrew/graphics/ac-generator.png}