From 5f85f6af8da94855c0209310aa0f3b460f7bf510 Mon Sep 17 00:00:00 2001 From: Andrew Lorimer Date: Sun, 9 Sep 2018 12:10:38 +1000 Subject: [PATCH] draft final cheatsheet --- physics/final.aux | 9 + physics/final.fdb_latexmk | 83 +++++ physics/final.fls | 144 +++++++++ physics/final.log | 421 +++++++++++++++++++++++++ physics/final.pdf | Bin 0 -> 547706 bytes physics/final.synctex.gz | Bin 0 -> 49513 bytes physics/final.tex | 106 ++++--- physics/graphics/ac-generator.png | Bin 0 -> 28991 bytes physics/graphics/ac-motor.png | Bin 0 -> 18626 bytes physics/graphics/banked-track.png | Bin 0 -> 51228 bytes physics/graphics/circ-forces.png | Bin 0 -> 17259 bytes physics/graphics/dc-motor-2.png | Bin 0 -> 53769 bytes physics/graphics/projectile-motion.png | Bin 0 -> 53128 bytes 13 files changed, 725 insertions(+), 38 deletions(-) create mode 100644 physics/final.aux create mode 100644 physics/final.fdb_latexmk create mode 100644 physics/final.fls create mode 100644 physics/final.log create mode 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zMYQHLr2@)nI2=fclOHRCYj-iWq1_}`RCAyz8(p8Hnt-TmdUrxhiw-Z^$&Ow|X7`nw zv;nmSWOCe1q}qQd0 U4thH~W`C!=Z51~CLKjk((DF6Tf literal 0 HcmV?d00001 diff --git a/physics/final.tex b/physics/final.tex index f809976..b37c41a 100644 --- a/physics/final.tex +++ b/physics/final.tex @@ -287,7 +287,7 @@ $1 \operatorname{eV} = 1.6 \times 10^{-19} \operatorname{J}$ - eaccelerated with $x$ V is given $x$ eV + e- accelerated with $x$ V is given $x$ eV \[W={1\over2}mv^2=qV \tag{field or points}\] \[v=\sqrt{{2qV} \over {m}}\tag{velocity of particle}\] @@ -297,9 +297,9 @@ \subsection*{Power transmission} % \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} \\ - V_{\operatorname{loss}}=IR + \[V_{\operatorname{rms}}={V_{\operatorname{p\rightarrow p}}\over \sqrt{2}} \] + \[P_{\operatorname{loss}} = \Delta V I = I^2 R = {{\Delta V^2} \over R} \] + \[V_{\operatorname{loss}}=IR \] % \end{align*} Use high-$V$ side for correct $|V_{drop}|$ @@ -331,19 +331,19 @@ \textbf{nodes:} fixed on graph \textbf{Longitudinal (motion $||$ wave)} - \includegraphics[height=4cm]{graphics/longitudinal-waves.png} + \includegraphics[width=6cm]{graphics/longitudinal-waves.png} \textbf{Transverse (motion $\perp$ wave)} - \includegraphics[height=4cm]{graphics/transverse-waves.png} + \includegraphics[width=6cm]{graphics/transverse-waves.png} % ----------------------- \subsection*{Motors} $T={1 \over f}\quad$(period: time for one cycle) - $v=f \lambda \quad$(speed: displacement per second) + $v=f \lambda \quad$(speed: displacement / sec) % ----------------------- \subsection*{Doppler effect} - When $P_1$ approaches $P_2$, each wave $w_n$ has slightly less distance to travel than $w_{n-1}$. Hence, $w_n$ reaches the observer sooner than $w_{n-1}$, increasing "apparent" wavelength. + When $P_1$ approaches $P_2$, each wave $w_n$ has slightly less distance to travel than $w_{n-1}$. $w_n$ reaches observer sooner than $w_{n-1}$ ("apparent" $\lambda$). % ----------------------- \subsection*{Interference} @@ -351,11 +351,11 @@ % ----------------------- \subsection*{Polarisation} - \includegraphics[height=4cm]{graphics/polarisation.png} + \includegraphics[height=3.5cm]{graphics/polarisation.png} % ----------------------- \subsection*{Refraction} - \includegraphics[height=4cm]{graphics/refraction.png} + \includegraphics[height=3.5cm]{graphics/refraction.png} Angle of incidence $\theta_i =$ angle of reflection $\theta_r$ @@ -369,24 +369,25 @@ % ----------------------- \subsection*{Planck's equation} - f={c \over \lambda},\quad E=hf={hc \over \lambda}=\rho c - - h=6.63 \times 10^{-34}\operatorname{J s}=4.14 \times 10^{-15} \operatorname{eV s} - - 1 \operatorname{eV} = 1.6 \times 10^{-19} \operatorname{J} + \[ f={c \over \lambda},\quad E=hf={hc \over \lambda}=\rho c \] + \[ h=6.63 \times 10^{-34}\operatorname{J s}=4.14 \times 10^{-15} \operatorname{eV s} \] + \[ 1 \operatorname{eV} = 1.6 \times 10^{-19} \operatorname{J} \] \subsection*{Force of electrons} - F={2P_{\text{in}}\over c} - - \text{photons per second}={\text{total energy} \over \text{energy per photon}}={{P_{\text{in}} \lambda} \over hc}={P_{\text{in}} \over hf} + \[ F={2P_{\text{in}}\over c} \] + % \begin{align*} + \[ \text{photons / sec} = {\text{total energy} \over \text{energy / photon}} \] + \[ ={{P_{\text{in}} \lambda} \over hc}={P_{\text{in}} \over hf} \] + % ={P_{\text{in}} \lambda} \over hc}={P_{\text{in}} \over hf} + % \end{align*} \subsection*{Photoelectric effect} \begin{itemize} \item $V_{\operatorname{supply}}$ does not affect photocurrent - \item $V_{\operatorname{sup}} > 0$: eattracted to collector anode + \item $V_{\operatorname{sup}} > 0$: e- attracted to collector anode \item $V_{\operatorname{sup}} < 0$: attracted to illuminated cathode, $I\rightarrow 0$ - \item $v$ of edepends on ionisation energy (shell) + \item $v$ of depends on ionisation energy (shell) \item max current depends on intensity \end{itemize} @@ -411,10 +412,12 @@ $V=h_{\text{eV}}(f-f_0)$ + \columnbreak + \subsection*{De Broglie's theory} - $\lambda = {h \over \rho} = {h \over mv}$ - $\rho = {hf \over c} = {h \over \lambda} = mv, \quad E = \rho c$ + \[ \lambda = {h \over \rho} = {h \over mv} \] + \[ \rho = {hf \over c} = {h \over \lambda} = mv, \quad E = \rho c \] \begin{itemize} \item cannot confirm with double-slit (slit $< r_{\operatorname{proton}}$) \item confirmed by similar e- and x-ray diff patterns @@ -433,33 +436,60 @@ \subsection*{Spectral analysis} \begin{itemize} - $n\item $\Delta E = hf = {hc \over \lambda}$ between ground / excited state - $n\item $E$ and $f$ of photon: $E_2 - E_1 = hf = {hc \over \lambda}$ - $n\item Ionisation energy - min $E$ required to remove e- - $n\item EMR is absorbed/emitted when $E_{\operatorname{K-in}}=\Delta E_{\operatorname{shells}}$ (i.e. $\lambda = {hc \over \Delta E_{\operatorname{shells}}}$) + \item $\Delta E = hf = {hc \over \lambda}$ between ground / excited state + \item $E$ and $f$ of photon: $E_2 - E_1 = hf = {hc \over \lambda}$ + \item Ionisation energy - min $E$ required to remove e- + \item EMR is absorbed/emitted when $E_{\operatorname{K-in}}=\Delta E_{\operatorname{shells}}$ (i.e. $\lambda = {hc \over \Delta E_{\operatorname{shells}}}$) + \item No. of lines - include all possible states \end{itemize} - \subsection{Indeterminancy principle} + \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. \subsection{Wave-particle duaity} wave model: - - \item cannot explain photoelectric effect - \item $f$ is irrelevant to photocurrent - \item predicts delay between incidence and ejection - \item speed depends on medium + \begin{itemize} + \item cannot explain photoelectric effect + \item $f$ is irrelevant to photocurrent + \item predicts delay between incidence and ejection + \item speed depends on medium + \end{itemize} particle model: - \item explains photoelectric effect - \item rate of photoelectron release $\propto$ intensity - \item no time delay - one photon releases one electron - \item double slit: photons interact. interference pattern still appears when a dim light source is used so that only one photon can pass at a time - \item light exerts force - \item light bent by gravity + \begin{itemize} + \item explains photoelectric effect + \item rate of photoelectron release $\propto$ intensity + \item no time delay - one photon releases one electron + \item double slit: photons interact. interference pattern still appears when a dim light source is used so that only one photon can pass at a time + \item light exerts force + \item light bent by gravity + \end{itemize} + + % +++++++++++++++++++++++ + \section{Uncertainty} + + \textbf{Absolute uncertainty} - $\Delta$ - same units as quantity. + \[ \Delta(m) = {{\mathcal{E}(m)} \over 100} \cdot m \] + + \[ (A \pm \Delta A) + (B \pm \Delta A) = (A+B) \pm (\Delta A + \Delta B) \] + \[ (A \pm \Delta A) - (B \pm \Delta A) = (A-B) \pm (\Delta A + \Delta B) \] + \[ c(A \pm \Delta A) = cA \pm c \Delta A \] + + \textbf{Relative uncertainty} - $\mathcal{E}$ - unitless. + \[ \mathcal{E}(m) = {{\Delta(m)} \over m} \cdot 100} \] + \[ (A \pm \mathcal{E} A) \cdot (B \pm \mathcal{E} B) = (A \cdot B) \pm (\mathcal{E} A + \mathcal{E} B) \] + \[ (A \pm \mathcal{E} A) \div (B \pm \mathcal{E} B) = (A \div B) \pm (\mathcal{E} A + \mathcal{E} B) \] + \[ (A \pm \mathcal{E} A)^n = (A^n \pm n \mathcal{E} A) \] + \[ c(A \pm \mathcal{E} A)=cA \pm \mathcal{E} A \] + + Uncertainty of a measurement is $1 \over 2$ the smallest division + + \textbf{Precision} - concordance of values \\ + \textbf{Accuracy} - closeness to actual value + diff 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