From: Andrew Lorimer Date: Sun, 9 Sep 2018 02:10:38 +0000 (+1000) Subject: draft final cheatsheet X-Git-Tag: yr11~44 X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/5f85f6af8da94855c0209310aa0f3b460f7bf510 draft final cheatsheet --- diff --git a/physics/final.aux b/physics/final.aux new file mode 100644 index 0000000..1202cb7 --- /dev/null +++ b/physics/final.aux @@ -0,0 +1,9 @@ +\relax +\@writefile{toc}{\contentsline {section}{\numberline {1}Motion}{}} +\@writefile{toc}{\contentsline {section}{\numberline {2}Relativity}{}} +\@writefile{toc}{\contentsline {section}{\numberline {3}Fields and power}{}} +\@writefile{toc}{\contentsline {section}{\numberline {4}Waves}{}} +\@writefile{toc}{\contentsline {section}{\numberline {5}Light and Matter}{}} +\@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Uncertainty principle}{}} +\@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Wave-particle duaity}{}} +\@writefile{toc}{\contentsline {section}{\numberline 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Proceed, with fingers crossed. + +./final.tex:407: Missing $ inserted. + + $ +l.407 + +I've inserted a begin-math/end-math symbol since I think +you left one out. 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But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. 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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 --git a/physics/graphics/ac-generator.png b/physics/graphics/ac-generator.png new file mode 100755 index 0000000..692a8c7 Binary files /dev/null and b/physics/graphics/ac-generator.png differ diff --git a/physics/graphics/ac-motor.png b/physics/graphics/ac-motor.png new file mode 100755 index 0000000..77fb85c Binary files /dev/null and b/physics/graphics/ac-motor.png differ diff --git a/physics/graphics/banked-track.png b/physics/graphics/banked-track.png new file mode 100644 index 0000000..f8268be Binary files /dev/null and b/physics/graphics/banked-track.png differ diff --git a/physics/graphics/circ-forces.png b/physics/graphics/circ-forces.png new file mode 100644 index 0000000..c74da56 Binary files /dev/null and b/physics/graphics/circ-forces.png differ diff --git a/physics/graphics/dc-motor-2.png b/physics/graphics/dc-motor-2.png new file mode 100755 index 0000000..d324682 Binary files /dev/null and b/physics/graphics/dc-motor-2.png differ diff --git a/physics/graphics/projectile-motion.png b/physics/graphics/projectile-motion.png new file mode 100644 index 0000000..67cc7aa Binary files /dev/null and b/physics/graphics/projectile-motion.png differ