$\text{elastic potential energy} = {1 \over 2}kx^2$
- $x={2mg \over k}
+ $x={2mg \over k}$
% -----------------------
\subsection*{Motion equations}
\[v=\sqrt{Gm_{\operatorname{planet}} \over r} = \sqrt{gr} = {{2 \pi r} \over T}\]
- \[T={\sqrt{4 \pi^2 r^3} \over {GM}}\tag{period}\]
+ \[T={\sqrt{4 \pi^2 r^3} \over {GM_\text{planet}}}\tag{period}\]
\[\sqrt[3]{{GMT^2}\over{4\pi^2}}\tag{radius}\]
\[{V_p \over V_s}={N_p \over N_s}={I_s \over I_p} \tag{xfmr coil ratios} \]
\textbf{Lenz's law:} $I_{\operatorname{emf}}$ opposes $\Delta \Phi$ \\
- % emf is gradient of flux-time graph
+ (emf creates $I$ with associated field that opposes $\Delta \phi$)
\textbf{Eddy currents:} counter movement within a field
\includegraphics[height=4cm]{graphics/dc-motor-2.png}
\includegraphics[height=3cm]{graphics/ac-motor.png} \\
+ Force on current-carying wire, not copper \\
$F=0$ for front & back of coil (parallel) \\
Any angle $> 0$ will produce force \\
% \end{wrapfigure}
% -----------------------
\subsection*{Doppler effect}
+
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}
+ \textbf{Standing waves} - constructive int. at resonant freq
+ \textbf{Coherent } - identical frequency, phase, direction (ie strong & directional). e.g. laser
- \textbf{Standing waves} - constructive int. at resonant freq
+ \textbf{Incoherent} - e.g. incandescent bulb
- \subsection*{Harmonics}
+ % -----------------------
+ \subsection*{Harmonics}
\(\lambda = {{al} \div n}\quad\) (\(\lambda\) for \(n^{th}\) harmonic)\\
\(f = {nv \div al}\quad\) (\(f\) for \(n_{th}\) harmonic at length
\(l\) = distance from source to observer\\
\(d\) = separation between each wave source (e.g. slit) \(=S_1-S_2\)
\item significant diffraction when ${\lambda \over \Delta x} \ge 1$
+ \item diffraction creates distortion (electron $>$ optical microscopes)
\end{itemize}
\textbf{Work function $\phi$}
- Minimum $E$ required to release photoelectrons. Magnitude of $y$-intercept of frequency vs $E_K$ graph. $\phi$ is determined by strength of bonding.
+ Minimum $E$ required to release photoelectrons. Magnitude of $y$-intercept of $f$ vs $E_K$ graph. $\phi$ is determined by strength of bonding. Units: eV or J.
- $\phi=hf_0$
+ $\phi=hf_0$
\textbf{Kinetic energy}
E_{\operatorname{k-max}}=hf - \phi
- voltage in circuit or stopping voltage = max $E_K$ in eV
- equal to $x$-intercept of volts vs current graph (in eV)
+ voltage in circuit or stopping voltage = max $E_K$ in eV \\
+ $E_K = x$-int of $V\cdot I$ graph (in eV) \\
+ dashed line below $E_K=0$ ($E_K < 0$ is impossible)
+
\textbf{Stopping potential $V$ for min $I$}
$V=h_{\text{eV}}(f-f_0)$
- % \columnbreak
-
\subsection*{De Broglie's theory}
\[ \lambda = {h \over \rho} = {h \over mv} \]
\textbf{Precision} - concordance of values \\
\textbf{Accuracy} - closeness to actual value\\
\textbf{Random errors} - unpredictable, reduced by more tests \\
- \textbf{Systematic errors} - not reduced by more tests
-
- \columnbreak
-
- \quad
-
-
-
-
-
+ \textbf{Systematic errors} - not reduced by more tests \\
+ \textbf{Uncertainty} - margin of potential error \\
+ \textbf{Error} - actual difference \\
+ \textbf{Hypothesis} - can be tested experimentally \\
+ \textbf{Model} - evidence-based but indirect representation
\end{multicols}
-% \includegraphics[height=5cm]{graphics/em-spectrum.png}
-
\end{document}