diff --git a/Latex conventions and formatting.pdf b/Latex conventions and formatting.pdf new file mode 100644 index 0000000..725ff9b Binary files /dev/null and b/Latex conventions and formatting.pdf differ diff --git a/worksheets/ApplyingNewtonLaws.pdf b/worksheets/ApplyingNewtonLaws.pdf new file mode 100644 index 0000000..320e07d Binary files /dev/null and b/worksheets/ApplyingNewtonLaws.pdf differ diff --git a/worksheets/ApplyingNewtonLaws.tex b/worksheets/ApplyingNewtonLaws.tex new file mode 100644 index 0000000..4f2fb59 --- /dev/null +++ b/worksheets/ApplyingNewtonLaws.tex @@ -0,0 +1,62 @@ +\documentclass[12pt]{article} + +\include{include/preambleworksheet} + +\begin{document} + +\begin{worksheet}{Physics Worksheet}{Applying Newton's Laws} + + +\question[0cm]{Indicate below which of these forces are "real" forces and which are not. Explain the origin of each force and how that determines if the force is fictitious of not:} + +\questionpart[2cm]{Gravitational force on a person towards the centre of The Earth} + +\questionpart[2cm]{Centrifugal force on a mass swinging in a circle} + +\questionpart[2cm]{Inertial force on a mass attached to the cieling of an accelerating car via string} + +\questionpart[2cm]{Friction force on a beach-ball rolling on sand} + + + + +\question[0.5cm]{Consider a block traveling along a counter clockwise along a circle that is slowing down. Draw the direction of the linear velocity $\vec{v}$, linear acceleration $\vec{a}$, angular velocity $\vec{\omega}$, and angular acceleratio $\vec{\alpha}$ for the block} + +\begin{tikzpicture} + +\draw[dash pattern=on 3pt off 2pt] (0,0) circle (2cm); +\draw[fill=gray] (1.7,-0.3) rectangle (2.3, 0.3); +\draw[line width = 2pt, color=black] (0,0)--(1.7,0); +\end{tikzpicture} + +\newpage + +\question[5cm]{A present is placed at rest on a plane that is inclined, at a distance $L$ from the bottom of the incline that makes an angle $\theta$ with the ground. At the bottom of the incline, the box is determined to have a speed $v$. If the box is instead released from a distance of $4L$ from the bottom of the incline, what will its speed at the bottom of the incline be?} + + + + + + + + + + +\question[0cm]{Imagine you are swinging a bucket full of water attached to a rope in a vertical circle} + + +\questionpart[4cm]{Where along the trajectory is the tension on the rope the highest?} + +\questionpart[4cm]{Why doesn't the water spill out of the bucket at the top of the circle? Give two explanations:} + +\questionpart[4cm]{What is the minimum speed required for the water to not spill out of the bucket?} + + + + + + + +\end{worksheet} + +\end{document} \ No newline at end of file diff --git a/worksheets/ApplyingNewtonLaws_Answers.pdf b/worksheets/ApplyingNewtonLaws_Answers.pdf new file mode 100644 index 0000000..8873dea Binary files /dev/null and b/worksheets/ApplyingNewtonLaws_Answers.pdf differ diff --git a/worksheets/ApplyingNewtonLaws_Answers.tex b/worksheets/ApplyingNewtonLaws_Answers.tex new file mode 100644 index 0000000..d8e28f9 --- /dev/null +++ b/worksheets/ApplyingNewtonLaws_Answers.tex @@ -0,0 +1,79 @@ +\documentclass[12pt]{article} + +\include{include/preambleworksheet} + +\begin{document} + +\begin{worksheet}{Physics Worksheet}{Applying Newton's Laws} + + +\question[0cm]{Indicate below which of these forces are "real" forces and which are not. Explain the origin of each force and how that determines if the force is fictitious of not:} + +\questionpart[0cm]{Gravitational force on a person towards the centre of The Earth} + +\textbf{real} +\vspace{1.5cm} + +\questionpart[0cm]{Centrifugal force on a mass swinging in a circle} + +\textbf{fake} +\vspace{1.5cm} + +\questionpart[0cm]{Inertial force on a mass attached to the cieling of an accelerating car via string} + +\textbf{fake} +\vspace{1.5cm} + +\questionpart[0cm]{Friction force on a beach-ball rolling on sand} + +\textbf{real} +\vspace{1.5cm} + + +\question[0.5cm]{Consider a block traveling along a counter clockwise along a circle that is slowing down. Draw the direction of the linear velocity $\vec{v}$, linear acceleration $\vec{a}$, angular velocity $\vec{\omega}$, and angular acceleratio $\vec{\alpha}$ for the block} + +\begin{tikzpicture} + +\draw[dash pattern=on 3pt off 2pt] (0,0) circle (2cm); +\draw[fill=gray] (1.7,-0.3) rectangle (2.3, 0.3); +\draw[line width = 2pt, color=black] (0,0)--(1.7,0); +\end{tikzpicture} + +\textbf{$\vec{v}$ points up, $\vec{a}$ points into the circle, $\vec{\omega}$ points out of the page, $\vec{\alpha}$ points into the page.} + +\newpage + +\question[0.5cm]{A present is placed at rest on a plane that is inclined, at a distance $L$ from the bottom of the incline that makes an angle $\theta$ with the ground. At the bottom of the incline, the box is determined to have a speed $v$. If the box is instead released from a distance of $4L$ from the bottom of the incline, what will its speed at the bottom of the incline be?} + + +\textbf{$\vec{v_2} = 2\vec{v_1}$} + + +\vspace{5cm} + + + + +\question[0cm]{Imagine you are swinging a bucket full of water attached to a rope in a vertical circle} + +\questionpart[0cm]{Where along the trajectory is the tension on the rope the highest?} + +\textbf{At the bottom becuase the tension directly opposes the weight of the bucket} +\vspace{4cm} + +\questionpart[0cm]{Why doesn't the water spill out of the bucket at the top of the circle? Give two explanations:} + +\textbf{1. The normal force, centripidal force and gravitational forces cancel each other out. 2. The water is actually in free-fall, however so is the bucket. and since they are in movement together the water stays within the bucket} +\vspace{2cm} + +\questionpart[0cm]{What is the minimum speed required for the water to not spill out of the bucket?} + + +\textbf{$v=\sqrt{gR}$ where R is the radius of the circular path the bucket is rotating around.} + + + + +\end{worksheet} + +\end{document} \ No newline at end of file diff --git a/worksheets/Bforce.pdf b/worksheets/Bforce.pdf new file mode 100644 index 0000000..5f564ea Binary files /dev/null and b/worksheets/Bforce.pdf differ diff --git a/worksheets/Bforce.tex b/worksheets/Bforce.tex new file mode 100644 index 0000000..cdf929d --- /dev/null +++ b/worksheets/Bforce.tex @@ -0,0 +1,48 @@ +\documentclass[12pt]{article} + +\include{include/preambleworksheet} + +\begin{document} + +\begin{worksheet}{Physics Worksheet}{Magnetic Force} + + +\question[0cm]{The following questions concern Earth's magnetic field} + +\questionpart[7cm]{Draw a diagram of Earth and its magnetic field and the resulting field lines. Indicate where the north and south pole are} + +\questionpart[5cm]{A proton moves East in Earth’s magnetic field, which way is it deflected?} + +\questionpart[5cm]{An electron moves towards Earth in its magnetic field. Which was is it deflected?} + +\newpage + +\question[9cm]{Show that the force on a charged particle with charge $q$ and mass $m$ undergoing uniform circular motion when traveling perpindicular to a magnetic field $B$ is \par $\vec{F_B} = \frac{q^2 B^2 R}{m}$} + + + + +\question[0cm]{Derive the equation for the amount of charge $Q$ going through a circular loop with radius $R$, experiencing a torque $T$ from a perpindicular magnetic field $B$ over a time $t$. What happens to the charge as time goes on assuming all other variables remain constant. Does your result make sense?} + + + + + + + + + + + + + + + + + + + + +\end{worksheet} + +\end{document} \ No newline at end of file diff --git a/worksheets/Bsource.pdf b/worksheets/Bsource.pdf new file mode 100644 index 0000000..5627052 Binary files /dev/null and b/worksheets/Bsource.pdf differ diff --git a/worksheets/Bsource.tex b/worksheets/Bsource.tex new file mode 100644 index 0000000..f994426 --- /dev/null +++ b/worksheets/Bsource.tex @@ -0,0 +1,33 @@ +\documentclass[12pt]{article} + +\include{include/preambleworksheet} + +\begin{document} + +\begin{worksheet}{Physics Worksheet}{Magnetic Source} + + + +\question[5cm]{A coil is made of N loops of current-carrying wire packed closely together. What is the +magnetic field at the centre of the coil?} + +\question[5cm]{What happens when two parallel wires are carrying charge in the same direction close to each other? Why?} + + + +\question[0cm]{Does Amp\`ere's law prove that there is no magnetic field in a loop that encloses no current? Provide an example with a diagram where poor use of Amp\`ere's law might appear to give this result} + +\newpage + +\question[7cm]{Derive the current density of a solenoid of radius $R$ emitting a magnetic field $B$ with $N$ loops?} + +\question[7cm]{Derive the current density of a toroid of radius $R$ emitting a magnetic field $B$ with $N$ loops?} + +\question[0cm]{What would happen to the current density and the magnetic field of a solenoid, if you were to make the two ends meet and create a toroid, such that the radius of the toroid is equal to the radius of one of the loops from the solenoid?} + + + + +\end{worksheet} + +\end{document} \ No newline at end of file diff --git a/worksheets/ChargesAndFields.pdf b/worksheets/ChargesAndFields.pdf new file mode 100644 index 0000000..be29c45 Binary files /dev/null and b/worksheets/ChargesAndFields.pdf differ diff --git a/worksheets/ChargesAndFields.tex b/worksheets/ChargesAndFields.tex new file mode 100644 index 0000000..4033bf7 --- /dev/null +++ b/worksheets/ChargesAndFields.tex @@ -0,0 +1,47 @@ +\documentclass[12pt]{article} + +\include{include/preambleworksheet} + +\begin{document} + +\begin{worksheet}{Physics Worksheet}{Electric Charges and Fields} + +\question[5cm]{How does a lightning rod work?} + +\question[5cm]{Show that the Coulomb Force is conservative} + +\question[5cm]{How much heavier would a proton have to be to counterect the repulsive field it exerts on a positive charge with it's gravitational field?} + + +\newpage + +\question[0cm]{Imagine an electric $\vec{E}$ field poitning East and a diapole submerged within it.} + +\questionpart[6cm]{Draw a diagram of this, where there is a net torque on the diapole} + +\questionpart[6cm]{Draw the two equilibriem states the diapole can be in. Label which is stable, and which is unstable} + + +\questionpart[0cm]{Which of the diagrams above has the highest, and the lowest potential energy} + + + + + + + + + + + + + + + + + + +\end{worksheet} + + +\end{document} \ No newline at end of file diff --git a/worksheets/Circuits.pdf b/worksheets/Circuits.pdf new file mode 100644 index 0000000..139099e Binary files /dev/null and b/worksheets/Circuits.pdf differ diff --git a/worksheets/Circuits.tex b/worksheets/Circuits.tex new file mode 100644 index 0000000..8ec0b00 --- /dev/null +++ b/worksheets/Circuits.tex @@ -0,0 +1,54 @@ +\documentclass[12pt]{article} + +\include{include/preambleworksheet} + +\begin{document} + +\begin{worksheet}{Physics Worksheet}{Electric Circuits} + + + + +\question[0cm]{The follwing question concerns RLC circuits} + +\questionpart[5cm]{Search online and draw a diagram of an RLC circuit and indicate all the components} + +\questionpart[5cm]{Look up what the "equation of motion" of an RLC circuit is. What motion does this equation describe?} + +\questionpart[5cm]{What are RLC circuits used for?} + +\newpage + + + + +\question[0cm]{What is the effective resistance of the below delta formation resistor if $R_1 = 1 \Omega$, $R_2 = 4 \Omega$, and $R_3 = 5 \Omega$. (Hint: look up "Delta-Wye Circuit Transformations")} + + + + + + + +\begin{circuitikz} + % Nodes + \draw + (0,0) node[anchor=east] {A} to[R=$R_{1}$] (3,0) node[anchor=west] {B} + to[R=$R_{2}$] (1.5,-2.6) node[below] {C} + to[R=$R_{3}$] (0,0); +\end{circuitikz} + + + + + + + + + + + +\end{worksheet} + + +\end{document} \ No newline at end of file diff --git a/worksheets/Derivatives.pdf b/worksheets/Derivatives.pdf new file mode 100644 index 0000000..f122403 Binary files /dev/null and b/worksheets/Derivatives.pdf differ diff --git a/worksheets/Derivatives.tex b/worksheets/Derivatives.tex new file mode 100644 index 0000000..b2fcfc5 --- /dev/null +++ b/worksheets/Derivatives.tex @@ -0,0 +1,81 @@ +\documentclass[12pt]{article} + +\include{include/preambleworksheet} + +\begin{document} + +\begin{worksheet}{Physics Worksheet}{Derivative Practice} + +%Polynomial +\question[4.75cm]{Compute: \vspace{-1cm}\begin{eqnarray*}\frac{d}{dx} (x^{5} + 3x^3 + \frac{1}{x}) \end{eqnarray*}} + +%Quotient rule +\question[4.75cm]{Compute: \vspace{-1cm}\begin{eqnarray*}\frac{d}{dx} (\frac{\cos{x}}{\sin{x}} ) \end{eqnarray*}} + +%Chain rule +\question[0cm]{Compute: \vspace{-1cm}\begin{eqnarray*}\frac{d}{dx} \: \ln(\cos (x))\end{eqnarray*}} + +\newpage + +%limit method +\question[7cm]{Compute $\frac{d}{dx} x^3$ using the limit definition of the derivative} + + +%Partial Derrivatives +\question[7cm]{You are standing on a mountain who's shape can be modelled as $z = 7 - \frac{1}{3}x^2 - 2y^4$. You are at the point of $(2, 1, \frac{13}{3})$ and wish to descend the mountain as quikcly as possible. What direction (in unit vector form) should you go in?} + + +%Plotting derrivatives +\question[1cm]{Below is a plot of the function $y = x^2$, compute and plot on the following two empty graphs the derrivatives: $\frac{d}{dx} (x^2)$ and $\frac{d^2}{dx^2}(x^2)$} + +\hspace{-3.5cm} +\begin{tikzpicture}[scale=0.9] + \begin{axis}[ + axis lines = middle, + xlabel = $x$, + ylabel = {\hspace{-1.2cm}$f(x) = x^2$}, + xmin=-4, xmax=4, + ymin=0, ymax=9, + samples=100, + grid=both, + ] + \addplot[blue, thick] {x^2}; + \end{axis} +\end{tikzpicture} +\hspace{0cm} +\begin{tikzpicture}[scale=0.9] + \begin{axis}[ + xmin=-4, xmax=4, + ymin=0, ymax=9, + axis lines=middle, + xlabel=$x$, ylabel={\hspace{-2.5cm}$f(x) = \frac{d}{dx}(x^2)$}, + xtick={-4,-2,0,2,4}, + ytick={0,2,4,6,8}, + xticklabel style={anchor=north}, + yticklabel style={anchor=east}, + grid=both, + ] + \end{axis} +\end{tikzpicture} +\hspace{0cm} +\begin{tikzpicture}[scale=0.9] + \begin{axis}[ + xmin=-4, xmax=4, + ymin=0, ymax=9, + axis lines=middle, + xlabel=$x$, ylabel={\hspace{-2.5cm}$f(x) = \frac{d^2}{dx^2}(x^2)$}, + xtick={-4,-2,0,2,4}, + ytick={0,2,4,6,8}, + xticklabel style={anchor=north}, + yticklabel style={anchor=east}, + grid=both, + ] + \end{axis} +\end{tikzpicture} + + + +\end{worksheet} + + +\end{document} \ No newline at end of file diff --git a/worksheets/ElectricCurrent.pdf b/worksheets/ElectricCurrent.pdf new file mode 100644 index 0000000..70b3d62 Binary files /dev/null and b/worksheets/ElectricCurrent.pdf differ diff --git a/worksheets/ElectricCurrent.tex b/worksheets/ElectricCurrent.tex new file mode 100644 index 0000000..9586513 --- /dev/null +++ b/worksheets/ElectricCurrent.tex @@ -0,0 +1,37 @@ +\documentclass[12pt]{article} + +\include{include/preambleworksheet} + +\begin{document} + +\begin{worksheet}{Physics Worksheet}{Electric Current} + +\question[0cm]{The following question concerns ideal insulators} + +\questionpart[4cm]{What is the conductivity of an ideal insulator?} + +\questionpart[4cm]{What is the resistivity $\rho$ of an ideal insulator? Does your result make sense?} + +\questionpart[4cm]{Where in the real world are ideal insulators used?} + +\question[0cm]{The following question concerns superconductorz} + +\questionpart[4cm]{What is the conductivity of a superconductor?} + + +\newpage + +\questionpart[4cm]{What is the resistivity $\rho$ of a superconductor? Does your result make sense?} + + +\questionpart[4cm]{Where in the real world would are super conductors used?} + +\question[4cm]{Sho that the current density inside a resistor is $\vec{j} = \sqrt{\frac{P}{R}} \frac{1}{A}$} + + + + +\end{worksheet} + + +\end{document} \ No newline at end of file diff --git a/worksheets/ElectricPotential.pdf b/worksheets/ElectricPotential.pdf new file mode 100644 index 0000000..eec3ead Binary files /dev/null and b/worksheets/ElectricPotential.pdf differ diff --git a/worksheets/ElectricPotential.tex b/worksheets/ElectricPotential.tex new file mode 100644 index 0000000..0ae0883 --- /dev/null +++ b/worksheets/ElectricPotential.tex @@ -0,0 +1,49 @@ +\documentclass[12pt]{article} + +\include{include/preambleworksheet} + +\begin{document} + +\begin{worksheet}{Physics Worksheet}{Electric Potential} + + + + + +\question[5cm]{Electric potential increases along the x axis. A proton and an electron are placed at +rest at the origin; in which direction do the charges move when released? Draw a diagram} + + +\question[5cm]{An electron experiences a change in potential of $\SI{200}{\volt}$. What is its speed?} + + + + + +\question[5cm]{Draw a diagram of a capacitor and the field lines of the electric field inside and outside of the capacitor} + + +\newpage + +\question[6cm]{You friend has a capacitor. They want it to have a greater capacitance, so they tell you they are going to pull the two plates of their capacitor farther apart from each other to make more room for charges inside. Is this wise?} + +\question[0cm]{Consider a capacitor} + +\questionpart[6cm]{The capacitor is filled with an insulating material that has a permittivity twice that of free space. It is comprised of $\SI{1.9}{\meter}$ radius circular plates, seperated by $\SI{1}{\micro\meter}$. What is its capacitance?} + +\questionpart[0cm]{How much power would it take to fill the capacitor with $\SI{3}{\coulomb}$ of charge in $\SI{4}{\milli\second}$?} + + + + + + + + + + + +\end{worksheet} + + +\end{document} \ No newline at end of file diff --git a/worksheets/ElectromagneticInduction.pdf b/worksheets/ElectromagneticInduction.pdf new file mode 100644 index 0000000..50bbaf4 Binary files /dev/null and b/worksheets/ElectromagneticInduction.pdf differ diff --git a/worksheets/ElectromagneticInduction.tex b/worksheets/ElectromagneticInduction.tex new file mode 100644 index 0000000..69587a1 --- /dev/null +++ b/worksheets/ElectromagneticInduction.tex @@ -0,0 +1,40 @@ +\documentclass[12pt]{article} + +\include{include/preambleworksheet} + +\begin{document} + +\begin{worksheet}{Physics Worksheet}{Electromagnetic Induction} + + +\question[4cm]{How much current does a motor generate at a time $t$?} + +\question[0cm]{The following question concerns electromagnetic induction} + +\questionpart[9cm]{A uniform time-varying magnetic field by: $\vec{B}(t) = B_0(\cos{t}\sin{t} - \frac{1}{2}\sin{2t})$ where $B_0$ is a positive constant. What is the induced voltage by the electric field?} + + + + +\questionpart[0cm]{What is a possible physical interpretation of your result?} + + +\newpage + + +\question[0cm]{A circular region with radius $R$ contains a magnetic field that is uniform, and decreasing exponentially with time: +$$\vec{B}(t) = B_0(1-ae^{-3x^2})$$} + +\questionpart[9cm]{Determine the electric field at a distance $r$ away from the origin \textit{inside} the region} + + +\questionpart[0cm]{Determine the electric field at a distance $r$ away from the origin \textit{outside} the region} + + + + + + +\end{worksheet} + +\end{document} \ No newline at end of file diff --git a/worksheets/Fluids.pdf b/worksheets/Fluids.pdf new file mode 100644 index 0000000..94e7aaa Binary files /dev/null and b/worksheets/Fluids.pdf differ diff --git a/worksheets/Fluids.tex b/worksheets/Fluids.tex new file mode 100644 index 0000000..696e7e4 --- /dev/null +++ b/worksheets/Fluids.tex @@ -0,0 +1,52 @@ +\documentclass[12pt]{article} + +\include{include/preambleworksheet} + +\begin{document} + +\begin{worksheet}{Physics Worksheet}{Fluid Mechanics} + + + +\question[0cm]{The following question concerns Bernoull'is principle} + +\questionpart[3cm]{What is Bernoulli's principle?} + +\questionpart[3cm]{How is the concept of Bernoulli's principle used to explain how lift on an aircraft works?} + +\questionpart[3cm]{How can Bernoulli's principle help explain why tornadoes rip roofs off of houses?} + +\question[0cm]{The following questions concern the buyoncy force} + +\questionpart[3cm]{What is the relationship between pressure and depth in water?} + +\newpage + +\questionpart[6cm]{As pressure increases with depth of the water, does the buyoncy force also increase? Explain why or why not:} + + + +\question[6cm]{Let's say you're filling a pot with water from a faucet. Why is the sound of the water crashing into the bottom of the pot louder if you hold the pot at the bottom of the sink rather than close to the top?} + + +\question[6cm]{If the air above a wing is $0.5$atm, what is the velocity of that air?} + + + + + + + + + + + + + + + + +\end{worksheet} + + +\end{document} \ No newline at end of file diff --git a/worksheets/Gauss.pdf b/worksheets/Gauss.pdf new file mode 100644 index 0000000..597c339 Binary files /dev/null and b/worksheets/Gauss.pdf differ diff --git a/worksheets/Gauss.tex b/worksheets/Gauss.tex new file mode 100644 index 0000000..e475529 --- /dev/null +++ b/worksheets/Gauss.tex @@ -0,0 +1,87 @@ +\documentclass[12pt]{article} + +\include{include/preambleworksheet} + +\begin{document} + +\begin{worksheet}{Physics Worksheet}{Gauss} + +\question[0cm]{All of these shapes surround the same source} + +\begin{tikzpicture} +\draw[-latex,line width = 2pt] (0,0) -- (0,1); +\draw[-latex,line width = 2pt] (0,0) -- (1,1); +\draw[-latex,line width = 2pt] (0,0) -- (1,0); +\draw[-latex,line width = 2pt] (0,0) -- (1,-1); +\draw[-latex,line width = 2pt] (0,0) -- (-1,-1); +\draw[-latex,line width = 2pt] (0,0) -- (0,-1); +\draw[-latex,line width = 2pt] (0,0) -- (-1,1); +\draw[-latex,line width = 2pt] (0,0) -- (-1,0); +\draw[fill=black] (0,0) circle (0.33cm); + +\draw[line width = 2pt] (-1.25,-1.25) -- (-1.25,1.25); +\draw[line width = 2pt] (-1.25,1.25) -- (1.25,1.25); +\draw[line width = 2pt] (1.25,1.25) -- (1.25,-1.25); +\draw[line width = 2pt] (-1.25,-1.25) -- (1.25,-1.25); + +\end{tikzpicture} +\hspace{1cm} +\begin{tikzpicture} +\draw[-latex,line width = 2pt] (0,0) -- (0,1); +\draw[-latex,line width = 2pt] (0,0) -- (1,1); +\draw[-latex,line width = 2pt] (0,0) -- (1,0); +\draw[-latex,line width = 2pt] (0,0) -- (1,-1); +\draw[-latex,line width = 2pt] (0,0) -- (-1,-1); +\draw[-latex,line width = 2pt] (0,0) -- (0,-1); +\draw[-latex,line width = 2pt] (0,0) -- (-1,1); +\draw[-latex,line width = 2pt] (0,0) -- (-1,0); +\draw[fill=black] (0,0) circle (0.33cm); + +\draw[line width = 2pt] (-2,-1.5) -- (2,-1.5); +\draw[line width = 2pt] (-2,-1.5) -- (0,1.5); +\draw[line width = 2pt] (2,-1.5) -- (0,1.5); +\end{tikzpicture} +\hspace{1cm} +\begin{tikzpicture} +\draw[-latex,line width = 2pt] (0,0) -- (0,1); +\draw[-latex,line width = 2pt] (0,0) -- (1,1); +\draw[-latex,line width = 2pt] (0,0) -- (1,0); +\draw[-latex,line width = 2pt] (0,0) -- (1,-1); +\draw[-latex,line width = 2pt] (0,0) -- (-1,-1); +\draw[-latex,line width = 2pt] (0,0) -- (0,-1); +\draw[-latex,line width = 2pt] (0,0) -- (-1,1); +\draw[-latex,line width = 2pt] (0,0) -- (-1,0); +\draw[fill=black] (0,0) circle (0.33cm); + +\draw[line width = 2pt] (0,0) circle (1.5cm); +\end{tikzpicture} + + +\questionpart[4cm]{Which of these shapes will report the highest flux? Explain} + +\questionpart[4cm]{Which of these shapes would make the process of calculating the flux easiest?} + +\question[0cm]{Consider an infinite wire carying a net positive charge} + +\questionpart[0cm]{Draw a diagram of the wire and the theoretical field lines coming from it from a front, and a top down view} + +\newpage + +\questionpart[5cm]{What Guassian shape would make it easiest to calculate the flux coming from the wire?} + +\questionpart[5cm]{Consider now a finite wire carrying a net positive charge. Why would calculating the flux coming from a finite wire more difficult that an infinire wire?} + + +\question[3cm]{What is the net flux coming out of an electric diapole?} + + + + + + + + +\end{worksheet} + + +\end{document} \ No newline at end of file diff --git a/worksheets/Gravity.pdf b/worksheets/Gravity.pdf new file mode 100644 index 0000000..f103c11 Binary files /dev/null and b/worksheets/Gravity.pdf differ diff --git a/worksheets/Gravity.tex b/worksheets/Gravity.tex new file mode 100644 index 0000000..9df153c --- /dev/null +++ b/worksheets/Gravity.tex @@ -0,0 +1,36 @@ +\documentclass[12pt]{article} + +\include{include/preambleworksheet} + +\begin{document} + +\begin{worksheet}{Physics Worksheet}{Gravity} + +\question[4cm]{Two small objects with different masses, $m_1$ and $m_2$, are located a distance r from a nearby star. What can you say about the magnitude of the gravitational field and the magnitude of the gravitational force on $m_1$ and $m_2$?} + + + +\question[4cm]{Honza has decided to embark on a great quest: climbing Mount Everest. Out of scientific interest, he decides to take a spring-scale with him and weigh himself at sea level and at the top of the mountain. What would his scale read for his weight at sea level and at the top of Mount Everest (up to 4 decimal points)? His true weight is $\SI{80}{\kilogram}$. Assume the spring scale is coded for a $g$ value of $\SI{9.8}{\meter\per\second\squared}$.} + +\question[0cm]{One of Jupiter's moons, Io, has a semi-major axis of $2.81 \times 10^-3 AU$. What is the period of its orbit?} + +\newpage + +\question[0cm]{Consider The Sun} + +\questionpart[4cm]{What is the Sun's escape velocity?} + +\questionpart[4cm]{Imagine now it condensed such that it has the same mass, but its radius is now $\SI{4}{\kilo\meter}$. What is The Sun's new escape velocity?} + +\questionpart[4cm]{What does this imply about what kind of celestial body the sun would now be?} + + +\question[4cm]{Derive the equation for the amount of work required for an object of mass $m$ to escape a celestial body of mass $M$ and radius $r$} + +\questionpart[0cm]{Does this result make sense? Explain why or why not:} + + + +\end{worksheet} + +\end{document} \ No newline at end of file diff --git a/worksheets/Integrals.pdf b/worksheets/Integrals.pdf new file mode 100644 index 0000000..328a804 Binary files /dev/null and b/worksheets/Integrals.pdf differ diff --git a/worksheets/Integrals.tex b/worksheets/Integrals.tex new file mode 100644 index 0000000..8cd7ccb --- /dev/null +++ b/worksheets/Integrals.tex @@ -0,0 +1,105 @@ +\documentclass[12pt]{article} + +\include{include/preambleworksheet} + +\begin{document} + +\begin{worksheet}{Physics Worksheet}{Integral Practice} + + +%Basic question +\question[4.5cm]{Compute: \vspace{-1cm}\begin{eqnarray*}\displaystyle \int 3x^2 + \frac{1}{x} + e^x \; dx \end{eqnarray*}} + + + + +%infinite sum +\question[0.5cm]{Ari is running with an inital velocity of \SI{1}{\metre\per\second} and an acceleration of $\frac{1}{5}x^4$ \SI{}{\metre\per\second\squared}} + +\questionpart[5cm]{How fast will ari be going after 5 seconds of running? Answer in the form of an infinite sum} + +\questionpart[0cm]{Construct and compute an integral to find the exact value} + + +\newpage + +%Conceptual question +\question[0.25cm]{Below is the function $f(x) = -x^2 +9$} +\\ +\questionpart[0.5cm]{Using the grid, approximate the area under the curve with increasing accuracy} + +\hspace{-3.5cm} +\begin{tikzpicture}[scale=0.95] + \begin{axis}[ + axis lines = middle, + xlabel = $x$, + ylabel = {\hspace{-1.2cm}$y$}, + xmin=-3, xmax=3, + ymin=0, ymax=10, + samples=100, +axis equal, + grid=both, + ] + \addplot[blue, thick] {-x^2 + 9}; + \end{axis} +\end{tikzpicture} +\hspace{0cm} +\begin{tikzpicture}[scale=0.95] + \begin{axis}[ + axis lines = middle, + xlabel = $x$, + ylabel = {\hspace{-1.2cm}$y$}, + xmin=-3, xmax=3, + ymin=0, ymax=10, + xtick={-4,-3,-2,-1,0,1,2,3,4}, + ytick={0,2,4,6,8}, + samples=100, +axis equal, + grid=both, + ] + \addplot[blue, thick] {-x^2 + 9}; + \end{axis} +\end{tikzpicture} +\hspace{0cm} +\begin{tikzpicture}[scale=0.95] + \begin{axis}[ + axis lines = middle, + xlabel = $x$, + ylabel = {\hspace{-1.2cm}$y$}, + xmin=-3, xmax=3, + ymin=0, ymax=10, + xtick={-4,-3,-2,-1,0,1,2,3,4}, + ytick={0,1,2,3,4,5,6,7,8,9}, + samples=100, +axis equal, + grid=both, + ] + \addplot[blue, thick] {-x^2 + 9}; + \end{axis} +\end{tikzpicture} +\vspace{2.5cm} + +\questionpart[4.5cm]{Find the true value of the area under the curve by computing $\displaystyle \int_{-3}^{3} (-x^2 + 9) \; dx$} + + + +%Derivation question +\question[0cm]{Derive: $\displaystyle x = x_0 +v_i t + \frac{1}{2}at^2$} + + + + + + + + + + + + + + + +\end{worksheet} + +\end{document} \ No newline at end of file diff --git a/worksheets/Kinematics.pdf b/worksheets/Kinematics.pdf new file mode 100644 index 0000000..e19a541 Binary files /dev/null and b/worksheets/Kinematics.pdf differ diff --git a/worksheets/Kinematics.synctex(busy) b/worksheets/Kinematics.synctex(busy) new file mode 100644 index 0000000..e69de29 diff --git a/worksheets/Kinematics.tex b/worksheets/Kinematics.tex new file mode 100644 index 0000000..19512d7 --- /dev/null +++ b/worksheets/Kinematics.tex @@ -0,0 +1,128 @@ +\documentclass[12pt]{article} + +\include{include/preambleworksheet} + +\begin{document} + +\begin{worksheet}{Physics Worksheet}{Kinematics} + +\question[0cm]{The acceleration of a cricket jumping sideways is observed to increase linearly with +time, that is, $ax(t) = a_0 + jt$, where $a_0$ and $j$ are constants. What can you say about +the velocity of the cricket as a function of time?} + +\questionpart[0cm]{It is constant} + +\questionpart[0cm]{It increases linearly with time $(v(t) \propto t)$} + +\questionpart[0cm]{It increases quadratically with time $(v(t) \propto t^2)$} + +\questionpart[0cm]{It increases with the cube of time $(v(t) \propto t^3)$} + + +\vspace{1cm} + + + +\question[0.5cm]{Plot below the $v(t)$ and $x(t)$ for the given $a(t)$ plot. Assume $v_0 = 0$ and $x_0 = 0$} + +\begin{tikzpicture} + \begin{axis}[ + axis lines=middle, + xlabel={$t$}, + ylabel={$a$}, + xtick=\empty, + ytick=\empty, + enlargelimits=true + ] + \addplot[ + thick, + domain=0:10, + samples=100, + mark=none + ] coordinates { + (0,-1) (2,2) % constant positive + (4,-1) % linear decrease + (6,1) % constant negative + (8,1) % linear increase + (8.1,3) (10,3) % jump to higher positive + (12,3) (12.1,0) % drop to zero + (14,0) % remains zero + }; + \end{axis} +\end{tikzpicture} + + + + + +\newpage + +\question[0.5cm]{Below, plot the function $x(t) = 2x^{\frac{1}{2}}$, plot this as well as $v(t)$ and $a(t)$ of the same function} + +\hspace{-3.4cm} +\begin{tikzpicture}[scale=0.85] + \begin{axis}[ + xmin=0, xmax=5, + ymin=-6, ymax=6, + axis lines=middle, + xlabel=$t$, ylabel={$x(t)$}, + xtick={0,1,2,3,4,5}, + ytick={-5,-3,-1,0,1,3,5}, + xticklabel style={anchor=north}, + yticklabel style={anchor=east}, + grid=both, + ] + \end{axis} +\end{tikzpicture} +\hspace{0cm} +\begin{tikzpicture}[scale=0.85] + \begin{axis}[ + xmin=0, xmax=5, + ymin=-6, ymax=6, + axis lines=middle, + xlabel=$t$, ylabel={$v(t)$}, + xtick={0,1,2,3,4,5}, + ytick={-5,-3,-1,0,1,3,5}, + xticklabel style={anchor=north}, + yticklabel style={anchor=east}, + grid=both, + ] + \end{axis} +\end{tikzpicture} +\hspace{0cm} +\begin{tikzpicture}[scale=0.85] + \begin{axis}[ + xmin=0, xmax=5, + ymin=-6, ymax=6, + axis lines=middle, + xlabel=$t$, ylabel={$a(t)$}, + xtick={0,1,2,3,4,5}, + ytick={-5,-3,-1,0,1,3,5}, + xticklabel style={anchor=north}, + yticklabel style={anchor=east}, + grid=both, + ] + \end{axis} +\end{tikzpicture} + +\vspace{4cm} + +%circular motion +\question[4cm]{A large motor is running at $4000$ rpm with an internal linear velocity of $v = \SI{20}{\meter\per\second}$. What is the radius $R$ of the motor and the frequency $f$ at which the motor is rotating?} + + +%relative motion +\question[0cm]{Enzo is driving a remote control car on a train that has just begun to move after making a stop at a station} + +\questionpart[3cm]{If the train is accelerating at $a = \SI{2}{\metre\per\second\squared}$ at $t = 0s$ and Enzo's toy car is going at a constant speed of $v = \SI{-3}{\metre\per\second}$, what is the toy car's position as a function of time as seen from the stationary platform of the train station?} + +\questionpart[0cm]{At what point in time will the toy car appear to be moving in the same direction as the train?} + + + + + + +\end{worksheet} + +\end{document} \ No newline at end of file diff --git a/worksheets/Kinematics_Answers.pdf b/worksheets/Kinematics_Answers.pdf new file mode 100644 index 0000000..92b641c Binary files /dev/null and b/worksheets/Kinematics_Answers.pdf differ diff --git a/worksheets/Kinematics_Answers.tex b/worksheets/Kinematics_Answers.tex new file mode 100644 index 0000000..db31367 --- /dev/null +++ b/worksheets/Kinematics_Answers.tex @@ -0,0 +1,127 @@ +\documentclass[12pt]{article} + +\include{include/preambleworksheet} + +\begin{document} + +\begin{worksheet}{Physics Worksheet}{Kinematics} + +\question[0cm]{The acceleration of a cricket jumping sideways is observed to increase linearly with +time, that is, $ax(t) = a_0 + jt$, where $a_0$ and $j$ are constants. What can you say about +the velocity of the cricket as a function of time?} + +\questionpart[0cm]{It is constant} + +\questionpart[0cm]{It increases linearly with time $(v(t) \propto t)$} + +\questionpart[0cm]{It increases quadratically with time $(v(t) \propto t^2)$} + +\questionpart[0cm]{It increases with the cube of time $(v(t) \propto t^3)$} + +\textbf{(c)} + + + +\question[0.5cm]{Plot below the $v(t)$ and $x(t)$ for the given $a(t)$ plot. Assume $v_0 = 0$ and $x_0 = 0$} + +\begin{tikzpicture} + \begin{axis}[ + axis lines=middle, + xlabel={$t$}, + ylabel={$a$}, + xtick=\empty, + ytick=\empty, + enlargelimits=true + ] + \addplot[ + thick, + domain=0:10, + samples=100, + mark=none + ] coordinates { + (0,-1) (2,2) % constant positive + (4,-1) % linear decrease + (6,1) % constant negative + (8,1) % linear increase + (8.1,3) (10,3) % jump to higher positive + (12,3) (12.1,0) % drop to zero + (14,0) % remains zero + }; + \end{axis} +\end{tikzpicture} + + + + + +\newpage + +\question[0.5cm]{Below, plot the function $x(t) = 2x^{\frac{1}{2}}$, plot this as well as $v(t)$ and $a(t)$ of the same function} + +\hspace{-3.4cm} +\begin{tikzpicture}[scale=0.85] + \begin{axis}[ + xmin=0, xmax=5, + ymin=-6, ymax=6, + axis lines=middle, + xlabel=$t$, ylabel={$x(t)$}, + xtick={0,1,2,3,4,5}, + ytick={-5,-3,-1,0,1,3,5}, + xticklabel style={anchor=north}, + yticklabel style={anchor=east}, + grid=both, + ] + \end{axis} +\end{tikzpicture} +\hspace{0cm} +\begin{tikzpicture}[scale=0.85] + \begin{axis}[ + xmin=0, xmax=5, + ymin=-6, ymax=6, + axis lines=middle, + xlabel=$t$, ylabel={$v(t)$}, + xtick={0,1,2,3,4,5}, + ytick={-5,-3,-1,0,1,3,5}, + xticklabel style={anchor=north}, + yticklabel style={anchor=east}, + grid=both, + ] + \end{axis} +\end{tikzpicture} +\hspace{0cm} +\begin{tikzpicture}[scale=0.85] + \begin{axis}[ + xmin=0, xmax=5, + ymin=-6, ymax=6, + axis lines=middle, + xlabel=$t$, ylabel={$a(t)$}, + xtick={0,1,2,3,4,5}, + ytick={-5,-3,-1,0,1,3,5}, + xticklabel style={anchor=north}, + yticklabel style={anchor=east}, + grid=both, + ] + \end{axis} +\end{tikzpicture} + +\vspace{4cm} + +%circular motion +\question[4cm]{A large motor is running at $4000$ rpm with an internal linear velocity of $v = \SI{20}{\meter\per\second}$. What is the radius $R$ of the motor and the frequency $f$ at which the motor is rotating?} + + +%relative motion +\question[0cm]{Enzo is driving a remote control car on a train that has just begun to move after making a stop at a station} + +\questionpart[3cm]{If the train is accelerating at $a = \SI{2}{\metre\per\second\squared}$ at $t = 0s$ and Enzo's toy car is going at a constant speed of $v = \SI{-3}{\metre\per\second}$, what is the toy car's position as a function of time as seen from the stationary platform of the train station?} + +\questionpart[0cm]{At what point in time will the toy car appear to be moving in the same direction as the train?} + + + + + + +\end{worksheet} + +\end{document} \ No newline at end of file diff --git a/worksheets/ModelAndExperiment.pdf b/worksheets/ModelAndExperiment.pdf new file mode 100644 index 0000000..91bf531 Binary files /dev/null and b/worksheets/ModelAndExperiment.pdf differ diff --git a/worksheets/ModelAndExperiment.tex b/worksheets/ModelAndExperiment.tex new file mode 100644 index 0000000..961ebc4 --- /dev/null +++ b/worksheets/ModelAndExperiment.tex @@ -0,0 +1,24 @@ +\documentclass[12pt]{article} + +\include{include/preambleworksheet} + + +\begin{document} + +\begin{worksheet}{Phys 101 Worksheet}{Comparing Model and Experiment} + +\question[3cm]{Suppose there's a theory "Dogs cannot be born with naturally blue fur." Can this theory be proven to be true? \textbf{Explain} why or why not.} + +\question[0.1cm]{Suppose you're a butterfly researcher. You find that rarer butterflies appear to be faster, and flutter their wings at a higher rate than more common butterflies. You invent a new unit, a "Whimsy" (denoted as $W$), which is the \textbf{product} the maximum velocity of a given species of butterfly, $v$, and the frequency at which it flaps its wings $f$.} + +\questionpart[2cm]{Explicitly write out the formula to calculate Whimsiness. What are it's dimensions?} + +\questionpart[3cm]{ Suppose now you want to create a formula that could predict the most whimsical butterfly any given butterfly catching machine could catch knowing only its mass, $m$ and the maximum force it can swing with $F_s$. Write a possible solution (within a constant) that could be a solution to the problem.} + +\questionpart[0cm]{Does the formula you've devised make sense? Explain wy or why not} + + +\end{worksheet} + + +\end{document} \ No newline at end of file diff --git a/worksheets/ModelAndExperiment_Answers.pdf b/worksheets/ModelAndExperiment_Answers.pdf new file mode 100644 index 0000000..620e30c Binary files /dev/null and b/worksheets/ModelAndExperiment_Answers.pdf differ diff --git a/worksheets/ModelAndExperiment_Answers.tex b/worksheets/ModelAndExperiment_Answers.tex new file mode 100644 index 0000000..54f08af --- /dev/null +++ b/worksheets/ModelAndExperiment_Answers.tex @@ -0,0 +1,37 @@ +\documentclass[12pt]{article} + +\include{include/preambleworksheet} + + +\begin{document} + +\begin{worksheet}{Phys 101 Worksheet}{Comparing Model and Experiment} + +\question[0.1cm]{Suppose there's a theory "Dogs cannot be born with naturally blue fur."Can this theory be proven to be true? \textbf{Explain} why or why not.} + +This theory \textbf{cannot be proven to be true}. It can only be disproved once a dog with naturally blue fir is discovered. + +\vspace{2cm} + +\question[0cm]{Suppose you're a butterfly researcher. You find that rarer butterflies appear to be faster, and flutter their wings at a higher rate than more common butterflies. You invent a new unit, a "Whimsy" (denoted as $W$), which is the \textbf{product} the maximum velocity of a given species of butterfly, $v$, and the frequency at which it flaps its wings $f$.} + +\questionpart[0cm]{Explicitly write out the formula to calculate Whimsiness. What are it's dimensions?} + +\textbf{$W = vf$. It has dimenions of: $\frac{L}{T^2}$} + +\vspace{1.5cm} + +\questionpart[0cm]{ Suppose now you want to create a formula that could predict the most whimsical butterfly any given butterfly catching machine could catch knowing only its mass, $m$ and the maximum force it can swing with $F_s$. Write a possible solution (within a constant) that could be a solution to the problem.} + +$W = k\frac{F_s}{m}$ + +\vspace{2.5cm} + +\questionpart[0cm]{Does the formula you've devised make sense? Explain wy or why not} + +It makes sense because the formula is dimensionally sound. As well, a bigger machine would be harder to carry and thus would not be able to catch as whimsical butterflies which will be faster and thus more difficult to catch. + +\end{worksheet} + + +\end{document} \ No newline at end of file diff --git a/worksheets/MomentumAndCM.pdf b/worksheets/MomentumAndCM.pdf new file mode 100644 index 0000000..1001270 Binary files /dev/null and b/worksheets/MomentumAndCM.pdf differ diff --git a/worksheets/MomentumAndCM.tex b/worksheets/MomentumAndCM.tex new file mode 100644 index 0000000..9d3bd6c --- /dev/null +++ b/worksheets/MomentumAndCM.tex @@ -0,0 +1,68 @@ +\documentclass[12pt]{article} + +\include{include/preambleworksheet} + +\begin{document} + +\begin{worksheet}{Physics Worksheet}{Momentum and Centre of Mass} + + + +\question[0cm]{Imagine a game of pool on a peculiar pool table. The white cue is struck and strikes the side of the table where it compresses a spring, it then collides with the 8-ball and sends it into a pocket for the win. Below is a list of the forces acting on the \textbf{system of the two cue balls}. Explain whether these forces are external or internal. If they are external, explain what objects we would need to include in our system for them to be internal.} + +\questionpart[1cm]{Applied force on the white cue from the player} + +\questionpart[1cm]{Applied force of the collision between the two cue balls} + +\questionpart[1cm]{Gravity between the balls and The Earth} + +\questionpart[1cm]{The spring force from the spring} + +\questionpart[1cm]{The gravity between the two cue balls} + +\questionpart[1cm]{The friction between the table and the cue balls} + +\question[1cm]{A $\SI{1}{\meter}$ catapult is able to expend $\SI{15}{\kilo\watt}$ of power over $\SI{0.1}{\second}$ before launching its payload. What is the impulse on the payload from the catapult?} + +\newpage + +\question[0.5cm]{The gray $\SI{0.75}{\kilo\gram}$ cue ball strikes the black $\SI{1.25}{\kilo\gram}$ and they go flying off in different directions. At what velocity (magnitude and direcction) does the gray cue ball go off in?} + +\begin{tikzpicture} + + +\draw[fill=gray!30] (0,0) circle (0.5cm); +\draw[-latex, line width = 2pt] (0.5,0)--(3,0) node[midway,below]{$\SI{1}{\meter\per\second}$}; + +\draw[fill=black] (3.5,0.3) circle (0.5cm); + +\draw[line width = 4pt, color = gray] (5,-2)--(5,2); + +\draw[fill=black] (6,0.3) circle (0.5cm); +\draw[-latex, line width =2pt] (6,0.3)--(9,1.5) node[pos=0.5, below]{$\theta = 55^\circ$} node[pos=0.5, above]{$\SI{0.3}{\meter\per\second}$}; +\draw[dotted, line width = 2pt] (6,0.3)--(8,0.3); + +\draw[fill=gray!30] (6,-0.4) circle (0.5cm); +\draw[-latex, line width =2pt] (6,-0.4)--(8.5,-2); + +\end{tikzpicture} + + +\vspace{5cm} + + +\question[0cm]{The following questions discuss centre of mass:} + +\questionpart[3cm]{Does the centre of mass always reside \textit{inside} of the object? What is an example of an object where this may not be the case} + +\questionpart[3cm]{In what situations might it be more useful/easier to describe the motion of the centre of mass of an object as oppose to the object as a whole?} + +\questionpart[0cm]{Describe a situation where object within a system are moving but the centre of mass of the system is stationary} + + + + + +\end{worksheet} + +\end{document} \ No newline at end of file diff --git a/worksheets/NewtonsLaws.pdf b/worksheets/NewtonsLaws.pdf new file mode 100644 index 0000000..eafffdf Binary files /dev/null and b/worksheets/NewtonsLaws.pdf differ diff --git a/worksheets/NewtonsLaws.tex b/worksheets/NewtonsLaws.tex new file mode 100644 index 0000000..9372f8f --- /dev/null +++ b/worksheets/NewtonsLaws.tex @@ -0,0 +1,74 @@ +\documentclass[12pt]{article} + +\include{include/preambleworksheet} + +\begin{document} + +\begin{worksheet}{Physics Worksheet}{Newton's Laws} + + +\question[5.5cm]{Explain in your own words, how Newton would have theoretically arrived to the conclusion of the existance of a gravitational force from an apple having fallen on his head while sitting under an apple tree.} + +\question[0cm]{Answer the following questions:} + +\questionpart[3.5cm]{Is The Earth an inertial reference frame? Explain why or why not:} + +\questionpart[3.5cm]{In what kind of situation could you approxomate The Earth to be an inertial reference frame?} + +\questionpart[0cm]{What's a real world example where you cannot make this approxomation?} + + +\newpage + + +\question[0cm]{A block is held motionless between 2 walls} + +\questionpart[0cm]{Make a free body diagram for the block and the left and right walls. Assume none of the surfaces are frictionless} + +\begin{tikzpicture}[scale=1] +\scalebox{1.0}{ +\draw[line width = 2pt] (0,0) -- (4,0); +\draw[line width = 2pt] (1,0) -- (1,4); +\draw[fill=gray!30] (0,0) rectangle (1,4); +\draw[line width = 2pt] (3,0) -- (3,4); +\draw[fill=gray!30] (3,0) rectangle (4,4); +\draw[line width = 2pt, color=blue] (1.05,3) -- (2.95,3); +\draw[line width = 2pt, color=blue] (1.05,2) -- (2.95,2); +\draw[line width = 2pt, color=blue] (1.05,2) -- (1.05,3); +\draw[line width = 2pt, color=blue] (2.95,2) -- (2.95,3); +\draw[fill=black] (1.07,2.03) rectangle (2.94,2.97); +} +\end{tikzpicture} +\vspace{2cm} + +\questionpart[3cm]{Write Newton's Second Law for the block and the left and right walls} + + +\question[0.25cm]{Below is a 2D cart with a vertical spring attached to a block. The cart also has 2 frictionless walls that hold the block motionless in the left and right directions relative to the cart. The system is currently at rest} + + +\begin{tikzpicture} +\scalebox{1.0}{ + \draw[fill=black] (0,0) rectangle (1,1); + + \draw[decorate, decoration={coil, aspect=0.1, segment length=10pt}, thick] (0.5,-1) -- (0.5,0); +\draw[fill=gray!30] (0,-1.5) rectangle (1,-1); + +\draw[fill=gray!30, fill opacity=0.99] (0.0,-1.5) circle (0.3cm); +\draw[fill=gray!30, fill opacity=0.99] (1,-1.5) circle (0.3cm); + +\draw[line width=2pt, color = gray!30] (0,-1.8)--(0, 1.8); +\draw[line width=2pt, color = gray!30] (1,-1.8)--(1, 1.8); +\draw[line width=2pt, color = black] (-0.5,-1.8)--(14, -1.8); +} + +\end{tikzpicture} + +\questionpart[0.25cm]{The cart is pushed to the right and the block is given an impulse in the downward direction both at $t = 0s$. Above, draw the theoretical trajectory of the block over time:} + + +\questionpart[0cm]{What simple function could describe the motion of the block $x(t)$?} + +\end{worksheet} + +\end{document} \ No newline at end of file diff --git a/worksheets/PotentialECons.pdf b/worksheets/PotentialECons.pdf new file mode 100644 index 0000000..ca88d40 Binary files /dev/null and b/worksheets/PotentialECons.pdf differ diff --git a/worksheets/PotentialECons.tex b/worksheets/PotentialECons.tex new file mode 100644 index 0000000..5d51665 --- /dev/null +++ b/worksheets/PotentialECons.tex @@ -0,0 +1,29 @@ +\documentclass[12pt]{article} + +\include{include/preambleworksheet} + +\begin{document} + +\begin{worksheet}{Physics Worksheet}{Conservation of Energy} + +\question[3cm]{Is the value of an an object’s mechanical energy meaningful, or is it only the difference in mechanical energy that is meaningful?} + + +\question[4cm]{Aditi and Adam are having a disagreement about potential energy (as you do). Adam picked his (very heavy) $\SI{1}{\kilo\gram}$ phone $\SI{0.5}{\meter}$ above a $\SI{0.5}{\meter}$ high coffee table. Adam states the phone has $\SI{9.8}{\joule}$ of potential energy, as where Aditi states it actually has $\SI{4.9}{\joule}$. Which one of them is correct?} + +\question[0cm]{Derive the formula for potential energy expressed as $mgh$. (Hint: look up gravitational potential energy)} + +\newpage + +\question[0cm]{This question concerns the spring force} + +\questionpart[4cm]{Is the spring force conservative? Explain with your own words why or why not \textit{and} prove it mathmatically} + +\questionpart[4cm]{Derive the potential energy for a spring. Justify why this is possible} + + +\question[0cm]{You are tasked to find how powerful of a propelling engine you need for a sattelite after it's initial launch. Your 1000kg sattelite needs to reach Earth's escape velocity ($\SI{11.0}{\kilo\meter\per\second}$) between the heights of $\SI{50}{\kilo\meter}$ and $\SI{100}{\kilo\meter}$ above the Earth's surface starting from a Lagrangian of $\SI{9.9e8}{\joule}$. Ignoring air drag, how much power will your engine have to expend?} + +\end{worksheet} + +\end{document} \ No newline at end of file diff --git a/worksheets/Relativity.pdf b/worksheets/Relativity.pdf new file mode 100644 index 0000000..457a398 Binary files /dev/null and b/worksheets/Relativity.pdf differ diff --git a/worksheets/Relativity.tex b/worksheets/Relativity.tex new file mode 100644 index 0000000..b59c1d7 --- /dev/null +++ b/worksheets/Relativity.tex @@ -0,0 +1,32 @@ +\documentclass[12pt]{article} + +\include{include/preambleworksheet} + +\begin{document} + +\begin{worksheet}{Physics Worksheet}{Relativity} + + + +\question[6cm]{What is the gamma factor for a speed of $v=0.8c$?} + + +\question[6cm]{What is the speed $v$ corrosponds to a gamma factor of $\gamma = 3.2$?} + + + + +\question[0cm]{What does the world line of a particle going the speed of light look like on a space time diagram?} + +\newpage + +\question[0cm]{Look up and describe two real world phenomena that are explained by special relativity.} + + + + + + +\end{worksheet} + +\end{document} \ No newline at end of file diff --git a/worksheets/RotationalDynamics.pdf b/worksheets/RotationalDynamics.pdf new file mode 100644 index 0000000..e07bd82 Binary files /dev/null and b/worksheets/RotationalDynamics.pdf differ diff --git a/worksheets/RotationalDynamics.tex b/worksheets/RotationalDynamics.tex new file mode 100644 index 0000000..37f0954 --- /dev/null +++ b/worksheets/RotationalDynamics.tex @@ -0,0 +1,79 @@ +\documentclass[12pt]{article} + +\include{include/preambleworksheet} + +\begin{document} + +\begin{worksheet}{Physics Worksheet}{Rotational Dynamics} + + +\question[5cm]{Is it possible for an object has a positive net torque but $F_{net}=0$? If so, what's an example of an object exibiting this behaviour?} + +\question[0.5cm]{Here is a top view of a rotating counter clockwise disk who is rotating at an increasing rate. Indicate which of the below options are \textbf{true} and explain why:} + + + +\begin{tikzpicture} + +\draw[fill=gray!30, fill opacity=0.99] (0,0) circle (2cm); +\draw[fill=black, fill opacity=1] (0,0) circle (.1cm); + +\draw[dotted, line width = 4pt] (0,0)--(1.75,0); + +\draw[fill=red, fill opacity=1] (1.75,0) circle (.1cm); +\node at (1.75,-0.3) {$R$}; + +\draw[fill=red, fill opacity=1] (0.75,0) circle (.1cm); +\node at (0.75,-0.3) {$r$}; + + +\end{tikzpicture} + + +\questionpart[0.25cm]{$R$ and $r$ have the \textbf{same} angular and linear velocity but \textbf{different} angular and linear acceleration} + +\questionpart[0.25cm]{$R$ and $r$ have the \textbf{same} angular and linear acceleration but \textbf{different} angular and linear velocity} + +\questionpart[0.25cm]{$R$ and $r$ have the \textbf{same} angular velocity but \textbf{different} angular acceleration and linear velocity and acceleration} + +\questionpart[3cm]{$R$ and $r$ have the \textbf{same} angular velocity and acceleration but \textbf{different} linear velocity and acceleration} + + +\newpage + + +\question[0cm]{Below is a "T" shape with the axis going through the top coming out of the page} + +\questionpart[0.5cm]{Calculate the moment of inertia through this point} + +\begin{tikzpicture}[scale=0.75] + +\draw[line width =8pt] (0,0)--(5,0); +\draw[line width =8pt] (2.5,0)--(2.5,-5); + +\draw[line width = 2pt, color=gray] (-0.1,0.5)--(5.1,0.5) node[midway, above]{$L$}; +\draw[line width = 2pt, color=gray] (-0.1,0.2)--(-0.1,0.5); +\draw[line width = 2pt, color=gray] (5.1,0.2)--(5.1,0.5); + + +\draw[line width = 2pt, color=gray] (5.5,-5.1)--(5.5,0.1) node[midway, right]{$L$}; +\draw[line width = 2pt, color=gray] (5.2,-5.1)--(5.5,-5.1); +\draw[line width = 2pt, color=gray] (5.2,0.1)--(5.5,0.1); + +\draw[fill=red] (2.5,0) circle (0.2cm); + +\end{tikzpicture} + +\vspace{4cm} + +\questionpart[5cm]{Where on the T is the moment of inertia the \textit{smallest}. Explain how you know the moment of inertia is minimal at that point} + +\questionpart[0cm]{Calculate the moment of inertia at this new point} + + + + +\end{worksheet} + + +\end{document} diff --git a/worksheets/RotationalEnergyAndMomentum.pdf b/worksheets/RotationalEnergyAndMomentum.pdf new file mode 100644 index 0000000..600062d Binary files /dev/null and b/worksheets/RotationalEnergyAndMomentum.pdf differ diff --git a/worksheets/RotationalEnergyAndMomentum.tex b/worksheets/RotationalEnergyAndMomentum.tex new file mode 100644 index 0000000..ff63653 --- /dev/null +++ b/worksheets/RotationalEnergyAndMomentum.tex @@ -0,0 +1,46 @@ +\documentclass[12pt]{article} + +\include{include/preambleworksheet} + +\begin{document} + +\begin{worksheet}{Physics Worksheet}{Rotational Energy and Momentum} + +\question[3cm]{A hoop, a disk, and a sphere roll without slipping down an incline. If they are all +released at the same time, in what order will they arrive at the bottom? Explain why:} + + +\question[4cm]{Take an elliptical orbit. Kepler's second law states that: a line from the sun to a planet sweeps out equal areas in equal time intervals. After reading this chapter, what is another way you can express this same concept?} + +\question[0.5cm]{Consider a perfect pendulum. What would a Lagrangian look like for the system using angular qualities?} + +\begin{tikzpicture} +\draw[dotted, line width = 3pt] (0,0)--(0,-3); +\draw[line width = 3pt] (0,0)--(1.5,-2.5); +\draw[fill=black] (1.5,-2.5) circle (0.25cm); +\node at (0.25,-1){$\theta$}; + + +\end{tikzpicture} + + + + +\newpage + +\question[7cm]{Your friend Atlas, just having finished the rotational dynamics unit, tells you they believe that if you were to throw a ball at the equator, and The Earth and everything else with it disappeared, the ball would go flying off into space at high speeds due because of the speed it got from The Earth's rotation energy. Design a model, estimate, and conclude whether Atlas is correct in their thinking or not.} + + + + +\question[0cm]{You are about to start climbing a mountain when a spherical rock suddenly rolls passed you down the mountain (without slipping) with a speed of $\SI{200}{\meter\per\second}$. If the mountain has an average of a $15^\circ$ slope, how tall is it?} + + + + + + +\end{worksheet} + + +\end{document} \ No newline at end of file diff --git a/worksheets/SimpleHarmonicMotion.pdf b/worksheets/SimpleHarmonicMotion.pdf new file mode 100644 index 0000000..52a9dda Binary files /dev/null and b/worksheets/SimpleHarmonicMotion.pdf differ diff --git a/worksheets/SimpleHarmonicMotion.tex b/worksheets/SimpleHarmonicMotion.tex new file mode 100644 index 0000000..5523eef --- /dev/null +++ b/worksheets/SimpleHarmonicMotion.tex @@ -0,0 +1,54 @@ +\documentclass[12pt]{article} + +\include{include/preambleworksheet} + +\begin{document} + +\begin{worksheet}{Physics Worksheet}{Simple Harmonic Motion} + + + +\question[0cm]{What is the SI unit for angular frequency?} + +\questionpart[0cm]{Hz} + +\questionpart[0cm]{rad/s} + +\questionpart[0cm]{$N^{1/2}m^{-1/2}kg^{-1/2}$} + +\questionpart[1cm]{All of the above} + + + + + +\question[5cm]{A spring-mass system with a weight $M$ is oscillating with a period $T$. What is the spring constant $k$ of the spring?} + + + + + + +\question[0cm]{Imagine your friend has a grandfather clock that is ticking too slowly} + +\questionpart[0cm]{They tell you they are opting to increase the weight of the mass at the end of the arm of the clock to speed it up. Will this have the desired effect? Explain why or why not} + +\newpage + +\questionpart[6cm]{Now your friend wants to bring his grandfather clock on the moon. What properties must the grandfather clock have such that it accurately tracks Earth seconds?} + + + +\question[0cm]{A hoop, disc, and sphere, all with radius $R$ and mass $M$ are all oscillating about a point on their outer edge} + +\questionpart[6cm]{Which of the shapes will have the shortest period of oscillation?} + +\questionpart[0cm]{How much bigger would the disc and hoop have to be to oscillate at the same speed as the sphere} + + + + +\end{worksheet} + + +\end{document} \ No newline at end of file diff --git a/worksheets/Vectors.pdf b/worksheets/Vectors.pdf new file mode 100644 index 0000000..cba5834 Binary files /dev/null and b/worksheets/Vectors.pdf differ diff --git a/worksheets/Vectors.tex b/worksheets/Vectors.tex new file mode 100644 index 0000000..344bbfc --- /dev/null +++ b/worksheets/Vectors.tex @@ -0,0 +1,76 @@ +\documentclass[12pt]{article} + +\include{include/preambleworksheet} + +\begin{document} + +\begin{worksheet}{Physics Worksheet}{Vectors} +%Algebra with vectors +\question[7cm]{A boat is traveling across a river. It's going south east with a velocity of: \\ $\vec{v_B} = (-5,-4) \si{\kilo\metre\per\hour}$. The river is flowing with a velocity of $\vec{v_w} = (2,1) \si{\kilo\metre\per\hour}$. With what velocity is the boat crossing the river?} + +%Scalar product +\question[0cm]{Aki and Luke go running off in different directions. $\vec{v_A}= (\frac{1}{3},2) \si{\metre\per\second}, \\ \vec{v_L}= (-1,\frac{3}{4})\si{\metre\per\second}$. What is the angle between their velocity vectors?} + + +\newpage + +%Cross product +\question[7cm]{A force $\vec{F} = (6,2)$ is applied to the edge of a disc centered at the origin at $\vec{r} = (1,1)$. What is the magnitude and direction of the angular acceleration? +\\ +\begin{tikzpicture}[scale=1] +\tikzmath{ +\R=0.75; +} +\scalebox{1.0}{ + +\fill[color=blue!60] circle (\R); +\fill[black] circle (1.5pt); + +\draw[-latex, line width = 2pt] (0,0) -- (45:\R) node[midway, below]{$\vec r$}; +\draw[dashed, line width = 2pt] (45:\R) -- + (45:\R); +\draw ($(45:\R)+(0.5,0.18)$) arc (25:50:0.5) node[midway, above right, yshift=-3pt]{$\theta$}; +\draw[-latex, line width = 1pt] (45:\R) -- + (3*\R,1*\R) node[midway, below]{$\vec F$}; + +} +\end{tikzpicture}} + + + + + + + + +%Right hand rule +\question[0cm]{Use the right hand rule to find the direction $\vec{a} \times \vec{b}$ for the first two sets of vectors, and find the rotation vector of the third figure.} +\\ +\begin{tikzpicture}[scale=1] +\scalebox{1.0}{ +\draw[-latex,line width = 2pt] (0,0) -- (3,0)node[midway, below]{$\vec a$}; +\draw[-latex,line width = 2pt] (0,0) -- (0,3)node[midway, left]{$\vec b$}; +} +\end{tikzpicture} +\noindent +\hspace{3cm} +\noindent +\begin{tikzpicture}[scale=1] +\scalebox{1.0}{ +\draw[line width = 2pt] (-0.3,-0.3) -- (0.3,0.3)node[midway, below]{$\vec a$}; +\draw[line width = 2pt] (0.3,-0.3) -- (-0.3,0.3); +\draw[-latex,line width = 2pt] (0,0) -- (0,3)node[midway, left]{$\vec b$}; +} +\end{tikzpicture} +\noindent +\hspace{3cm} +\begin{tikzpicture}[scale=1] +\scalebox{1.0}{ +\draw[line width = 0pt] (0,0) -- (0,0); +\draw[-latex, line width = 2pt] (2,1.5) arc[start angle=0, end angle=-270, radius=1cm]node[pos=0.33, below]{$\vec a$}; +} +\end{tikzpicture} + + +\end{worksheet} + + +\end{document} \ No newline at end of file diff --git a/worksheets/Waves.pdf b/worksheets/Waves.pdf new file mode 100644 index 0000000..80bfcfb Binary files /dev/null and b/worksheets/Waves.pdf differ diff --git a/worksheets/Waves.tex b/worksheets/Waves.tex new file mode 100644 index 0000000..c53b1ca --- /dev/null +++ b/worksheets/Waves.tex @@ -0,0 +1,37 @@ +\documentclass[12pt]{article} + +\include{include/preambleworksheet} + +\begin{document} + +\begin{worksheet}{Physics Worksheet}{Waves} + + +\question[5cm]{Rank the following mediums from fasted to slowest wave speed and explain why: Ice, vapour, water, vaccuum of space} + +\question[0cm]{Imagine someone is strumming a guitar infront of you} + +\questionpart[5cm]{Which strings on the guitar make a higher pitched noise and why?} + +\questionpart[3cm]{If all the strings are strum at the same time, which string will you hear the noise from first?} + + +\newpage + +\question[6cm]{Show that the work done by a spherical wave over the course of its period T in a fluid is: $W = \omega^3 A^2 r^2 \sqrt{B \rho}$} + + +\question[6cm]{In movies, when a glass shatters due to someone singing a very high note, what are the theoretical physics behind what is happening?} + + +\question[0cm]{For a standing wave on a string, at which harmonic will the velocity be such that it travels across the full lenght of string $L$ in one period T?} + + + + + + +\end{worksheet} + + +\end{document} \ No newline at end of file diff --git a/worksheets/WorkEnergy.pdf b/worksheets/WorkEnergy.pdf new file mode 100644 index 0000000..405a645 Binary files /dev/null and b/worksheets/WorkEnergy.pdf differ diff --git a/worksheets/WorkEnergy.tex b/worksheets/WorkEnergy.tex new file mode 100644 index 0000000..d77e274 --- /dev/null +++ b/worksheets/WorkEnergy.tex @@ -0,0 +1,52 @@ +\documentclass[12pt]{article} + +\include{include/preambleworksheet} + +\begin{document} + +\begin{worksheet}{Physics Worksheet}{Work and Energy} + +\question[4cm]{Would gravity do more et work on you if you were to drive or fly from Ottowa to Kingston?} + + +\question[5cm]{Aki is a high jumper. She has a mass of 70kg. She is attempting to clear a $\SI{2}{\meter}$ high bar. Her muscles exert $\SI{2400}{\joule}$ of energy and are $50\%$ efficient at converting this into her jump. Does she clear the bar?} + + + + +\question[0cm]{Two cars ($a$ and $b$) with identical weight $m$ drive for the same amount of time $t$ from rest. Car $b$ has an engine that is 4 times more powerful than car $a$'s. What are the final velocities of the two cars?} + + +\newpage + +\question[0.5cm]{Below, a moterized cart travels across a road. The road has a coffiecient of friction of $\mu = 0.5$. $\theta_1 = 30^\circ$ and $\theta_2 = 45^\circ$. The cart weighs $\SI{100}{\kilogram}$} + +\begin{tikzpicture} + +\draw[fill=gray!30] (0,-1.5) rectangle (1,-1); + +\draw[fill=gray!30, fill opacity=0.99] (0.0,-1.5) circle (0.3cm); +\draw[fill=gray!30, fill opacity=0.99] (1,-1.5) circle (0.3cm); + +\draw[line width = 2pt, color = black] (0.0,-1.8)--(3.5,-1.8) node[midway, below]{$5m$}; + +\draw[line width = 2pt, color = black] (3,-1.8)--(4.5,-0.94) node[midway, above]{$3m$} node[pos=0.5, below]{$\theta_1$}; + +\draw[line width = 2pt, color = gray] (4.5,-2.2)--(4.5,2) node[midway, left]{$a$} node[midway, right]{$b$}; + +\draw[line width = 2pt, color = black] (4.5,-0.94)--(8,-0.94) node[midway, below]{$4m$}; + +\draw[line width = 2pt, color = black] (7.5,-0.94)--(9,0.56) node[midway, above]{$4m$} node[pos=0.5, below]{$\theta_2$}; + + +\end{tikzpicture} + +\questionpart[6cm]{Does the friction force do more work in part $a$ or $b$ of the road?} + +\questionpart[5cm]{How much work does gravity do in part $a$ and $b$?} + +\questionpart[0cm]{If it takes the cart $\SI{5}{\second}$ to complete part $a$, and $\SI{7}{\second}$ to complete part $b$, which part required the cart's motor to exert more power?} + +\end{worksheet} + +\end{document} \ No newline at end of file diff --git a/worksheets/include/figures/bmdwlogo.pdf b/worksheets/include/figures/bmdwlogo.pdf new file mode 100644 index 0000000..660dbbf Binary files /dev/null and b/worksheets/include/figures/bmdwlogo.pdf differ diff --git a/worksheets/include/preambleworksheet.tex b/worksheets/include/preambleworksheet.tex new file mode 100644 index 0000000..4e724a5 --- /dev/null +++ b/worksheets/include/preambleworksheet.tex @@ -0,0 +1,97 @@ +\usepackage[a4paper, margin=1in]{geometry} +\usepackage{graphicx} +\usepackage[absolute, overlay]{textpos} +\usepackage{fancyhdr} +\usepackage{siunitx} +\usepackage{tikz} +\usepackage{pgfplots} +\usepackage{amsmath} +\usepackage{circuitikz} +\usetikzlibrary{decorations.pathmorphing} +\usetikzlibrary{math} +\usetikzlibrary{calc} + +\pgfplotsset{compat=1.18} + +\pagestyle{fancy} %for footers + +\newcommand{\customsubject}{} +\newcommand{\customtitle}{} + +\newcounter{questionpartcounter} %Setup for question part counter for a,b,c listing +\renewcommand{\thequestionpartcounter} +{\alph{questionpartcounter}} + +\newcounter{questionpartpartcounter} %Setup for question part partcounter for a,b,c listing +\renewcommand{\thequestionpartpartcounter} +{\roman{questionpartcounter}} + +\pagestyle{fancy} %for footers +\renewcommand{\headrulewidth}{0pt} +\fancyhf{} +\fancyfoot[R]{\thepage} + +\newenvironment{worksheet}[2] +{ + + \global\renewcommand{\customtitle}{#1} + \global\renewcommand{\customsubject}{#2} + + + \begin{textblock*}{5cm}(0.4cm,0.4cm) + \includegraphics[width=4cm]{include/figures/bmdwlogo} +\end{textblock*} + + \vspace*{-1cm} + + {\large\textbf{\begin{center}\customtitle\end{center}}} + + \begin{center}\customsubject\end{center} + + \vspace{0.3cm} + + \hspace*{-1.5cm}\textbf{Name:\ \rule{4cm}{0.4pt}}\; + \textbf{Student \#: \ \rule{3cm}{0.4pt}}\; + \textbf{Student Email \#: \ \rule{1.53cm}{0.4pt}} + + \vspace{0.5cm} + + + \begin{enumerate} +} +{ + \end{enumerate} + % \begin{textblock*}{10cm}(1cm, 28cm) {\footnotesize \scriptsize \customsubject} + +%\end{textblock*} +} + + + +\newcommand{\question}[2][1cm]{% + \item + \setcounter{questionpartcounter}{0} + \setcounter{questionpartpartcounter}{0} + {#2} + \vspace{#1} +} + +\newcommand{\questionpart}[2][1cm]{% + \setcounter{questionpartpartcounter}{0} + \stepcounter{questionpartcounter} + (\thequestionpartcounter)~#2 + \vspace{#1} +} + +\newcommand{\questionpartpart}[2][1cm]{% + \stepcounter{questionpartpartcounter} + \thequestionpartpartcounter.~#2 + \vspace{#1} +} + +\newcommand{\operation}[1]{% +{\large $ +#1 +$} +} +