[spec] tidy up tension diagrams in notes

diff --git a/spec/dynamics.pdf b/spec/dynamics.pdf
index dc59835e128918c05f5f7faeb3a93f4cea6c7a8f..fb01f97dc4745ffa501ceeb161f88704272cbbde 100644 (file)
Binary files a/spec/dynamics.pdf and b/spec/dynamics.pdf differ

diff --git a/spec/dynamics.tex b/spec/dynamics.tex
index 7856ca90eab3056143248c1de2479573e0337f72..ac373c314afc99003ad741aa060975bb61a8c4bb 100644 (file)
--- a/spec/dynamics.tex
+++ b/spec/dynamics.tex
@@ -70,7 +70,7 @@ A mass of \(m\) kg has force of \(mg\) acting on it
 \def\arcr{0.5cm} % Radius of the arc used to indicate angles
 
 \tikzset{
 \def\arcr{0.5cm} % Radius of the arc used to indicate angles
 
 \tikzset{

-  force/.style={->,draw=blue,fill=blue},
+  force/.style={->,draw=blue,fill=blue, thick},

   axis/.style={densely dashed,gray,font=\small},
   M/.style={rectangle,draw,fill=lightgray,minimum size=0.5cm,thin},
   m/.style={rectangle,draw=black,fill=lightgray,minimum size=0.3cm,thin},
   axis/.style={densely dashed,gray,font=\small},
   M/.style={rectangle,draw,fill=lightgray,minimum size=0.5cm,thin},
   m/.style={rectangle,draw=black,fill=lightgray,minimum size=0.3cm,thin},


@@ -78,8 +78,30 @@ A mass of \(m\) kg has force of \(mg\) acting on it
   string/.style={draw=red, thick},
   pulley/.style={thick}
 }
   string/.style={draw=red, thick},
   pulley/.style={thick}
 }

-
-  \begin{center}\begin{tikzpicture}
+\tikzset{
+  % style to apply some styles to each segment of a path
+  on each segment/.style={
+    decorate,
+    decoration={
+      show path construction,
+      moveto code={},
+      lineto code={
+        \path [#1]
+        (\tikzinputsegmentfirst) -- (\tikzinputsegmentlast);
+      },
+      closepath code={
+        \path [#1]
+        (\tikzinputsegmentfirst) -- (\tikzinputsegmentlast);
+      },
+    },
+  },
+  % style to add an arrow in the middle of a path
+  mid arrow/.style={postaction={decorate,decoration={
+        markings,
+        mark=at position .5 with {\arrow[#1]{stealth}}
+      }}},
+}
+  \begin{center}\begin{tikzpicture}[scale=1.8]

 
     \pgfmathsetmacro{\Fnorme}{2}
     \pgfmathsetmacro{\Fangle}{30}
 
     \pgfmathsetmacro{\Fnorme}{2}
     \pgfmathsetmacro{\Fangle}{30}


@@ -88,26 +110,26 @@ A mass of \(m\) kg has force of \(mg\) acting on it
       \node[M,transform shape] (M) {};
       \coordinate (xmin) at ($(M.south west)-({abs(1.1*\Fnorme*sin(-\Fangle))},0)$);
       \coordinate (xmax) at ($(M.south east)+({abs(1.1*\Fnorme*sin(-\Fangle))},0)$);
       \node[M,transform shape] (M) {};
       \coordinate (xmin) at ($(M.south west)-({abs(1.1*\Fnorme*sin(-\Fangle))},0)$);
       \coordinate (xmax) at ($(M.south east)+({abs(1.1*\Fnorme*sin(-\Fangle))},0)$);

-      \coordinate (ymax) at ($(M.north)+(0, {abs(1.1*\Fnorme*cos(-\Fangle))})$);
-      \coordinate (ymin) at ($(M.south)-(0, 1cm)$);
+      \coordinate (ymax) at ($(M.center)+(0,{cos(\Fangle)})$);
+      \coordinate (ymin) at ($(M.center)-(0,{cos(\Fangle)})$);

       \coordinate (axiscentre) at ($(M.south)+(0.5cm, 0.5cm)$);
       \coordinate (axiscentre) at ($(M.south)+(0.5cm, 0.5cm)$);

-      \draw[postaction={decorate, decoration={border, segment length=2pt, angle=-45},draw,red}] (xmin) -- (xmax);
-      \coordinate (N) at ($(M.center)+(0,{\Fnorme*cos(-\Fangle)})$);
+      \draw[postaction={decorate, decoration={border, segment length=4pt, angle=-45},draw,red}] (xmin) -- (xmax);

       \coordinate (fr) at ($(M.center)+({\Fnorme*sin(-\Fangle)}, 0)$);
       \coordinate (fr) at ($(M.center)+({\Fnorme*sin(-\Fangle)}, 0)$);

-      {[axis,-]
-      \draw (ymin) -- (M.center);
-      }

       {[axis,->]
       {[axis,->]

-      \draw ($(M)+(1,0)$) -- ($(M)+(2,0)$) node[above right] {\(\boldsymbol{i}\)};
-      \draw ($(M)+(1,0)$) -- ($(M)+(1,1)$) node[above right] {\(\boldsymbol{j}\)};
+      \draw ($(M)+(1,0)$) -- ($(M)+(1.5,0)$) node[above right] {\(\boldsymbol{i}\)};
+      \draw ($(M)+(1,0)$) -- ($(M)+(1,0.5)$) node[above right] {\(\boldsymbol{j}\)};

       }
       {[force,->]
       }
       {[force,->]

-        \draw (M.center) -- (N) node [right] {\(R\)};
+        \draw (M.center) -- (ymax) node [right] {\(R\)};

         \draw (M.center) -- (fr) node [left] {\(\mu R\)};
       }
     \end{scope}
     \draw[force,->] (M.center) -- ++(0,-1) node[below] {$mg$};
         \draw (M.center) -- (fr) node [left] {\(\mu R\)};
       }
     \end{scope}
     \draw[force,->] (M.center) -- ++(0,-1) node[below] {$mg$};

-    \draw (M.center)+(-90:\arcr) arc [start angle=-90,end angle=\iangle-90,radius=\arcr] node [below, pos=.5] {\footnotesize\(\theta\)};
+    \draw (xmin)+(0:\arcr) arc [start angle=0, end angle=\iangle, radius=\arcr] node [right, midway] {\footnotesize\(\theta\)};
+      \coordinate (xbottom) at ($(1, {4*\Fnorme*-cos(\Fangle)})$);
+      \draw [->] (xmin) -- ++($({1.35*\Fnorme*cos(\Fangle)}, 0)$);
+      \begin{scope}[darkgray, rotate=\iangle] \path [draw=darkgray, postaction={on each segment={mid arrow}}] (M.center) -- (ymin) node [pos=0.5, right] {\(mg \cos \theta\)} -- ++(-0.5,0) node[pos=0.5, below right] {\(mg \sin \theta\)};
+      \end{scope}

   \end{tikzpicture}\end{center}
 
 \subsection*{Connected particles}
   \end{tikzpicture}\end{center}
 
 \subsection*{Connected particles}


@@ -115,15 +137,15 @@ A mass of \(m\) kg has force of \(mg\) acting on it
 \def\boxwidth{0.5}
 \tikzset{
   box/.style={rectangle,draw,fill=lightgray,minimum width=\boxwidth,thin},
 \def\boxwidth{0.5}
 \tikzset{
   box/.style={rectangle,draw,fill=lightgray,minimum width=\boxwidth,thin},

-  m/.style={rectangle,draw=black,fill=lightgray,minimum size=\boxwidth, font=\footnotesize, thin}
+  m/.style={rectangle,draw=black,fill=lightgray,minimum size=\boxwidth, thin}

 }
 
 
 \begin{center}
 }
 
 
 \begin{center}

-  \begin{tikzpicture}
+  \begin{tikzpicture}[scale=1.5]

 
 

-    \matrix[column sep=1cm] {
-      \begin{scope}
+    \matrix {
+      \begin{scope}[scale=1.5]

 
         \coordinate (O) at (0,0);
         \coordinate (A) at ($({3*cos(\iangle)},{3*sin(\iangle)})$);
 
         \coordinate (O) at (0,0);
         \coordinate (A) at ($({3*cos(\iangle)},{3*sin(\iangle)})$);


@@ -138,17 +160,18 @@ A mass of \(m\) kg has force of \(mg\) acting on it
         \draw[plane] (O) -- (A) -- (B) -- (O);
         \draw (O)+(\arcr,0) arc [start angle=0,end angle=\iangle,radius=\arcr] node [right, pos=.75] {\footnotesize\(\theta\)};
 
         \draw[plane] (O) -- (A) -- (B) -- (O);
         \draw (O)+(\arcr,0) arc [start angle=0,end angle=\iangle,radius=\arcr] node [right, pos=.75] {\footnotesize\(\theta\)};
 

-        \draw [rotate=\iangle, m] (C) rectangle ++(\boxwidth,\boxwidth) node (z) [rotate=\iangle, midway, font=\footnotesize] {\(m_1\)};
+        \draw [rotate=\iangle, m] (C) rectangle ++(\boxwidth,\boxwidth) node (z) [rotate=\iangle, midway] {\(m_1\)};

         \draw [pulley] (A) -- (X) ++(0.5*\boxwidth, 0) arc[rotate=\iangle, start angle=0, delta angle=360, x radius=0.25, y radius=0.25] node(r) [midway, rotate=\iangle] {};
         \draw [pulley] (A) -- (X) ++(0.5*\boxwidth, 0) arc[rotate=\iangle, start angle=0, delta angle=360, x radius=0.25, y radius=0.25] node(r) [midway, rotate=\iangle] {};

-        \draw [string] (E) -- (Y) arc (90+\iangle:0:0.25) -- ++($(0,{-1.5*sin(\iangle)})$) node[m] {\(m_2\)};
+        \draw [string] (E) -- (Y) arc (90+\iangle:0:0.25) -- ++($(0,{-1.5*sin(\iangle)-\boxwidth})$) node (p) {};
+        \coordinate (Z) at ($(p.center)+({-0.5*\boxwidth},0)$);
+        \draw [m] (Z) rectangle ++(\boxwidth, \boxwidth) node [midway] {\(m_2\)};

 
       \end{scope}
 
       \end{scope}

+\\

 
 

-      &
-
-      \begin{scope}[rotate=\iangle]
+      \begin{scope}[rotate=\iangle, scale=1.5]

 
 

-        \draw [m] ++(-0.5*\boxwidth,-0.5*\boxwidth) rectangle ++(\boxwidth,\boxwidth) node (m1) [rotate=\iangle, midway, font=\footnotesize] {\(m_1\)};
+        \draw [m] ++(-0.5*\boxwidth,-0.5*\boxwidth) rectangle ++(\boxwidth,\boxwidth) node (n) [rotate=\iangle, midway] {\(m_1\)};

 
         {[axis,-]
           \draw (0,-1) -- (0,0);
 
         {[axis,-]
           \draw (0,-1) -- (0,0);


@@ -157,9 +180,9 @@ A mass of \(m\) kg has force of \(mg\) acting on it
         }
 
         {[force,->]
         }
 
         {[force,->]

-          \draw (M.center) -- ++(0,{cos(\iangle)}) node[above right] {\(R_1\)};
-          \draw (M.west) -- ++(-0.5,0) node[left] {\(\mu R_1\)};
-          \draw (M.east) -- ++(1,0) node[above] {\(T_1\)};
+          \draw (n.center) -- ++(0,{cos(\iangle)}) node[above right] {\(R_1\)};
+          \draw (n.west) -- ++(-0.5,0) node[left] {\(\mu R_1\)};
+          \draw (n.east) -- ++(1,0) node[above] {\(T_1\)};

         }
 
         \draw[force,->, rotate=-\iangle] (M.center) -- ++(0,-1) node[below] {\(m_1 g\)};
         }
 
         \draw[force,->, rotate=-\iangle] (M.center) -- ++(0,-1) node[below] {\(m_1 g\)};


@@ -167,13 +190,15 @@ A mass of \(m\) kg has force of \(mg\) acting on it
       \end{scope}
 
       &
       \end{scope}
 
       &

+      \begin{scope}[scale=1.5]

 
 

-      \draw [m] ++(-0.5*\boxwidth,-0.5*\boxwidth) rectangle ++(\boxwidth,\boxwidth) node [midway, font=\footnotesize] {\(m_2\)};
+      \draw [m] ++(-0.5*\boxwidth,-0.5*\boxwidth) rectangle ++(\boxwidth,\boxwidth) node [midway] {\(m_2\)};

 
       {[force,->]
         \draw (0,0.5*\boxwidth) -- ++(0,1) node[above] {\(T_2\)};
         \draw (0,-0.5*\boxwidth) -- ++(0,-1) node[right] {\(m_2 g\)};
       }
 
       {[force,->]
         \draw (0,0.5*\boxwidth) -- ++(0,1) node[above] {\(T_2\)};
         \draw (0,-0.5*\boxwidth) -- ++(0,-1) node[right] {\(m_2 g\)};
       }

+      \end{scope}

       \\
     };
   \end{tikzpicture}
       \\
     };
   \end{tikzpicture}


@@ -182,16 +207,18 @@ A mass of \(m\) kg has force of \(mg\) acting on it
 \begin{itemize}
   \item \textbf{Suspended pulley:} tension in both sections of rope are equal \\
     \(|a| = g \frac{m_1 - m_2}{m_1 + m_2}\) where \(m_1\) accelerates down \\
 \begin{itemize}
   \item \textbf{Suspended pulley:} tension in both sections of rope are equal \\
     \(|a| = g \frac{m_1 - m_2}{m_1 + m_2}\) where \(m_1\) accelerates down \\

-    With tension: \\
+    With tension:

     \[ \begin{cases}m_1 g - T = m_1 a\\ T - m_2 g = m_2 a\end{cases} \\ \implies m_1 g - m_2 g = m_1 a + m_2 a \]
     \[ \begin{cases}m_1 g - T = m_1 a\\ T - m_2 g = m_2 a\end{cases} \\ \implies m_1 g - m_2 g = m_1 a + m_2 a \]

-  \item \textbf{String pulling mass on inclined pane:} Resolve parallel to plane \\
+  \item \textbf{String pulling mass on inclined pane:} Resolve parallel to plane

     \[ T-mg \sin \theta = ma \]
   \item \textbf{Linear connection:} find acceleration of system first
   \item \textbf{Pulley on right angle:} \(a = \frac{m_2g}{m_1+m_2}\) where \(m_2\) is suspended (frictionless on both surfaces)
   \item \textbf{Pulley on edge of incline:} find downwards force \(W_2\) and components of mass on plane
 \end{itemize}
 
     \[ T-mg \sin \theta = ma \]
   \item \textbf{Linear connection:} find acceleration of system first
   \item \textbf{Pulley on right angle:} \(a = \frac{m_2g}{m_1+m_2}\) where \(m_2\) is suspended (frictionless on both surfaces)
   \item \textbf{Pulley on edge of incline:} find downwards force \(W_2\) and components of mass on plane
 \end{itemize}
 

-\hspace{2em}\parbox{8em}{In this example, note \(T_1 \ne T_2\):}
+\begin{tabular}{rl}
+  \parbox[t][][t]{8em}{In this example, note \(T_1 \ne T_2\):} &
+  \parbox{12em}{

   \begin{tikzpicture}
 
       \begin{scope}
   \begin{tikzpicture}
 
       \begin{scope}


@@ -221,7 +248,9 @@ A mass of \(m\) kg has force of \(mg\) acting on it
 
       \end{scope}
 
 
       \end{scope}
 

-  \end{tikzpicture}
+  \end{tikzpicture}}
+\end{tabular}
+

 \subsection*{Equilibrium}
 
 \[ \dfrac{A}{\sin a} = \dfrac{B}{\sin b} = \dfrac{C}{\sin c} \tag{Lami's theorem}\]
 \subsection*{Equilibrium}
 
 \[ \dfrac{A}{\sin a} = \dfrac{B}{\sin b} = \dfrac{C}{\sin c} \tag{Lami's theorem}\]

diff --git a/spec/spec-collated.pdf b/spec/spec-collated.pdf
index 7aa2159ebf421d89567fbb2924c33b3875b71986..def810118956fe37581f55bf2ea46a7adc6fdc83 100644 (file)
Binary files a/spec/spec-collated.pdf and b/spec/spec-collated.pdf differ

diff --git a/spec/spec-collated.tex b/spec/spec-collated.tex
index 0525085edb4a24ea2b82239d61b478374fc9ce3b..e747466de93d642db8a9f7785a72ac874570398d 100644 (file)
--- a/spec/spec-collated.tex
+++ b/spec/spec-collated.tex
@@ -22,6 +22,7 @@
     decorations,
     decorations.markings,
     decorations.text,
     decorations,
     decorations.markings,
     decorations.text,

+    decorations.pathreplacing,

     scopes
 }
 \usetikzlibrary{datavisualization.formats.functions}
     scopes
 }
 \usetikzlibrary{datavisualization.formats.functions}