Impulse

Impact, impulse, average force over time

Edit and compile if you like:

% Author: Izaak Neutelings (October 2020)
\documentclass[border=3pt,tikz]{standalone}
\usepackage{physics}
\usepackage{tikz}
\tikzset{>=latex} % for LaTeX arrow head

\colorlet{xcol}{blue!70!black}
\colorlet{myred}{red!65!black}
\colorlet{mypurple}{blue!60!red!65!black}
\def\tick#1#2{\draw[thick] (#1) ++ (#2:0.1) --++ (#2-180:0.2)}

\begin{document}


% IMPULSE
\def\xmax{3.6}
\def\ymax{2.5}
\begin{tikzpicture}
  \def\Fmax{0.8*\ymax}
  \def\Fave{0.4*\ymax}
  \def\ta{0.12*\xmax}
  \def\tb{0.43*\xmax}
  \def\tc{0.82*\xmax}
  \def\impulse{
    (0.02*\xmax,0) -- (\ta,0) to[out=0,in=180,looseness=0.7] (\tb,\Fmax)
                              to[out=0,in=180,looseness=0.7] (\tc,0) -- (0.9*\xmax,0);
  }
  \fill[mypurple!20] (\ta,0) rectangle (\tc,\Fave);
  \fill[myred!20] \impulse;
  \draw[->,thick] (-0.1*\xmax,0) -- (\xmax,0) node[right=4,below left=1] {$t$};
  \draw[->,thick] (0,-0.1*\ymax) -- (0,\ymax) node[left=1] {$F$};
  \draw[thick,myred!80!black] \impulse;
  \draw[dashed,mypurple]
    (\ta,0) --++ (0,\Fave) (\tc,0) --++ (0,\Fave) (0,\Fave) --++ (\ta,0);
  \draw[dashed,myred]
    (0,\Fmax) --++ (1.15*\tb,0);
  \draw[thick,mypurple] (\ta,\Fave) -- (\tc,\Fave);
  \tick{\ta,0}{90} node[scale=0.9,below=-1] {$t_1$};
  \tick{\tc,0}{90} node[scale=0.9,below=-1] {$t_2$};
  \tick{0,\Fave}{0} node[scale=0.9,left=-1] {$\overline{F}$};
  \tick{0,\Fmax}{0} node[scale=0.9,left=-1] {$F_\text{max}$};
\end{tikzpicture}


% IMPULSE thin (car crash)
\begin{tikzpicture}
  \def\Fmax{0.8*\ymax}
  \def\Fave{0.68*\ymax}
  \def\ta{0.17*\xmax}
  \def\tb{0.22*\xmax}
  \def\tc{0.27*\xmax}
  \def\td{0.32*\xmax}
  \def\impulse{
    (0.02*\xmax,0) -- (\ta,0) to[out=0,in=180,looseness=0.12] (\tb,\Fmax)
                   -- (\tc,\Fmax) to[out=0,in=180,looseness=0.12] (\td,0) -- (0.9*\xmax,0);
  }
  \fill[mypurple!20] (\ta,0) rectangle (\td,\Fave);
  \fill[myred!20] \impulse;
  \draw[->,thick] (-0.1*\xmax,0) -- (\xmax,0) node[right=4,below left=1] {$t$};
  \draw[->,thick] (0,-0.1*\ymax) -- (0,\ymax) node[left=1] {$F$};
  \draw[thick,myred!80!black] \impulse;
  \draw[dashed,mypurple]
    (\ta,0) --++ (0,\Fave) (\td,0) --++ (0,\Fave) (0,\Fave) --++ (\ta,0);
  \draw[dashed,myred]
    (0,\Fmax) --++ (1.15*\td,0);
  \draw[thick,mypurple] (\ta,\Fave) -- (\td,\Fave);
  \tick{\ta,0}{90} node[scale=0.9,left=1,below=-1] {$t_1$};
  \tick{\td,0}{90} node[scale=0.9,right=1,below=-1] {$t_2$};
  \tick{0,\Fave}{0} node[scale=0.9,left=-1] {$\overline{F}$};
\end{tikzpicture}


% IMPULSE flattened (airbag)
\begin{tikzpicture}
  \def\Fmax{0.18*\ymax}
  \def\Fave{0.15*\ymax}
  \def\ta{0.05*\xmax}
  \def\tb{0.2*\xmax}
  \def\tc{0.7*\xmax}
  \def\td{0.85*\xmax}
  \def\impulse{
    (0.02*\xmax,0) -- (\ta,0) to[out=0,in=180,looseness=1.2] (\tb,\Fmax)
                   -- (\tc,\Fmax) to[out=0,in=180,looseness=1.2] (\td,0) -- (0.95*\xmax,0);
  }
  \fill[mypurple!20] (\ta,0) rectangle (\td,\Fave);
  \fill[myred!20] \impulse;
  \draw[->,thick] (-0.1*\xmax,0) -- (\xmax,0) node[right=4,below left=1] {$t$};
  \draw[->,thick] (0,-0.1*\ymax) -- (0,\ymax) node[left=1] {$F$};
  \draw[thick,myred!80!black] \impulse;
  \draw[dashed,mypurple]
    (\ta,0) --++ (0,\Fave) (\td,0) --++ (0,\Fave) (0,\Fave) --++ (\ta,0);
  \draw[dashed,myred]
    (0,\Fmax) --++ (1.15*\tc,0);
  \draw[thick,mypurple] (\ta,\Fave) -- (\td,\Fave);
  \tick{\ta,0}{90} node[scale=0.9,left=1,below=-1] {$t_1$};
  \tick{\td,0}{90} node[scale=0.9,right=1,below=-1] {$t_2$};
  \tick{0,\Fave}{0} node[scale=0.9,left=-1] {$\overline{F}$};
\end{tikzpicture}


\end{document}