TikZ: how to draw arrows from the y axis to a curve?

Question

I should draw this:

This is what I have done so far.

I do not know how to draw the horizontal arrows. Besides, in order to draw the dashed line from point Q to point P, I wrote

\draw [fill] (0.3,2) circle (1.5pt) node [above] (Q) {Q};
\draw [fill] (1.1,-1.6) circle (1.5pt) node [left] (P) {P};
\draw [thick,densely dashed] (0.3,2) -- (1.1,-1.6);

Is there a faster way, something like

\draw [thick,densely dashed] (Q) -- (P);

? This is my code:

\documentclass[border=3cm]{standalone}
\usepackage{tikz}

\begin{document}
\begin{tikzpicture}
% \draw [help lines] (0,0) grid (7,7);
\draw plot [mark=none, smooth] coordinates {(1.16,-2.4) (1.6,-0.8) (2,1.6) (2.04,2.8)};
\draw [thick,-latex] (0,0) -- (5,0.0) node (xaxis)[below] {$x$};
\draw [thick,-latex] (0,-4) -- (0,4) node (yaxis)[left]  {$y$};
\node at (2.5,2.6) {$U(y)$};
\draw [thick,latex-latex] (3,1) -- (3,-1) node [midway,xshift=0.4cm,yshift=0.3cm]  {$2l_{m}$};
\draw [thick,-latex] (1.3,-0.2) -- (2.2,-0.2) node [below]  {$\tau_{xy}$};
\draw [thick,-latex] (0.5,0.2) -- (-0.5,0.2) node [above]  {$\tau_{xy}$};
\draw [fill] (0.3,2) circle (1.5pt) node [above] (Q) {Q};
\draw [fill] (1.1,-1.6) circle (1.5pt) node [left] (P) {P};
\draw [thick,densely dashed] (0.3,2) -- (1.1,-1.6);
\end{tikzpicture}
\end{document}

Edit: thanks to this and this I managed to draw the arrows. Here is the code and the output:

\documentclass[border=3cm]{standalone}
\usepackage{tikz}
\usetikzlibrary{intersections}

\begin{document}
\begin{tikzpicture}
% \draw [help lines] (0,0) grid (7,7);
\draw [thick, name path=curve] (1.16,-2.4) .. controls (1.6, -0.8) and (2, 1.6) .. (2.04, 2.8);
\draw [thick,-latex] (0,0) -- (5,0.0) node (xaxis)[below] {$x$};
\draw [thick,-latex] (0,-4) -- (0,4) node (yaxis)[left]  {$y$};
\node at (2.5,2.6) {$U(y)$};
\draw [thick,latex-latex] (3,1) -- (3,-1) node [midway,xshift=0.4cm,yshift=0.3cm]  {$2l_{m}$};
\draw [thick,-latex] (1.3,-0.2) -- (2.2,-0.2) node [below]  {$\tau_{xy}$};
\draw [thick,-latex] (0.5,0.2) -- (-0.5,0.2) node [above]  {$\tau_{xy}$};
\coordinate (Q) at (0.3,2);
\coordinate (P) at (1.1,-1.6);
\fill (Q) circle (1.5pt) node [above] {Q};
\fill (P) circle (1.5pt) node [below,xshift=-1mm] {P};
\draw [thick,densely dashed] (Q)--(P);
%
\foreach \y [count=\yi] in {-2,-1.6,...,2}{%
    \path[name path=a\yi] (0,\y) --++ (3,0);
    \draw[name intersections={of=curve and a\yi},semithick,-latex] (0,\y) -- (intersection-1);
}
\end{tikzpicture}
\end{document}