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I need to draw a pulley system as in the figure. Can you help?

    begin{tikzpicture}

    fill[pattern=north east lines] (-3,0) rectangle (3,.3);

    draw(-3,0)--(3,0);

    draw(-2.5,0)--(-2.5,-2.4);

    draw(2.5,0)--(2.5,-1);



    draw[fill=white] (-2.5,-2.4) circle (.3);

    draw[fill=white] (2.5,-1) circle (.3);

    draw[fill=white] (0,-3) circle (.153);



draw

(2.5,-1) coordinate (a) node[right] {}

-- (0,-3) coordinate (b) node[left] {}

-- (0,-2.75) coordinate (c) node[above right] {}

pic["$beta$", draw=orange, <->, angle eccentricity=1.2172, angle radius=.51cm]

{angle=a--b--c};



draw

(0,-2.75) coordinate (a) node[right] {}

-- (0,-3) coordinate (b) node[left] {}

-- (-2.5,-2.4) coordinate (c) node[above right] {}

pic["$alpha$", draw=orange, <->, angle eccentricity=.72172, angle radius=.751cm]

{angle=a--b--c};

draw[dashed] (0,-3)--(0,-1);

draw[fill=white] (-2.5,-2.4) circle (.3);

draw[fill=white] (2.5,-1) circle (.3);



draw[fill=white] (0,-3) circle (.153);





    end{tikzpicture}

In order to compute the tangents it is advantageous to make the circles nodes and to use tangent cs:, which comes with calc. And the angles can be conveniently drawn with the angles library, where quotes makes it somewhat simpler to add alpha and beta.

documentclass[tikz,border=3.14mm]{standalone}

usetikzlibrary{patterns,calc,angles,quotes}

begin{document}

begin{tikzpicture}

fill[pattern=north east lines] (-3,0) rectangle (3,.3);

 begin{scope}[thick]

 draw(-3,0)--(3,0);



 path (-2.5,-2.4) node[circle,draw,inner sep=.3cm] (L){}

 (2.5,-1) node[circle,draw,inner sep=.3cm] (R){}

 (0,-3) node[circle,draw,inner sep=.153cm,label=below:$m$] (M){};

 draw (L.north) -- (L.north|-0,0) (R.north) -- (R.north|-0,0);

 draw[dashed] (M) -- (0,-1)coordinate (M1);

  draw (M)  -- (tangent cs:node=L,point={(M.center)},solution=1) coordinate (L1)

  let p1=($(L1)-(L.center)$),n1={atan2(y1,x1)},n2={veclen(y1,x1)} in

  arc(n1:180:n2) -- ++(0,-1.5) node[below,draw]{$m_1$};

  draw (M)  -- (tangent cs:node=R,point={(M.center)},solution=2) coordinate (R1)

  let p1=($(R1)-(R.center)$),n1={atan2(y1,x1)},n2={veclen(y1,x1)} in

  arc(n1:00:n2) -- ++(0,-1.5) node[below,draw]{$m_2$};

 end{scope}

 path pic [draw,angle radius=0.5cm,"$alpha$",angle eccentricity=1.5] {angle = M1--M--L1} 

   pic [draw,angle radius=0.7cm,"$beta$",angle eccentricity=1.5] {angle = R1--M--M1} ;

end{tikzpicture}

end{document}