Tracé de l’expérience du poids de l’Hospital en noir et blanc (fiziko)

Auteur ou autrice : Sergey Slyusarev.

Mise en ligne le 28 janvier 2023

Code

%@Auteur: Sergey Slyusarev
%@Année: 2019

input fiziko.mp;

vardef lHopitalPulley (expr AB, l, m) = % distance AB between the suspension points of the ropes and their lengths l and m. “Why no units of length?”, you may ask. It's because some calculations inside can cause arithmetic overflow in MetaPost.
save A, B, C, D, E, o, a, x, y, d, w, h, support;
image(
pair A, B, C, D, E, o[];
path support;
numeric a, x[], y[], d[], w, h;
x1 := (l**2 + abs(l)*((sqrt(8)*AB)++l))/4AB; % the solution
y1 := l+-+x1; % second coordinate is trivial
y2 := m - ((AB-x1)++y1); % as well as the weight's position
A := (0, 0);
B := (AB*cm, 0);
D := (x1*cm, -y1*cm);
C := D shifted (0, -y2*cm);
d1 := 2/3cm; d2 := 1cm; d3 := 5/6d1; % diameters of the pulley, weight and the pulley wheel
w := 2/3cm; h := 1/3cm; % parameters of the wood block
o1 := (unitvector(C-D) rotated 90 scaled 1/2d3);
o2 := (unitvector(D-B) rotated 90 scaled 1/2d3);
E := whatever [D shifted o1, C shifted o1]
= whatever [D shifted o2, B shifted o2]; % pulley's center
a := angle(A-D);
support := A shifted (-w, 0) -- B shifted (w, 0) -- B shifted (w, h) -- A shifted (-w, h) -- cycle;
draw woodenThing(support, 0); % wood block everything is suspended from
draw pulley (d1, a - 90) shifted E; % the pulley
draw image(
draw A -- D -- B withpen thickpen;
draw D -- C withpen thickpen;
) maskedWith (pulleyOutline shifted E); % ropes should be covered with the pulley
draw sphere.c(d2) shifted C shifted (0, -1/2d2); % sphere as a weight
dotlabel.llft(btex $A$ etex, A);
dotlabel.lrt(btex $B$ etex, B);
dotlabel.ulft(btex $C$ etex, C);
label.llft(btex $l$ etex, 1/2[A, D]);
)
enddef;

beginfig(18);
draw lHopitalPulley (3, 5/2, 3);
endfig;

end.