Can you make a model like the video ? It's so amazing that I want to check it out.
$\begingroup$
$\endgroup$
3
-
$\begingroup$ Do you mean elastic collisions of two blocks? $\endgroup$– Alex TrounevCommented Sep 15, 2020 at 22:56
-
$\begingroup$ Yes. As in the video, one side is the wall, and there is a full elastic collision between the two connections and the wall. $\endgroup$– MilkCommented Sep 15, 2020 at 23:04
-
$\begingroup$ I am happy that you got the answer, it is indeed a beautiful model. But please update the question to make it self-contained. External links may disappear, they should only play a supporting role. Also, it is in the rules of this forum to show some preliminary work. The absence of it explains so many downvotes (not me). $\endgroup$– yarchikCommented Sep 16, 2020 at 19:03
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
1
It is really amazing that Pi pops up. Here is a simulation, using constant energy and elastic collision with momentum conservation. Note that by a collision with the wall, energy stays constant, but momentum changes.
m1 = 1; m2 = 10;(*masses*)
x10 = 1; x20 = 2; (*initial locations*)
v10 = 0; v20 = -1;(*inital velocities*)
etot = m1 v10^2 + m2 v20^2;(*const energy*)
tmax =10; (*max. time for solution*)
newvelocity[vv1_,
vv2_] := (tsol =
Quiet[Solve[{m1 vn1 + m2 vn2 == m1 vv1 + m2 vv2,
m1 vn1^2 + m2 vn2^2 == etot}, {vn1, vn2}]]; {vn1, vn2} /.
If[Sign[tsol[[1, 1, 2]]] != Sign[vv1], tsol[[1]], tsol[[2]]]);
sol = NDSolve[{x1'[t] == v1[t], x2'[t] == v2[t], x1[0] == x10,
x2[0] == x20, v1[0] == v10, v2[0] == v20,
WhenEvent[
x1[t] == x2[t], {tsol = newvelocity[v1[t], v2[t]],
v1[t] -> tsol[[1]], v2[t] -> tsol[[2]] }],
WhenEvent[x1[t] == 0, v1[t] -> -v1[t]]}, {x1, x2, v1, v2}, {t, 0,
tmax}, DiscreteVariables -> {v1, v2}];
Plot[{ x1[t], x2[t]} /. sol // Evaluate, {t, 0, tmax},
PlotLegends -> {"m1", "m2"}, AxesLabel -> {"time", "space"}, PlotLabel ->
"Expected # of collisions:"<>ToString[Floor[Pi/ArcTan[Sqrt[m1/m2]]]]]
answered Sep 16, 2020 at 15:31