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I am using a Wolfram demonstration that shows Newton’s Second Law: https://demonstrations.wolfram.com/TwoMassesOnInclinedPlaneWithPulley/

I am not too familiar with creating animations and I was hoping my question will help me learn more. My question is

Is it possible to create a tracker for this demonstration/animation that will plot the velocity of one of the blocks over time or the displacement over time.

What would I need to add to the source code so that I can create a plot of the velocity over time as the simulation/animation runs. Could the points on the plot be created infinitesimally or incrementally as the blocks are moving. Could the plot be created under the animation.

I am not too sure if this is possible in Mathematica, but I would really hope to see how to accomplish this if possible.

Thank you!


EDIT: I tried applying the first answer to my notebook which has some modification:

Manipulate[
 With[{a = 
    If[m2 > m1 (\[Mu] Cos[\[Theta]] + Sin[\[Theta]]), (
     9.8 (m2 - \[Mu] m1 Cos[\[Theta]] - m1 Sin[\[Theta]]))/(
     m1 + m2), (
     9.8 (m2 + \[Mu] m1 Cos[\[Theta]] - m1 Sin[\[Theta]]))/(m1 + m2)],
    v = If[m2 > m1 (\[Mu] Cos[\[Theta]] + Sin[\[Theta]]), (
     9.8 t (m2 - \[Mu] m1 Cos[\[Theta]] - m1 Sin[\[Theta]]))/(
     m1 + m2), (
     9.8 t (m2 + \[Mu] m1 Cos[\[Theta]] - m1 Sin[\[Theta]]))/(
     m1 + m2)], 
   x = If[m2 > m1 (\[Mu] Cos[\[Theta]] + Sin[\[Theta]]), (
     9.8 t^2 (m2 - \[Mu] m1 Cos[\[Theta]] - m1 Sin[\[Theta]]))/(
     2 (m1 + m2)), (
     9.8 t^2 (m2 + \[Mu] m1 Cos[\[Theta]] - m1 Sin[\[Theta]]))/(
     2 (m1 + m2))], 
   T = If[m2 > m1 (\[Mu] Cos[\[Theta]] + Sin[\[Theta]]), (
     9.8 m1 m2 (1 + \[Mu] Cos[\[Theta]] + Sin[\[Theta]]))/(m1 + m2), (
     9.8 m1 m2 (1 - \[Mu] Cos[\[Theta]] + Sin[\[Theta]]))/(m1 + m2)]},
   With[{t = 
     Which[-.75 <= a t <= 1.75, t, a t < -.75, -1/a, True, 1.75/a]}, 
   Overlay[{Graphics[{EdgeForm[RGBColor[0.5, 0.5, 0.5]], 
       Rotate[
        Line[{{-1.75 + a t, 3.25}, {.4, 3.25}}], \[Theta], {0, 3}], 
       Line[{{.25, 3.4}, {.25, 2. - a t}}], 
       Rotate[{Line[{{0, 3}, {0.25, 3.25}}], 
         Disk[{0.25, 3.25}, .25]}, \[Theta]/2, {0, 3}], Gray, 
       Polygon[{{0, 0}, {0, 3}, {3 Cos[\[Theta] + \[Pi]], 
          3 Sin[\[Theta] + \[Pi]] + 3}, {3 Cos[\[Theta] + \[Pi]], 
          0}}], RGBColor[0.06, 0.23, 0.27], 
       Rotate[Rectangle[{-2.25 + a t, 3}, {-1.75 + a t, 
          3.5}], \[Theta], {0, 3}], RGBColor[0.08, 0.2, 0.08], 
       Rectangle[{0, 2 - a t}, {.5, 1.5 - a t}]},
      ImageSize -> 400, PlotRange -> {{-3.5, 1}, {-.5, 4}}, 
      PlotLabel -> 
       Row[{Style["a", Italic], " = ", NumberForm[a, {3, 2}], 
         Style[" m/\!\(\*SuperscriptBox[\(s\), \(2\)]\)", 
          SingleLetterItalics -> False], Spacer[10], "|", Spacer[10], 
         Style["v", Italic], " = ", NumberForm[v, {3, 2}], 
         Style[" m/s", SingleLetterItalics -> False], Spacer[10], "|",
          Spacer[10], Style["x", Italic], " = ", 
         NumberForm[x, {3, 2}], 
         Style[" m", SingleLetterItalics -> False], Spacer[10], "|", 
         Spacer[10], Style["T", Italic], " = ", NumberForm[T, {3, 2}],
          " N"}]], 
     Plot[a x, {x, 0, t}, ImageSize -> 200, 
      PlotRange -> {{0, Pi/2}, {-2, 3.}}]}, 
    Alignment -> {Left, 0.8}]]], {{t, 0., Style["t", Italic]}, 
  0, \[Pi]/6, .01, ImageSize -> Tiny, 
  Appearance -> "Labeled"}, {{\[Theta], 0}, 0, 0, .01, 
  ImageSize -> Tiny, 
  Appearance -> "Labeled"}, {{m1, .5, 
   Text@Subscript[Style["m", Italic], 1]}, .25, .75, .01, 
  ImageSize -> Tiny, 
  Appearance -> "Labeled"}, {{m2, .5, 
   Text@Subscript[Style["m", Italic], 2]}, .25, .75, .01, 
  ImageSize -> Tiny, 
  Appearance -> "Labeled"}, {{\[Mu], .1}, .0, .0 .2, .01, 
  ImageSize -> Tiny, Appearance -> "Labeled"}, 
 ControlPlacement -> Left]

But, this didn't work. It is just pink and not plotting anything. What did I do wrong?

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1 Answer 1

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Here is an example with Overlay[]:

Manipulate[
 With[{a = 
    If[m2 > m1 (\[Mu] Cos[\[Theta]] + Sin[\[Theta]]), (
     9.8 (m2 - \[Mu] m1 Cos[\[Theta]] - m1 Sin[\[Theta]]))/(
     m1 + m2), (
     9.8 (m2 + \[Mu] m1 Cos[\[Theta]] - m1 Sin[\[Theta]]))/(m1 + m2)],
    T = If[m2 > m1 (\[Mu] Cos[\[Theta]] + Sin[\[Theta]]), (
     9.8 m1 m2 (1 + \[Mu] Cos[\[Theta]] + Sin[\[Theta]]))/(m1 + m2), (
     9.8 m1 m2 (1 - \[Mu] Cos[\[Theta]] + Sin[\[Theta]]))/(m1 + m2)]},
   With[{t = 
     Which[-.75 <= a t <= 1.75, t, a t < -.75, -1/a, True, 1.75/a]}, 
   Overlay[{Graphics[{EdgeForm[Black], 
       Rotate[Line[{{-1.75 + a t, 3.25}, {.4, 3.25}}], \[Theta], {0, 
         3}], Line[{{.25, 3.4}, {.25, 2. - a t}}], 
       Rotate[{Line[{{0, 3}, {0.25, 3.25}}], 
         Disk[{0.25, 3.25}, .25]}, \[Theta]/2, {0, 3}], Cyan, 
       Polygon[{{0, 0}, {0, 3}, {3 Cos[\[Theta] + \[Pi]], 
          3 Sin[\[Theta] + \[Pi]] + 3}, {3 Cos[\[Theta] + \[Pi]], 
          0}}], Brown, 
       Rotate[Rectangle[{-2.25 + a t, 3}, {-1.75 + a t, 
          3.5}], \[Theta], {0, 3}], Darker@Green, 
       Rectangle[{0, 2 - a t}, {.5, 1.5 - a t}]},
      
      ImageSize -> 400, PlotRange -> {{-3.5, 1}, {-.5, 4}}, 
      PlotLabel -> 
       Row[{Style["a", Italic], " = ", NumberForm[a, {3, 2}],
         Style[" m/\!\(\*SuperscriptBox[\(s\), \(2\)]\)", 
          SingleLetterItalics -> False], Spacer[10], "|", Spacer[10], 
         Style["T", Italic], " = ", NumberForm[T, {3, 2}], " N"}]], 
     Plot[a x, {x, 0, t}, ImageSize -> 200, 
      PlotRange -> {{0, Pi/2}, {-2, 3.}}]}, 
    Alignment -> {Left, 0.8}]]], {{t, 0.01, Style["t", Italic]}, 
  0.01, \[Pi]/2, .01, ImageSize -> Tiny, 
  Appearance -> "Labeled"}, {{\[Theta], .78}, 0, \[Pi]/2, .01, 
  ImageSize -> Tiny, 
  Appearance -> "Labeled"}, {{m1, .5, 
   Text@Subscript[Style["m", Italic], 1]}, .25, .75, .01, 
  ImageSize -> Tiny, 
  Appearance -> "Labeled"}, {{m2, .5, 
   Text@Subscript[Style["m", Italic], 2]}, .25, .75, .01, 
  ImageSize -> Tiny, 
  Appearance -> "Labeled"}, {{\[Mu], .5}, .25, .75, .01, 
  ImageSize -> Tiny, Appearance -> "Labeled"}, 
 ControlPlacement -> Left]

enter image description here

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  • $\begingroup$ What does this line : Plot[a x, {x, 0, t}, plot? How can I modify it to plot velocity over time $\endgroup$
    – usernew
    Feb 25, 2021 at 20:49
  • $\begingroup$ @usernew The purpose was just to show a way to include a dynamic plot with your animation. I did not analyze the code from the point of view of physics. I used t because it is changing but I am not quite sure about what it represents (I see it is assigned an inverse of a in a Which statement) . $\endgroup$ Feb 25, 2021 at 22:36

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