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ClassicalMechanicsPrograms/5-23.html
2021-09-28 18:48:30 -07:00

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This work is licensed under CC BY-NC-ND 4.0
Link to license: http://creativecommons.org/licenses/by-nc-nd/4.0/
Attribute to Russell Georgi
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<html>
<head>
<title>
Problem 5-23
</title>
<style>
html, body {
width: 100%;
height: 100%;
margin: 0px;
border: 0;
overflow: hidden;
display: block;
}
canvas {
position: absolute;
}
.dropbtn {
background-color: #04AA6D;
color: white;
padding: 16px;
font-size: 16px;
border: none;
}
.dropbtnm {
background-color: #04AA6D;
color: white;
padding: 16px;
font-size: 16px;
border: none;
}
.dropdown {
position: absolute;
display: inline-block;
}
.dropdown-content {
display: none;
position: relative;
background-color: #f1f1f1;
box-shadow: 0px 8px 16px 0px rgba(0,0,0,0.2);
z-index: 1;
}
.dropdown-content button {
color: black;
padding: 12px 16px;
width: 100px;
text-decoration: none;
display: block;
}
#m {
left: 110px;
}
.dropdown-content a:hover {background-color: #ddd;}
.dropdown:hover .dropdown-content {display: block;}
.dropdown:hover .dropbtn {background-color: #3e8e41;}
</style>
</head>
<body>
<canvas id="myCanvas" width="1" height="1" style="border:1px solid #ffffff;">
Your browser does not support the HTML5 canvas tag.</canvas>
<script>
var c = document.getElementById("myCanvas");
var ctx = c.getContext("2d");
ctx.canvas.width = window.innerWidth;
ctx.canvas.height = window.innerHeight;
var n = 10;
var g = 20;
var h = 55;
var r1 = 50;
var rf = 0.25;
var dr = 0.2;
var drc = 0.1;
var ballPositions = new Array(n);
var ballVelocities = new Array(n);
var t = 0;
var dt = 0.025;
var xPos = 0;
var yPos = -200;
ctx.translate(ctx.canvas.width / 2, ctx.canvas.height / 2);
ctx.scale(1.5, -1.5);
ballPositions[0] = h;
ballVelocities[0] = 0;
for (i = 1; i < ballPositions.length; i++)
{
ballPositions[i] = ballPositions[i-1] + (rf ** (i-1)) * r1 + (rf ** i) * r1 + dr;
ballVelocities[i] = 0;
}
function Clear(ctx)
{
ctx.clearRect(-c.width, -c.height, c.width * 2, c.height * 2);
}
function Update()
{
Clear(ctx);
Draw();
t += dt;
for (i = 0; i < ballPositions.length; i++)
{
ballVelocities[i] -= g * dt;
ballPositions[i] += ballVelocities[i] * dt;
}
for (i = 0; i < ballPositions.length; i++)
{
if (i == 0 && ballPositions[i] - r1 < drc)
{
ballVelocities[i] = -ballVelocities[i];
ballPositions[i] += ballVelocities[i] * dt;
} else if (i != 0 && ballPositions[i] - r1 * (rf ** i) < ballPositions[i - 1] + r1 * (rf ** (i - 1)) + drc)
{
ballVelocities[i] = -ballVelocities[i] + 2 * ballVelocities[i - 1];
ballPositions[i] += ballVelocities[i] * dt;
}
}
setTimeout(Update, 1000/60)
}
function Draw()
{
ctx.beginPath();
ctx.moveTo(-c.width, yPos);
ctx.lineTo(c.width, yPos);
ctx.stroke();
for (i = 0; i < ballPositions.length; i++)
{
ctx.beginPath();
ctx.arc(0, ballPositions[i] + yPos, r1 * (rf ** i), 0, Math.PI * 2);
ctx.stroke();
}
}
window.addEventListener('resize', function(event) {
c.width = window.innerWidth;
c.height = window.innerHeight;
ctx.translate(c.width / 2, c.height / 2);
ctx.scale(1.5, -1.5);
}, true);
Update();
</script>
</body>
<p xmlns:cc="http://creativecommons.org/ns#" style="font-size: 1vw; bottom: 0px; position: absolute;">
This work is licensed under
<a href="http://creativecommons.org/licenses/by-nc-nd/4.0/?ref=chooser-v1" target="_blank" rel="license noopener noreferrer" style="display:inline-block;">CC BY-NC-ND 4.0<img style="height:22px!important;margin-left:3px;vertical-align:text-bottom;" src="https://mirrors.creativecommons.org/presskit/icons/cc.svg?ref=chooser-v1"><img style="height:22px!important;margin-left:3px;vertical-align:text-bottom;" src="https://mirrors.creativecommons.org/presskit/icons/by.svg?ref=chooser-v1"><img style="height:22px!important;margin-left:3px;vertical-align:text-bottom;" src="https://mirrors.creativecommons.org/presskit/icons/nc.svg?ref=chooser-v1"><img style="height:22px!important;margin-left:3px;vertical-align:text-bottom;" src="https://mirrors.creativecommons.org/presskit/icons/nd.svg?ref=chooser-v1"></a></p>
</html>