8-20 and 8-66
This commit is contained in:
195
8-20.html
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195
8-20.html
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<!--
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This work is licensed under CC BY-NC-ND 4.0
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Link to license: http://creativecommons.org/licenses/by-nc-nd/4.0/
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Attribute to Russell Georgi
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-->
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<html>
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<head>
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<title>
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Problem 8-20
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</title>
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<style>
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html, body {
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width: 100%;
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height: 100%;
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margin: 0px;
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border: 0;
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overflow: hidden;
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display: block;
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}
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canvas {
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position: absolute;
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}
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.greenSlider {
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-webkit-appearance: none;
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border-radius: 5px;
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height: 10px;
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background: #d3d3d3;
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outline: none;
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opacity: 0.7;
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-webkit-transition: .2s;
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transition: opacity .2s;
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}
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.greenSlider::-webkit-slider-thumb {
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-webkit-appearance: none;
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appearance: none;
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background: #000000;
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border-radius: 50%;
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width: 15px;
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height: 15px;
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cursor: pointer;
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}
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.greenSlider::-moz-range-thumb {
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background: #000000;
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border-radius: 50%;
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width: 15px;
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height: 15px;
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cursor: pointer;
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}
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</style>
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</head>
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<body>
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<canvas id="myCanvas" width="1" height="1" style="border:1px solid #ffffff;">
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Your browser does not support the HTML5 canvas tag.</canvas>
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<div class="slidecontainer">
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<t>Vx</t>
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<input type="range" min="-200" max="200" value="20" step="0.1" class="greenSlider" id="vxSlider">
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<br>
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<t>ω</t>
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<input type="range" min="-50" max="50" value="20" step="0.1" class="greenSlider" id="wSlider">
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</div>
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<script>
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var c = document.getElementById("myCanvas");
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var ctx = c.getContext("2d");
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c.width = window.innerWidth;
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c.height = window.innerHeight;
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//Time step
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var dt = 0.002;
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var t = 0;
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var g = -500;
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var y = 100;
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var vy = 0;
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var x = 0;
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var vx = 20;
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var omega = 20;
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var theta = 0;
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var r = 10;
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//Relative position of canvas
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var xPos = 0;
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var yPos = -70;
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//Moves and scales canvas
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ctx.translate(ctx.canvas.width / 2, ctx.canvas.height / 2)
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ctx.scale(2, -2);
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vxSlider.oninput = function()
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{
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vx = parseFloat(this.value);
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Reset();
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}
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wSlider.oninput = function()
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{
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omega = parseFloat(this.value);
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Reset();
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}
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function BounceDown()
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{
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vy = -vy;
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tempVx = vx;
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vx = 3 * vx / 7 - 4 * r * omega / 7;
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omega = (-10 * tempVx / 7 - 3 * r * omega / 7) / r;
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}
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function BounceUp()
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{
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vy = -vy;
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tempVx = vx;
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vx = 3 * vx / 7 - 4 * r * -omega / 7;
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omega = - (-10 * tempVx / 7 - 3 * r * -omega / 7) / r;
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}
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function Clear(ctx)
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{
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ctx.clearRect(-c.width, -c.height, c.width * 2, c.height * 2);
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}
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function Update()
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{
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Clear(ctx);
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Draw();
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t += dt;
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x += vx * dt;
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y += vy * dt;
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vy += g * dt;
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theta += omega * dt;
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if (y <= r)
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{
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BounceDown();
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}
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if (y >= 200 - r)
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{
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BounceUp();
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}
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setTimeout(Update, 5);
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}
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function Reset()
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{
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x = 0;
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y = 100;
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vy = 0;
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theta = 0;
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vx = parseFloat(document.getElementById("vxSlider").value);
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omega = parseFloat(document.getElementById("wSlider").value);
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}
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function Draw()
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{
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ctx.beginPath();
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ctx.moveTo(-c.width, yPos);
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ctx.lineTo(c.width, yPos);
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ctx.stroke();
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ctx.beginPath();
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ctx.arc(xPos + x, yPos + y, r, 0, Math.PI * 2);
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ctx.stroke();
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ctx.beginPath();
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ctx.moveTo(xPos + x, yPos + y);
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ctx.lineTo(xPos + x + r * Math.cos(theta), yPos + y + r * Math.sin(theta));
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ctx.stroke();
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ctx.beginPath();
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ctx.moveTo(xPos + x, yPos + y);
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ctx.lineTo(xPos + x + r * Math.cos(theta + Math.PI / 2), yPos + y + r * Math.sin(theta + Math.PI / 2));
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ctx.stroke();
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ctx.beginPath();
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ctx.moveTo(xPos + x, yPos + y);
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ctx.lineTo(xPos + x + r * Math.cos(theta + Math.PI), yPos + y + r * Math.sin(theta + Math.PI));
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ctx.stroke();
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ctx.beginPath();
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ctx.moveTo(xPos + x, yPos + y);
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ctx.lineTo(xPos + x + r * Math.cos(theta - Math.PI / 2), yPos + y + r * Math.sin(theta - Math.PI / 2));
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ctx.stroke();
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}
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window.addEventListener('resize', function(event) {
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c.width = window.innerWidth;
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c.height = window.innerHeight;
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ctx.translate(c.width / 2, c.height / 2);
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ctx.scale(2, -2);
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}, true);
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Update();
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</script>
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</body>
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<p xmlns:cc="http://creativecommons.org/ns#" style="font-size: 1vw; bottom: 0px; position: absolute;">
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This work is licensed under
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<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>
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</html>
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299
8-66.html
Normal file
299
8-66.html
Normal file
@@ -0,0 +1,299 @@
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<!--
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||||
This work is licensed under CC BY-NC-ND 4.0
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||||
Link to license: http://creativecommons.org/licenses/by-nc-nd/4.0/
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||||
Attribute to Russell Georgi
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||||
-->
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||||
<html>
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<head>
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<title>
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Exercise 8-66
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</title>
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<style>
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html, body {
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width: 100%;
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height: 100%;
|
||||
margin: 0px;
|
||||
border: 0;
|
||||
overflow: hidden;
|
||||
display: block;
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}
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canvas {
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position: absolute;
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}
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.greenSlider {
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-webkit-appearance: none;
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border-radius: 5px;
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height: 10px;
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background: #d3d3d3;
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outline: none;
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opacity: 0.7;
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-webkit-transition: .2s;
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transition: opacity .2s;
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}
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.greenSlider::-webkit-slider-thumb {
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-webkit-appearance: none;
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appearance: none;
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background: #000000;
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border-radius: 50%;
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width: 15px;
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height: 15px;
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cursor: pointer;
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}
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.greenSlider::-moz-range-thumb {
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background: #000000;
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border-radius: 50%;
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width: 15px;
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height: 15px;
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cursor: pointer;
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}
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</style>
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</head>
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||||
<body>
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||||
<canvas id="myCanvas" width="1" height="1" style="border:1px solid #ffffff;">
|
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Your browser does not support the HTML5 canvas tag.</canvas>
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<div class="slidecontainer">
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<t>Vx</t>
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<input type="range" min="-200" max="200" value="20" step="0.1" class="greenSlider" id="vxSlider">
|
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<br>
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<br>
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<t>ω</t>
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<input type="range" min="-50" max="50" value="20" step="0.1" class="greenSlider" id="wSlider">
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<br>
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<br>
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<t>y</t>
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<input type="range" min="20" max="300" value="110" step="0.1" class="greenSlider" id="ySlider">
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<br>
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<br>
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<t>g</t>
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<input type="range" min="0" max="1000" value="500" step="0.1" class="greenSlider" id="gSlider">
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<br>
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<br>
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<t>h</t>
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<input type="range" min="30" max="200" value="120" step="0.1" class="greenSlider" id="hSlider">
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<br>
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<br>
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<t>vy</t>
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<input type="range" min="-200" max="200" value="0" step="0.1" class="greenSlider" id="vySlider">
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<br>
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<br>
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<t>r</t>
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<input type="range" min="5" max="40" value="10" step="0.1" class="greenSlider" id="rSlider">
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</div>
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<script>
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var c = document.getElementById("myCanvas");
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var ctx = c.getContext("2d");
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c.width = window.innerWidth;
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c.height = window.innerHeight;
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//Time step
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var dt = 0.002;
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var t = 0;
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var g = -500;
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var y = 110;
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var vy = 0;
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var x = 0;
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var vx = 20;
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var h = 120;
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var omega = 20;
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var theta = 0;
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var r = 10;
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var positionsX = [0];
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var positionsY = [110];
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var canBounce = false;
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var numBounces = 0;
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var maxBounces = 3;
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//Relative position of canvas
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var xPos = 0;
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var yPos = -120;
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//Moves and scales canvas
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ctx.translate(ctx.canvas.width / 2, ctx.canvas.height / 2)
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ctx.scale(2, -2);
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Reset();
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vxSlider.oninput = function()
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{
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vx = parseFloat(this.value);
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Reset();
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||||
}
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wSlider.oninput = function()
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{
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omega = parseFloat(this.value);
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Reset();
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||||
}
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ySlider.oninput = function()
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{
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y = parseFloat(this.value);
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Reset();
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}
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gSlider.oninput = function()
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{
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g = -parseFloat(this.value);
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Reset();
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}
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hSlider.oninput = function()
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{
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h = parseFloat(this.value);
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Reset();
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}
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rSlider.oninput = function()
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{
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r = parseFloat(this.value);
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Reset();
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}
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vySlider.oninput = function()
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{
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vy = parseFloat(this.value);
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Reset();
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}
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function BounceDown()
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||||
{
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vy = -vy;
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||||
tempVx = vx;
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vx = 3 * vx / 7 - 4 * r * omega / 7;
|
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omega = (-10 * tempVx / 7 - 3 * r * omega / 7) / r;
|
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}
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||||
|
||||
function BounceUp()
|
||||
{
|
||||
vy = -vy;
|
||||
tempVx = vx;
|
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vx = 3 * vx / 7 - 4 * r * -omega / 7;
|
||||
omega = - (-10 * tempVx / 7 - 3 * r * -omega / 7) / r;
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||||
}
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||||
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||||
function Clear(ctx)
|
||||
{
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||||
ctx.clearRect(-c.width, -c.height, c.width * 2, c.height * 2);
|
||||
}
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||||
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||||
function Update()
|
||||
{
|
||||
Clear(ctx);
|
||||
Draw();
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||||
t += dt;
|
||||
x += vx * dt;
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||||
y += vy * dt;
|
||||
vy += g * dt;
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||||
positionsX.push(x);
|
||||
positionsY.push(y);
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||||
theta += omega * dt;
|
||||
if (y <= r - 0.1 && canBounce)
|
||||
{
|
||||
BounceDown();
|
||||
numBounces += 1;
|
||||
if (numBounces >= maxBounces)
|
||||
{
|
||||
canBounce = false;
|
||||
}
|
||||
}
|
||||
if (y >= h + 0.1 - r && canBounce)
|
||||
{
|
||||
BounceUp();
|
||||
numBounces += 1;
|
||||
if (numBounces >= maxBounces)
|
||||
{
|
||||
canBounce = false;
|
||||
}
|
||||
} else if (y < r + 1 && numBounces == 0)
|
||||
{
|
||||
canBounce = true;
|
||||
}
|
||||
setTimeout(Update, 5);
|
||||
}
|
||||
|
||||
function Reset()
|
||||
{
|
||||
numBounces = 0;
|
||||
x = 0;
|
||||
y = parseFloat(document.getElementById("ySlider").value);
|
||||
if (y > h - r)
|
||||
{
|
||||
canBounce = false;
|
||||
} else
|
||||
{
|
||||
canBounce = true;
|
||||
}
|
||||
vy = parseFloat(document.getElementById("vySlider").value);
|
||||
theta = 0;
|
||||
vx = parseFloat(document.getElementById("vxSlider").value);
|
||||
omega = parseFloat(document.getElementById("wSlider").value);
|
||||
positionsX = [0];
|
||||
positionsY = [y];
|
||||
}
|
||||
|
||||
function Draw()
|
||||
{
|
||||
ctx.strokeStyle = "#000000";
|
||||
ctx.beginPath();
|
||||
ctx.moveTo(-c.width, yPos);
|
||||
ctx.lineTo(c.width, yPos);
|
||||
ctx.stroke();
|
||||
ctx.beginPath();
|
||||
ctx.moveTo(-c.width, yPos + h);
|
||||
ctx.lineTo(c.width, yPos + h);
|
||||
ctx.stroke();
|
||||
ctx.fillStyle = "#ffffff";
|
||||
if (!canBounce)
|
||||
{
|
||||
ctx.beginPath();
|
||||
ctx.arc(xPos + x, yPos + y, r + r, 0, Math.PI * 2);
|
||||
ctx.fill();
|
||||
}
|
||||
|
||||
ctx.beginPath();
|
||||
ctx.arc(xPos + x, yPos + y, r, 0, Math.PI * 2);
|
||||
ctx.stroke();
|
||||
ctx.beginPath();
|
||||
ctx.moveTo(xPos + x, yPos + y);
|
||||
ctx.lineTo(xPos + x + r * Math.cos(theta), yPos + y + r * Math.sin(theta));
|
||||
ctx.stroke();
|
||||
ctx.beginPath();
|
||||
ctx.moveTo(xPos + x, yPos + y);
|
||||
ctx.lineTo(xPos + x + r * Math.cos(theta + Math.PI / 2), yPos + y + r * Math.sin(theta + Math.PI / 2));
|
||||
ctx.stroke();
|
||||
ctx.beginPath();
|
||||
ctx.moveTo(xPos + x, yPos + y);
|
||||
ctx.lineTo(xPos + x + r * Math.cos(theta + Math.PI), yPos + y + r * Math.sin(theta + Math.PI));
|
||||
ctx.stroke();
|
||||
ctx.beginPath();
|
||||
ctx.moveTo(xPos + x, yPos + y);
|
||||
ctx.lineTo(xPos + x + r * Math.cos(theta - Math.PI / 2), yPos + y + r * Math.sin(theta - Math.PI / 2));
|
||||
ctx.stroke();
|
||||
ctx.strokeStyle = "#ee0000";
|
||||
ctx.beginPath();
|
||||
ctx.moveTo(xPos + positionsX[0], yPos + positionsY[0]);
|
||||
for (i = 1; i < positionsX.length; i++)
|
||||
{
|
||||
ctx.lineTo(xPos + positionsX[i], yPos + positionsY[i]);
|
||||
}
|
||||
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(2, -2);
|
||||
}, 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>
|
||||
21
index.html
21
index.html
@@ -184,6 +184,27 @@
|
||||
<t>Other example problem from chapter 4</t>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<th colspan = "2">
|
||||
<t>Chapter 8: Angular momentum part 1</t>
|
||||
</th>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<a href='8-20.html'>Problem 8-20</a>
|
||||
</td>
|
||||
<td>
|
||||
<t>Superball bouncing</t>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<a href='8-66.html'>Exercises 8-66 & 8-77</a>
|
||||
</td>
|
||||
<td>
|
||||
<t>Superball bouncing under a table</t>
|
||||
</td>
|
||||
</tr>
|
||||
</table>
|
||||
<p xmlns:cc="http://creativecommons.org/ns#" >
|
||||
This work is licensed under
|
||||
|
||||
Reference in New Issue
Block a user