杠杆原理教学演示
2025-10-07 12:10:39
发布于：安徽
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<!DOCTYPE html>
<html lang="zh-CN">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>杠杆原理互动实验室</title>
<script src="https://cdn.tailwindcss.com"></script>
<link href="https://cdn.jsdelivr.net/npm/font-awesome@4.7.0/css/font-awesome.min.css" rel="stylesheet">
<!-- 配置Tailwind自定义颜色和字体 -->
<script>
tailwind.config = {
theme: {
extend: {
colors: {
primary: '#667eea',
secondary: '#764ba2',
force: '#3b82f6', // 动力蓝色
weight: '#ef4444', // 阻力红色
balanced: '#22c55e', // 平衡绿色
unbalanced: '#ef4444', // 不平衡红色
lever: '#9ca3af', // 杠杆灰色
},
fontFamily: {
sans: ['Inter', 'system-ui', 'sans-serif'],
},
}
}
}
</script>
<style type="text/tailwindcss">
@layer utilities {
.content-auto {
content-visibility: auto;
}
.bg-gradient-primary {
background: linear-gradient(135deg, #667eea 0%, #764ba2 100%);
}
.text-shadow {
text-shadow: 0 2px 4px rgba(0,0,0,0.1);
}
.card-hover {
transition: all 0.3s ease;
}
.card-hover:hover {
transform: translateY(-5px);
box-shadow: 0 10px 25px -5px rgba(0, 0, 0, 0.1), 0 10px 10px -5px rgba(0, 0, 0, 0.04);
}
.btn-glow {
position: relative;
overflow: hidden;
}
.btn-glow::after {
content: '';
position: absolute;
top: -50%;
left: -50%;
width: 200%;
height: 200%;
background: linear-gradient(
to right,
rgba(255, 255, 255, 0) 0%,
rgba(255, 255, 255, 0.3) 50%,
rgba(255, 255, 255, 0) 100%
);
transform: rotate(30deg);
animation: glow 3s infinite;
}
@keyframes glow {
0% { transform: translateX(-100%) rotate(30deg); }
100% { transform: translateX(100%) rotate(30deg); }
}
.slider-thumb::-webkit-slider-thumb {
-webkit-appearance: none;
appearance: none;
width: 20px;
height: 20px;
border-radius: 50%;
cursor: pointer;
transition: all 0.2s ease;
}
.slider-thumb::-webkit-slider-thumb:hover {
transform: scale(1.2);
}
}
</style>
</head>
<body class="bg-gradient-primary min-h-screen text-gray-800 font-sans">
<!-- 顶部导航栏 -->
<nav class="bg-white shadow-md py-3 px-6 sticky top-0 z-50">
<div class="container mx-auto flex justify-between items-center">
<div class="flex items-center space-x-3">
<i class="fa fa-balance-scale text-primary text-2xl"></i>
<h1 class="text-xl md:text-2xl font-bold text-gray-800">杠杆原理互动实验室</h1>
</div>
<div class="hidden md:block">
<p class="text-gray-600 italic">探索力与平衡的奥秘</p>
</div>
</div>
</nav>
<!-- 主内容区 -->
<div class="container mx-auto px-4 py-8">
<div class="grid grid-cols-1 lg:grid-cols-3 gap-8">
<!-- 左栏：实验原理说明 -->
<div class="bg-white rounded-xl shadow-lg p-6 card-hover">
<h2 class="text-xl font-bold mb-4 text-primary border-b pb-2">
<i class="fa fa-book mr-2"></i>实验原理
</h2>
<div class="space-y-4">
<p class="text-gray-700">杠杆是一种简单机械，由一个支点和一根能绕支点转动的硬棒组成。杠杆原理表明，当杠杆平衡时，动力乘以动力臂等于阻力乘以阻力臂。</p>
<div class="bg-blue-50 p-4 rounded-lg border border-blue-100">
<h3 class="font-bold text-center mb-2 text-primary">杠杆平衡公式</h3>
<div class="text-center text-xl font-bold my-3">F × L₁ = W × L₂</div>
<div class="grid grid-cols-2 gap-2 text-sm">
<div><span class="font-semibold">F:</span> 动力 (N)</div>
<div><span class="font-semibold">L₁:</span> 动力臂 (cm)</div>
<div><span class="font-semibold">W:</span> 阻力 (N)</div>
<div><span class="font-semibold">L₂:</span> 阻力臂 (cm)</div>
</div>
</div>
<h3 class="font-bold text-lg text-primary">杠杆三要素</h3>
<ul class="list-disc list-inside space-y-1 text-gray-700">
<li><span class="font-semibold">支点(O):</span> 杠杆绕其转动的点</li>
<li><span class="font-semibold">动力(F):</span> 使杠杆转动的力</li>
<li><span class="font-semibold">阻力(W):</span> 阻碍杠杆转动的力</li>
</ul>
<h3 class="font-bold text-lg text-primary">机械利益</h3>
<p class="text-gray-700">机械利益 = L₁/L₂</p>
<ul class="list-disc list-inside space-y-1 text-gray-700">
<li>机械利益 > 1: 省力杠杆</li>
<li>机械利益 = 1: 等臂杠杆</li>
<li>机械利益 < 1: 费力杠杆</li>
</ul>
</div>
</div>
<!-- 中栏：实验画布和控制面板 -->
<div class="bg-white rounded-xl shadow-lg p-6 card-hover">
<h2 class="text-xl font-bold mb-4 text-primary border-b pb-2">
<i class="fa fa-flask mr-2"></i>实验区域
</h2>
<!-- 杠杆类型切换按钮 -->
<div class="flex justify-center space-x-3 mb-6">
<button id="type1" class="btn-glow bg-primary hover:bg-primary/90 text-white px-4 py-2 rounded-lg transition-all duration-300 font-medium">
第一类杠杆 (F-O-W)
</button>
<button id="type2" class="bg-gray-200 hover:bg-gray-300 text-gray-800 px-4 py-2 rounded-lg transition-all duration-300 font-medium">
第二类杠杆 (O-W-F)
</button>
<button id="type3" class="bg-gray-200 hover:bg-gray-300 text-gray-800 px-4 py-2 rounded-lg transition-all duration-300 font-medium">
第三类杠杆 (O-F-W)
</button>
</div>
<!-- 预设配置按钮 -->
<div class="flex justify-center space-x-3 mb-6">
<button id="preset-balance" class="bg-balanced/20 hover:bg-balanced/30 text-balanced px-3 py-1 rounded-lg transition-all duration-300 text-sm font-medium">
平衡状态
</button>
<button id="preset-easy" class="bg-green-100 hover:bg-green-200 text-green-800 px-3 py-1 rounded-lg transition-all duration-300 text-sm font-medium">
省力杠杆
</button>
<button id="preset-hard" class="bg-red-100 hover:bg-red-200 text-red-800 px-3 py-1 rounded-lg transition-all duration-300 text-sm font-medium">
费力杠杆
</button>
</div>
<!-- Canvas画布 -->
<div class="relative bg-blue-50 rounded-lg border border-blue-100 mb-6 overflow-hidden">
<canvas id="leverCanvas" width="800" height="400" class="w-full max-w-full"></canvas>
<!-- 画布上的指示器 -->
<div id="tiltIndicator" class="absolute top-4 left-4 bg-white/80 px-2 py-1 rounded text-sm font-medium shadow">
↕️ 倾斜方向：水平
</div>
<div id="balanceIndicator" class="absolute top-4 right-4 bg-white/80 px-2 py-1 rounded text-sm font-medium shadow text-balanced">
⚖️ 平衡
</div>
<div id="structureIndicator" class="absolute bottom-4 left-4 bg-white/80 px-2 py-1 rounded text-sm font-medium shadow">
结构：F-O-W
</div>
<div id="forceDirIndicator" class="absolute bottom-4 right-4 bg-white/80 px-2 py-1 rounded text-sm font-medium shadow">
力方向：F↓ W↓
</div>
</div>
<!-- 参数控制面板 -->
<div class="space-y-6">
<div>
<div class="flex justify-between mb-1">
<label for="forceF" class="text-force font-medium">动力 (F): <span id="forceFValue">50</span>N</label>
<input type="range" id="forceF" min="10" max="200" value="50"
class="w-2/3 slider-thumb" style="accent-color: #3b82f6;">
</div>
</div>
<div>
<div class="flex justify-between mb-1">
<label for="lengthL1" class="text-force font-medium">动力臂 (L₁): <span id="lengthL1Value">30</span>cm</label>
<input type="range" id="lengthL1" min="5" max="100" value="30"
class="w-2/3 slider-thumb" style="accent-color: #3b82f6;">
</div>
</div>
<div>
<div class="flex justify-between mb-1">
<label for="weightW" class="text-weight font-medium">阻力 (W): <span id="weightWValue">50</span>N</label>
<input type="range" id="weightW" min="10" max="200" value="50"
class="w-2/3 slider-thumb" style="accent-color: #ef4444;">
</div>
</div>
<div>
<div class="flex justify-between mb-1">
<label for="lengthL2" class="text-weight font-medium">阻力臂 (L₂): <span id="lengthL2Value">30</span>cm</label>
<input type="range" id="lengthL2" min="5" max="100" value="30"
class="w-2/3 slider-thumb" style="accent-color: #ef4444;">
</div>
</div>
</div>
</div>
<!-- 右栏：杠杆特点和计算结果 -->
<div class="bg-white rounded-xl shadow-lg p-6 card-hover">
<h2 class="text-xl font-bold mb-4 text-primary border-b pb-2">
<i class="fa fa-info-circle mr-2"></i>实验信息
</h2>
<!-- 杠杆特点介绍 -->
<div class="mb-6">
<h3 class="font-bold text-lg mb-2 text-gray-800">杠杆特点</h3>
<div id="leverFeatures" class="bg-gray-50 p-4 rounded-lg border border-gray-100 text-gray-700">
动力F和阻力W分别在支点O的两边，可以改变力的方向
</div>
<h3 class="font-bold text-lg mt-4 mb-2 text-gray-800">生活实例</h3>
<div id="leverExamples" class="flex flex-wrap gap-2">
<span class="bg-blue-100 text-blue-800 px-2 py-1 rounded-full text-sm">剪刀</span>
<span class="bg-blue-100 text-blue-800 px-2 py-1 rounded-full text-sm">天平</span>
<span class="bg-blue-100 text-blue-800 px-2 py-1 rounded-full text-sm">跷跷板</span>
<span class="bg-blue-100 text-blue-800 px-2 py-1 rounded-full text-sm">撬棍</span>
</div>
</div>
<!-- 实验数据计算结果 -->
<div>
<h3 class="font-bold text-lg mb-3 text-gray-800">计算结果</h3>
<div class="space-y-3">
<div class="bg-gray-50 p-3 rounded-lg border border-gray-100">
<div class="flex justify-between">
<span class="text-gray-600">动力矩 (F×L₁):</span>
<span id="momentF" class="text-force font-bold">1500 N·cm</span>
</div>
</div>
<div class="bg-gray-50 p-3 rounded-lg border border-gray-100">
<div class="flex justify-between">
<span class="text-gray-600">阻力矩 (W×L₂):</span>
<span id="momentW" class="text-weight font-bold">1500 N·cm</span>
</div>
</div>
<div class="bg-yellow-50 p-3 rounded-lg border border-yellow-100">
<div class="flex justify-between">
<span class="text-gray-600">力矩差值:</span>
<span id="momentDiff" class="text-yellow-700 font-bold">0 N·cm</span>
</div>
</div>
<div class="bg-gray-50 p-3 rounded-lg border border-gray-100">
<div class="flex justify-between">
<span class="text-gray-600">机械利益 (L₁/L₂):</span>
<span id="mechanicalAdvantage" class="text-blue-700 font-bold">1.00</span>
</div>
</div>
<div class="bg-gray-50 p-3 rounded-lg border border-gray-100">
<div class="flex justify-between">
<span class="text-gray-600">杠杆类型:</span>
<span id="leverTypeText" class="text-blue-700 font-bold">等臂杠杆</span>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
<!-- 页脚 -->
<footer class="bg-white mt-12 py-6 px-6 shadow-inner">
<div class="container mx-auto text-center text-gray-600">
<p>杠杆原理互动实验室 © 2023 | 物理教学互动工具</p>
</div>
</footer>
<script>
// 获取DOM元素
const canvas = document.getElementById('leverCanvas');
const ctx = canvas.getContext('2d');
const forceFSlider = document.getElementById('forceF');
const lengthL1Slider = document.getElementById('lengthL1');
const weightWSlider = document.getElementById('weightW');
const lengthL2Slider = document.getElementById('lengthL2');
const forceFValue = document.getElementById('forceFValue');
const lengthL1Value = document.getElementById('lengthL1Value');
const weightWValue = document.getElementById('weightWValue');
const lengthL2Value = document.getElementById('lengthL2Value');
const momentF = document.getElementById('momentF');
const momentW = document.getElementById('momentW');
const momentDiff = document.getElementById('momentDiff');
const mechanicalAdvantage = document.getElementById('mechanicalAdvantage');
const leverTypeText = document.getElementById('leverTypeText');
const tiltIndicator = document.getElementById('tiltIndicator');
const balanceIndicator = document.getElementById('balanceIndicator');
const structureIndicator = document.getElementById('structureIndicator');
const forceDirIndicator = document.getElementById('forceDirIndicator');
const leverFeatures = document.getElementById('leverFeatures');
const leverExamples = document.getElementById('leverExamples');
const type1Btn = document.getElementById('type1');
const type2Btn = document.getElementById('type2');
const type3Btn = document.getElementById('type3');
const presetBalanceBtn = document.getElementById('preset-balance');
const presetEasyBtn = document.getElementById('preset-easy');
const presetHardBtn = document.getElementById('preset-hard');
// 实验参数
let params = {
leverType: 1, // 1:第一类, 2:第二类, 3:第三类
F: 50, // 动力 (N)
L1: 30, // 动力臂 (cm)
W: 50, // 阻力 (N)
L2: 30, // 阻力臂 (cm)
currentAngle: 0, // 当前角度 (弧度)
targetAngle: 0, // 目标角度 (弧度)
centerX: canvas.width / 2,
centerY: canvas.height / 2 + 50,
scale: 5, // 缩放比例 (像素/cm)
maxAngle: 0.2 // 最大倾斜角度 (弧度)
};
// 杠杆类型配置
const leverConfigs = {
1: {
structure: "F-O-W",
forceDir: "F↓ W↓",
features: "动力F和阻力W分别在支点O的两边，可以改变力的方向",
examples: ["剪刀", "天平", "跷跷板", "撬棍"],
getPositions: (params) => {
const fulcrumX = params.centerX;
const forceX = fulcrumX - params.L1 * params.scale;
const weightX = fulcrumX + params.L2 * params.scale;
return { fulcrumX, forceX, weightX };
},
drawForceArrows: (params, positions) => {
// 动力箭头向下
drawArrow(ctx, positions.forceX, params.centerY,
positions.forceX, params.centerY + params.F * 1.5,
'#3b82f6', 5);
// 阻力箭头向下
drawArrow(ctx, positions.weightX, params.centerY,
positions.weightX, params.centerY + params.W * 1.5,
'#ef4444', 5);
}
},
2: {
structure: "O-W-F",
forceDir: "F↑ W↓",
features: "阻力W在支点O和动力F之间，必定省力",
examples: ["独轮车", "开瓶器", "铡刀", "胡桃夹"],
getPositions: (params) => {
const fulcrumX = params.centerX - params.L1 * params.scale / 2;
const weightX = fulcrumX + params.L2 * params.scale;
const forceX = fulcrumX + params.L1 * params.scale;
return { fulcrumX, forceX, weightX };
},
drawForceArrows: (params, positions) => {
// 动力箭头向上
drawArrow(ctx, positions.forceX, params.centerY,
positions.forceX, params.centerY - params.F * 1.5,
'#3b82f6', 5);
// 阻力箭头向下
drawArrow(ctx, positions.weightX, params.centerY,
positions.weightX, params.centerY + params.W * 1.5,
'#ef4444', 5);
}
},
3: {
structure: "O-F-W",
forceDir: "F↑ W↓",
features: "动力F在支点O和阻力W之间，必定费力但动作灵活",
examples: ["钓鱼竿", "筷子", "人的前臂", "扫帚"],
getPositions: (params) => {
const fulcrumX = params.centerX - params.L2 * params.scale / 2;
const forceX = fulcrumX + params.L1 * params.scale;
const weightX = fulcrumX + params.L2 * params.scale;
return { fulcrumX, forceX, weightX };
},
drawForceArrows: (params, positions) => {
// 动力箭头向上
drawArrow(ctx, positions.forceX, params.centerY,
positions.forceX, params.centerY - params.F * 1.5,
'#3b82f6', 5);
// 阻力箭头向下
drawArrow(ctx, positions.weightX, params.centerY,
positions.weightX, params.centerY + params.W * 1.5,
'#ef4444', 5);
}
}
};
// 预设配置
const presets = {
balance: { F: 50, L1: 30, W: 75, L2: 20 },
easy: { F: 30, L1: 45, W: 90, L2: 15 },
hard: { F: 80, L1: 15, W: 30, L2: 40 }
};
// 初始化滑块值
forceFSlider.value = params.F;
lengthL1Slider.value = params.L1;
weightWSlider.value = params.W;
lengthL2Slider.value = params.L2;
// 事件监听器
forceFSlider.addEventListener('input', (e) => {
params.F = parseInt(e.target.value);
updateDisplay();
});
lengthL1Slider.addEventListener('input', (e) => {
params.L1 = parseInt(e.target.value);
updateDisplay();
});
weightWSlider.addEventListener('input', (e) => {
params.W = parseInt(e.target.value);
updateDisplay();
});
lengthL2Slider.addEventListener('input', (e) => {
params.L2 = parseInt(e.target.value);
updateDisplay();
});
// 杠杆类型切换
type1Btn.addEventListener('click', () => {
setLeverType(1);
type1Btn.className = "btn-glow bg-primary hover:bg-primary/90 text-white px-4 py-2 rounded-lg transition-all duration-300 font-medium";
type2Btn.className = "bg-gray-200 hover:bg-gray-300 text-gray-800 px-4 py-2 rounded-lg transition-all duration-300 font-medium";
type3Btn.className = "bg-gray-200 hover:bg-gray-300 text-gray-800 px-4 py-2 rounded-lg transition-all duration-300 font-medium";
});
type2Btn.addEventListener('click', () => {
setLeverType(2);
type1Btn.className = "bg-gray-200 hover:bg-gray-300 text-gray-800 px-4 py-2 rounded-lg transition-all duration-300 font-medium";
type2Btn.className = "btn-glow bg-primary hover:bg-primary/90 text-white px-4 py-2 rounded-lg transition-all duration-300 font-medium";
type3Btn.className = "bg-gray-200 hover:bg-gray-300 text-gray-800 px-4 py-2 rounded-lg transition-all duration-300 font-medium";
});
type3Btn.addEventListener('click', () => {
setLeverType(3);
type1Btn.className = "bg-gray-200 hover:bg-gray-300 text-gray-800 px-4 py-2 rounded-lg transition-all duration-300 font-medium";
type2Btn.className = "bg-gray-200 hover:bg-gray-300 text-gray-800 px-4 py-2 rounded-lg transition-all duration-300 font-medium";
type3Btn.className = "btn-glow bg-primary hover:bg-primary/90 text-white px-4 py-2 rounded-lg transition-all duration-300 font-medium";
});
// 预设配置按钮
presetBalanceBtn.addEventListener('click', () => applyPreset('balance'));
presetEasyBtn.addEventListener('click', () => applyPreset('easy'));
presetHardBtn.addEventListener('click', () => applyPreset('hard'));
// 设置杠杆类型
function setLeverType(type) {
params.leverType = type;
// 设置各类型的初始值
if (type === 1) {
params.F = 50;
params.L1 = 30;
params.W = 50;
params.L2 = 30;
} else if (type === 2) {
params.F = 30;
params.L1 = 40;
params.W = 120;
params.L2 = 10;
} else if (type === 3) {
params.F = 90;
params.L1 = 15;
params.W = 30;
params.L2 = 45;
}
// 更新滑块显示
forceFSlider.value = params.F;
lengthL1Slider.value = params.L1;
weightWSlider.value = params.W;
lengthL2Slider.value = params.L2;
// 更新杠杆特点和示例
leverFeatures.textContent = leverConfigs[type].features;
// 更新示例标签
leverExamples.innerHTML = '';
leverConfigs[type].examples.forEach(example => {
const span = document.createElement('span');
span.className = 'bg-blue-100 text-blue-800 px-2 py-1 rounded-full text-sm';
span.textContent = example;
leverExamples.appendChild(span);
});
// 更新结构和力方向显示
structureIndicator.textContent = `结构：${leverConfigs[type].structure}`;
forceDirIndicator.textContent = `力方向：${leverConfigs[type].forceDir}`;
updateDisplay();
}
// 应用预设配置
function applyPreset(presetName) {
const preset = presets[presetName];
params.F = preset.F;
params.L1 = preset.L1;
params.W = preset.W;
params.L2 = preset.L2;
// 更新滑块
forceFSlider.value = params.F;
lengthL1Slider.value = params.L1;
weightWSlider.value = params.W;
lengthL2Slider.value = params.L2;
updateDisplay();
}
// 更新显示
function updateDisplay() {
// 更新数值显示
forceFValue.textContent = params.F;
lengthL1Value.textContent = params.L1;
weightWValue.textContent = params.W;
lengthL2Value.textContent = params.L2;
// 计算力矩
const momentFValue = params.F * params.L1;
const momentWValue = params.W * params.L2;
const diff = Math.abs(momentFValue - momentWValue);
// 更新力矩显示
momentF.textContent = `${momentFValue} N·cm`;
momentW.textContent = `${momentWValue} N·cm`;
momentDiff.textContent = `${diff} N·cm`;
// 计算机械利益
const ma = params.L1 / params.L2;
mechanicalAdvantage.textContent = ma.toFixed(2);
// 确定杠杆类型文本
if (ma > 1) {
leverTypeText.textContent = "省力杠杆";
leverTypeText.className = "text-green-700 font-bold";
} else if (ma < 1) {
leverTypeText.textContent = "费力杠杆";
leverTypeText.className = "text-red-700 font-bold";
} else {
leverTypeText.textContent = "等臂杠杆";
leverTypeText.className = "text-blue-700 font-bold";
}
// 确定平衡状态
if (diff < 50) {
balanceIndicator.textContent = "⚖️ 平衡";
balanceIndicator.className = "absolute top-4 right-4 bg-white/80 px-2 py-1 rounded text-sm font-medium shadow text-balanced";
params.targetAngle = 0;
tiltIndicator.textContent = "↕️ 倾斜方向：水平";
} else {
balanceIndicator.textContent = "⚠️ 不平衡";
balanceIndicator.className = "absolute top-4 right-4 bg-white/80 px-2 py-1 rounded text-sm font-medium shadow text-unbalanced";
// 计算目标角度
const largerMoment = Math.max(momentFValue, momentWValue);
const angleRatio = diff / largerMoment;
const angle = Math.min(angleRatio * params.maxAngle, params.maxAngle);
// 确定倾斜方向
if (momentFValue > momentWValue) {
params.targetAngle = -angle; // 动力端下降
tiltIndicator.textContent = "↕️ 倾斜方向：动力端下降";
} else {
params.targetAngle = angle; // 阻力端下降
tiltIndicator.textContent = "↕️ 倾斜方向：阻力端下降";
}
}
// 重绘
draw();
}
// 绘制箭头的辅助函数
function drawArrow(ctx, x1, y1, x2, y2, color, lineWidth) {
const headLength = 10;
const dx = x2 - x1;
const dy = y2 - y1;
const angle = Math.atan2(dy, dx);
// 绘制线
ctx.beginPath();
ctx.moveTo(x1, y1);
ctx.lineTo(x2, y2);
ctx.strokeStyle = color;
ctx.lineWidth = lineWidth;
ctx.stroke();
// 绘制箭头头部
ctx.beginPath();
ctx.moveTo(x2, y2);
ctx.lineTo(
x2 - headLength * Math.cos(angle - Math.PI / 6),
y2 - headLength * Math.sin(angle - Math.PI / 6)
);
ctx.lineTo(
x2 - headLength * Math.cos(angle + Math.PI / 6),
y2 - headLength * Math.sin(angle + Math.PI / 6)
);
ctx.closePath();
ctx.fillStyle = color;
ctx.fill();
}
// 绘制网格背景
function drawGrid() {
const gridSize = 40;
ctx.strokeStyle = 'rgba(173, 216, 230, 0.3)'; // 浅蓝色半透明
ctx.lineWidth = 1;
// 绘制水平线
for (let y = 0; y <= canvas.height; y += gridSize) {
ctx.beginPath();
ctx.moveTo(0, y);
ctx.lineTo(canvas.width, y);
ctx.stroke();
}
// 绘制垂直线
for (let x = 0; x <= canvas.width; x += gridSize) {
ctx.beginPath();
ctx.moveTo(x, 0);
ctx.lineTo(x, canvas.height);
ctx.stroke();
}
}
// 绘制杠杆
function drawLever() {
const config = leverConfigs[params.leverType];
const positions = config.getPositions(params);
// 计算杠杆的起点和终点
const leverStartX = Math.min(positions.fulcrumX, positions.forceX, positions.weightX) - 50;
const leverEndX = Math.max(positions.fulcrumX, positions.forceX, positions.weightX) + 50;
// 保存当前状态
ctx.save();
// 平移到支点
ctx.translate(positions.fulcrumX, params.centerY);
// 旋转杠杆
ctx.rotate(params.currentAngle);
// 绘制杠杆（灰色渐变）
const leverGradient = ctx.createLinearGradient(leverStartX - positions.fulcrumX, 0, leverEndX - positions.fulcrumX, 0);
leverGradient.addColorStop(0, '#6b7280');
leverGradient.addColorStop(0.5, '#9ca3af');
leverGradient.addColorStop(1, '#6b7280');
ctx.fillStyle = leverGradient;
ctx.fillRect(leverStartX - positions.fulcrumX, -5, leverEndX - leverStartX, 10);
// 绘制刻度线
for (let x = leverStartX; x <= leverEndX; x += 10) {
if (x !== positions.fulcrumX) { // 不在支点处绘制刻度
ctx.beginPath();
ctx.moveTo(x - positions.fulcrumX, -5);
ctx.lineTo(x - positions.fulcrumX, 5);
ctx.strokeStyle = '#4b5563';
ctx.lineWidth = 1;
ctx.stroke();
}
}
// 恢复状态
ctx.restore();
}
// 绘制支点
function drawFulcrum(x) {
ctx.save();
// 平移到支点位置并考虑旋转
ctx.translate(x, params.centerY);
ctx.rotate(params.currentAngle);
// 绘制蓝色三角形支点
ctx.beginPath();
ctx.moveTo(0, -15);
ctx.lineTo(-10, 15);
ctx.lineTo(10, 15);
ctx.closePath();
const fulcrumGradient = ctx.createLinearGradient(-10, -15, 10, 15);
fulcrumGradient.addColorStop(0, '#3b82f6');
fulcrumGradient.addColorStop(1, '#2563eb');
ctx.fillStyle = fulcrumGradient;
ctx.fill();
// 绘制支点标签 "O"
ctx.fillStyle = 'white';
ctx.font = 'bold 14px Arial';
ctx.textAlign = 'center';
ctx.textBaseline = 'middle';
ctx.fillText('O', 0, 0);
ctx.restore();
}
// 绘制力的标签
function drawForceLabels(forceX, weightX) {
// 保存状态
ctx.save();
// 绘制动力标签 F
ctx.fillStyle = '#3b82f6';
ctx.font = 'bold 14px Arial';
ctx.textAlign = 'center';
if (params.leverType === 1) {
ctx.textBaseline = 'top';
ctx.fillText(`F=${params.F}N`, forceX, params.centerY + params.F * 1.5 + 5);
} else {
ctx.textBaseline = 'bottom';
ctx.fillText(`F=${params.F}N`, forceX, params.centerY - params.F * 1.5 - 5);
}
// 绘制阻力标签 W
ctx.fillStyle = '#ef4444';
ctx.textAlign = 'center';
ctx.textBaseline = 'top';
ctx.fillText(`W=${params.W}N`, weightX, params.centerY + params.W * 1.5 + 5);
// 恢复状态
ctx.restore();
}
// 绘制力臂
function drawArms(fulcrumX, forceX, weightX) {
// 保存状态
ctx.save();
// 平移到支点并旋转
ctx.translate(fulcrumX, params.centerY);
ctx.rotate(params.currentAngle);
// 绘制动力臂（虚线）
ctx.beginPath();
ctx.setLineDash([5, 5]);
ctx.moveTo(0, -40);
ctx.lineTo(forceX - fulcrumX, -40);
ctx.strokeStyle = '#3b82f6';
ctx.lineWidth = 2;
ctx.stroke();
// 绘制动力臂标签 L₁
ctx.fillStyle = '#3b82f6';
ctx.font = '12px Arial';
ctx.textAlign = 'center';
ctx.textBaseline = 'middle';
ctx.fillText(`L₁=${params.L1}cm`, (forceX - fulcrumX) / 2, -50);
// 绘制阻力臂（虚线）
ctx.beginPath();
ctx.setLineDash([5, 5]);
ctx.moveTo(0, -25);
ctx.lineTo(weightX - fulcrumX, -25);
ctx.strokeStyle = '#ef4444';
ctx.lineWidth = 2;
ctx.stroke();
// 绘制阻力臂标签 L₂
ctx.fillStyle = '#ef4444';
ctx.font = '12px Arial';
ctx.textAlign = 'center';
ctx.textBaseline = 'middle';
ctx.fillText(`L₂=${params.L2}cm`, (weightX - fulcrumX) / 2, -35);
// 重置线条样式
ctx.setLineDash([]);
// 恢复状态
ctx.restore();
}
// 绘制整个场景
function draw() {
// 清除画布
ctx.clearRect(0, 0, canvas.width, canvas.height);
// 绘制背景渐变
const bgGradient = ctx.createLinearGradient(0, 0, 0, canvas.height);
bgGradient.addColorStop(0, 'rgba(224, 242, 254, 0.8)');
bgGradient.addColorStop(1, 'rgba(191, 219, 254, 0.8)');
ctx.fillStyle = bgGradient;
ctx.fillRect(0, 0, canvas.width, canvas.height);
// 绘制网格
drawGrid();
// 获取当前杠杆配置和位置
const config = leverConfigs[params.leverType];
const positions = config.getPositions(params);
// 绘制杠杆
drawLever();
// 绘制支点
drawFulcrum(positions.fulcrumX);
// 绘制力臂
drawArms(positions.fulcrumX, positions.forceX, positions.weightX);
// 绘制力箭头
config.drawForceArrows(params, positions);
// 绘制力标签
drawForceLabels(positions.forceX, positions.weightX);
}
// 动画循环
function animate() {
// 平滑过渡到目标角度
params.currentAngle += (params.targetAngle - params.currentAngle) * 0.1;
// 重绘
draw();
// 继续动画
requestAnimationFrame(animate);
}
// 初始化
function init() {
updateDisplay();
animate();
}
// 启动应用
init();
</script>
</body>
</html>
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