Physics Equation Demonstrations

Projectile Motion

y = v₀t sinθ - ½gt²

Simple Harmonic Motion

x(t) = A cos(ωt + φ)

Newton's Second Law (F=ma)

F = m·a

// Physics constants const g = 9.8; // gravity (m/s²) // Projectile Motion const projectileCanvas = document.getElementById('projectile-canvas'); const projectileCtx = projectileCanvas.getContext('2d'); let projectileAnimationId; let projectileTime = 0; const projectileInitialVelocity = 50; // m/s const projectileAngle = Math.PI / 4; // 45 degrees const projectileMass = 1; // kg // Simple Harmonic Motion const shmCanvas = document.getElementById('shm-canvas'); const shmCtx = shmCanvas.getContext('2d'); let shmAnimationId; let shmTime = 0; const shmAmplitude = 100; const shmAngularFrequency = 0.05; const shmPhase = 0; // Newton's Second Law const newtonCanvas = document.getElementById('newton-canvas'); const newtonCtx = newtonCanvas.getContext('2d'); let newtonAnimationId; let newtonTime = 0; const newtonMass = 2; // kg let newtonForce = 10; // N let newtonVelocity = 0; let newtonPosition = 50; // Projectile Motion Functions function drawProjectile() { projectileCtx.clearRect(0, 0, projectileCanvas.width, projectileCanvas.height); // Calculate position const v0x = projectileInitialVelocity * Math.cos(projectileAngle); const v0y = projectileInitialVelocity * Math.sin(projectileAngle); const x = v0x * projectileTime; const y = projectileCanvas.height - (v0y * projectileTime - 0.5 * g * projectileTime * projectileTime); // Draw ground projectileCtx.fillStyle = '#8BC34A'; projectileCtx.fillRect(0, projectileCanvas.height - 10, projectileCanvas.width, 10); // Draw projectile projectileCtx.beginPath(); projectileCtx.arc(x, y, 10, 0, Math.PI * 2); projectileCtx.fillStyle = '#FF5722'; projectileCtx.fill(); // Draw velocity vector projectileCtx.beginPath(); projectileCtx.moveTo(x, y); projectileCtx.lineTo(x + v0x, y - (v0y - g * projectileTime)); projectileCtx.strokeStyle = '#2196F3'; projectileCtx.lineWidth = 2; projectileCtx.stroke(); // Draw info projectileCtx.fillStyle = '#333'; projectileCtx.font = '14px Arial'; projectileCtx.fillText(`Time: ${projectileTime.toFixed(1)}s`, 10, 20); projectileCtx.fillText(`Position: (${x.toFixed(1)}, ${(projectileCanvas.height - y).toFixed(1)})m`, 10, 40); projectileTime += 0.05; if (y > projectileCanvas.height - 10) { cancelAnimationFrame(projectileAnimationId); } else { projectileAnimationId = requestAnimationFrame(drawProjectile); } } // Simple Harmonic Motion Functions function drawSHM() { shmCtx.clearRect(0, 0, shmCanvas.width, shmCanvas.height); // Calculate position const x = shmCanvas.width / 2 + shmAmplitude * Math.cos(shmAngularFrequency * shmTime + shmPhase); const y = shmCanvas.height / 2; // Draw spring shmCtx.beginPath(); shmCtx.moveTo(50, y); shmCtx.lineTo(x - 20, y); for (let i = 0; i < 5; i++) { const offset = i % 2 === 0 ? 10 : -10; shmCtx.lineTo(x - 20 + i * 30, y + offset); } shmCtx.lineTo(x - 10, y); shmCtx.strokeStyle = '#795548'; shmCtx.lineWidth = 2; shmCtx.stroke(); // Draw mass shmCtx.fillStyle = '#607D8B'; shmCtx.fillRect(x - 20, y - 20, 40, 40); // Draw equilibrium position shmCtx.beginPath(); shmCtx.moveTo(shmCanvas.width / 2, y - 30); shmCtx.lineTo(shmCanvas.width / 2, y + 30); shmCtx.strokeStyle = '#F44336'; shmCtx.setLineDash([5, 5]); shmCtx.stroke(); shmCtx.setLineDash([]); // Draw info shmCtx.fillStyle = '#333'; shmCtx.font = '14px Arial'; shmCtx.fillText(`Time: ${shmTime.toFixed(1)}s`, 10, 20); shmCtx.fillText(`Displacement: ${(x - shmCanvas.width / 2).toFixed(1)}px`, 10, 40); shmTime += 0.5; shmAnimationId = requestAnimationFrame(drawSHM); } // Newton's Second Law Functions function drawNewton() { newtonCtx.clearRect(0, 0, newtonCanvas.width, newtonCanvas.height); // Calculate acceleration and update velocity/position const acceleration = newtonForce / newtonMass; newtonVelocity += acceleration * 0.1; newtonPosition += newtonVelocity * 0.1; // Draw ground newtonCtx.fillStyle = '#8BC34A'; newtonCtx.fillRect(0, newtonCanvas.height - 10, newtonCanvas.width, 10); // Draw box newtonCtx.fillStyle = '#3F51B5'; newtonCtx.fillRect(newtonPosition, newtonCanvas.height - 60, 50, 50); // Draw force arrow newtonCtx.beginPath(); newtonCtx.moveTo(newtonPosition + 60, newtonCanvas.height - 35); newtonCtx.lineTo(newtonPosition + 80, newtonCanvas.height - 35); newtonCtx.strokeStyle = '#FF5722'; newtonCtx.lineWidth = 2; newtonCtx.stroke(); // Draw arrowhead newtonCtx.beginPath(); newtonCtx.moveTo(newtonPosition + 80, newtonCanvas.height - 35); newtonCtx.lineTo(newtonPosition + 75, newtonCanvas.height - 30); newtonCtx.lineTo(newtonPosition + 75, newtonCanvas.height - 40); newtonCtx.closePath(); newtonCtx.fillStyle = '#FF5722'; newtonCtx.fill(); // Draw info newtonCtx.fillStyle = '#333'; newtonCtx.font = '14px Arial'; newtonCtx.fillText(`Time: ${newtonTime.toFixed(1)}s`, 10, 20); newtonCtx.fillText(`Force: ${newtonForce}N, Mass: ${newtonMass}kg`, 10, 40); newtonCtx.fillText(`Acceleration: ${acceleration.toFixed(2)}m/s²`, 10, 60); newtonCtx.fillText(`Velocity: ${newtonVelocity.toFixed(2)}m/s`, 10, 80); newtonTime += 0.1; if (newtonPosition > newtonCanvas.width) { cancelAnimationFrame(newtonAnimationId); } else { newtonAnimationId = requestAnimationFrame(drawNewton); } } // Event Listeners document.getElementById('projectile-start').addEventListener('click', () => { cancelAnimationFrame(projectileAnimationId); projectileTime = 0; drawProjectile(); }); document.getElementById('projectile-reset').addEventListener('click', () => { cancelAnimationFrame(projectileAnimationId); projectileTime = 0; projectileCtx.clearRect(0, 0, projectileCanvas.width, projectileCanvas.height); }); document.getElementById('shm-start').addEventListener('click', () => { cancelAnimationFrame(shmAnimationId); shmTime = 0; drawSHM(); }); document.getElementById('shm-reset').addEventListener('click', () => { cancelAnimationFrame(shmAnimationId); shmTime = 0; shmCtx.clearRect(0, 0, shmCanvas.width, shmCanvas.height); }); document.getElementById('newton-start').addEventListener('click', () => { cancelAnimationFrame(newtonAnimationId); newtonTime = 0; newtonVelocity = 0; newtonPosition = 50; drawNewton(); }); document.getElementById('newton-reset').addEventListener('click', () => { cancelAnimationFrame(newtonAnimationId); newtonTime = 0; newtonVelocity = 0; newtonPosition = 50; newtonCtx.clearRect(0, 0, newtonCanvas.width, newtonCanvas.height); });