Physics Work and Power Concepts

Work

• Formula: Work (W) = Force (F) × Distance (d) × cos(Φ)
  • W: Joules (J)
  • F: Newtons (N)
  • d: meters (m)
  • Φ: Angle between force and direction of motion
• Examples:
  • Lifting a 10 kg box 2 meters: 196 J
  • Pushing a cart with 50 N force over 5 meters: 250 J
  • Pulling a sled with 30 N at 30° over 10 meters: 259.8 J

Power

• Mechanical Power Formula: Power (P) = Work (W) / Time (t)
  • P: Watts (W)
  • W: Joules (J)
  • t: Seconds (s)
• Examples:
  • Lifting weights with 500 J of work in 10 seconds: 50 W
• Force and Velocity Formula: Power (P) = Force (F) × Velocity (v)
  • P: Watts (W)
  • F: Newtons (N)
  • v: meters per second (m/s)
• Example: A force of 100 N moves an object at 5 m/s: 500 W
• Force and Distance Over Time Formula: Power (P) = Force (F) × Distance (d) / Time (t)
  • P: Watts (W)
  • F: Newtons (N)
  • d: meters (m)
  • t: seconds (s)
• Example: A force of 200 N moves an object 10 meters in 5 seconds: 400 W

Kinetic Energy

• Formula: Kinetic Energy (KE) = ½ × mass (m) × velocity² (v²)
  • KE: Joules (J)
  • m: kilograms (kg)
  • v: meters per second (m/s)
• Examples:
  • 1000 kg car at 20 m/s: 200,000 J
  • 70 kg person at 5 m/s: 875 J
  • 2 kg object at 10 m/s: 100 J

Potential Energy

• Formula: Potential Energy (PE) = mass (m) × acceleration due to gravity (g) × height (h)
• PE: Joules (J)
• m: kilograms (kg)
• g: 9.8 m/s²
• h: meters (m)
• Examples:
  • 5 kg object at 10 meters: 490 J
  • 1000 kg water at 5 meters: 49,000 J
  • 2 kg pendulum bob at 2 meters: 39.2 J

Elastic Potential Energy

• Formula: Elastic Potential Energy (EPE) = ½ × spring constant (k) × displacement² (x²)
  • EPE: Joules (J)
  • k: Newtons per meter (N/m)
  • x: meters (m)
• Examples:
  • Spring with k = 200 N/m compressed by 0.5 meters: 25 J
  • Rubber band with k = 30 N/m stretched by 0.2 meters: 0.6 J
  • Bungee cord with k = 50 N/m stretched by 1 meter: 25 J