Work, Energy and Power Cheatsheet

Cheat Codes & Shortcuts

• Work Definition: Work is the transfer of energy when a force displaces an object. \( W = F \cdot d \cdot \cos\theta \)
• Kinetic Energy: Energy due to motion. \( KE = \frac{1}{2}mv^2 \)
• Potential Energy (Gravitational): Energy due to position. \( PE = mgh \)
• Power: Rate of doing work. \( P = \frac{W}{t} \) or \( P = F \cdot v \cdot \cos\theta \)
• Work-Energy Theorem: Work done equals change in kinetic energy. \( W = \Delta KE \)
• Conservation of Mechanical Energy: \( KE_i + PE_i = KE_f + PE_f \) (no non-conservative forces).
• Elastic Potential Energy: Stored in springs. \( PE = \frac{1}{2}kx^2 \)
• Mechanical Advantage: Ratio of output to input force in machines.
• Efficiency: Ratio of useful work output to total work input. \( \eta = \frac{W_{\text{out}}}{W_{\text{in}}} \)
• Momentum and Energy: For elastic collisions, both momentum and kinetic energy are conserved.

Quick Reference Table

Advice

Work, Energy and Power Quick Tips

• Work Calculation: Use \( W = F \cdot d \cdot \cos\theta \) for force at an angle.
• Kinetic Energy: Relate velocity to energy with \( KE = \frac{1}{2}mv^2 \).
• Potential Energy: Use \( PE = mgh \) for gravitational systems.
• Power Efficiency: Calculate power with \( P = \frac{W}{t} \) and check efficiency.
• Conservation Laws: Apply energy conservation for systems without friction.