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
| Type | Formula | Description |
|---|---|---|
| Work | \( W = F \cdot d \cdot \cos\theta \) | Work done by a force over a displacement. |
| Kinetic Energy | \( KE = \frac{1}{2}mv^2 \) | Energy of an object in motion. |
| Potential Energy | \( PE = mgh \) | Gravitational potential energy due to height. |
| Power | \( P = \frac{W}{t} \) | Rate of energy transfer or work done. |
| Elastic Energy | \( PE = \frac{1}{2}kx^2 \) | Energy stored in a compressed or stretched spring. |
| Conservation | \( KE_i + PE_i = KE_f + PE_f \) | Mechanical energy is conserved without non-conservative forces. |
Advice
Identify Forces: Determine all forces acting to calculate work correctly.
Check Units: Ensure consistency (e.g., Joules for energy, Watts for power).
Angle Matters: Use \( \cos\theta \) in work calculations for force-displacement angle.
Energy Conservation: Apply conservation laws when no external work is done.
Verify: Double-check calculations by ensuring energy and power units align.
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.
Work, Energy and Power Speed Quiz
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